in inches per foot run The Inch Rise gives you the corresponding scale number to use on the square and is calculated as follows. For example, you've measured out a distance of 3 miles (run) with a change in altitude of 396 feet (rise).  The table below shows common roof pitches and the equivalent grade, degrees, and radians for each. Another method to find the roof pitch is to go into the attic and measure the rise for a 12″ run of the roof rafters, which allows finding the pitch without going on the roof. We also cover more about roof replacement cost in detail in our cost guide. For easier readability, numbers between .001 and 1,000 will A 50 ft reel is 2.8 inches in diameter. Set the level on the edge of the speed square as shown below then place the heel of the speed square on a rafter or gable edge of the roof.


- How do you find 70 percent of a number?
- How do I calculate a percentage?
- How do I find the percentage of two numbers without a calculator?
- What number is 15% of 100?
- What is the easiest way to calculate percentages?
- What is 60 out of 100 as a percentage?
- How do you find 75%?
- How do you find 30% of a number?
- What is percentage and its formula?
- What number is 25 percent of 80?
- What number of 15% is 80?
- How do you find 15% of a number?
- How do I work out a percentage of two numbers?
- What is percentage of a number?
- How do you calculate percentage manually?
- What is the formula for calculating percentage with example?
How do you find 70 percent of a number?
Find 70% of 80.
Following the shortcut, we write this as 0.7 × 80.
Remember that in decimal multiplication, you multiply as if there were no decimal points, and the answer will have as many “decimal digits” to the right of the decimal point as the total number of decimal digits of all of the factors..
How do I calculate a percentage?
How To Calculate PercentDetermine the total or whole amount.Divide the number to be expressed as a percent by the total. In most cases, you’ll divide the smaller number by the larger number.Multiple the resulting value by 100.Feb 6, 2020
How do I find the percentage of two numbers without a calculator?
Divide the number by 10 to find 10%. In this case, 10% is 24. Multiply this number by how many tens are in the percentage you’re looking for – in this case, that’s 3, so you work out 30% to be 24 x 3 = 72. If your percentage number was a multiple of ten, this is your answer!
What number is 15% of 100?
0.1515 percent of 100? = 0.15.
What is the easiest way to calculate percentages?
1. How to calculate percentage of a number. Use the percentage formula: P% * X = YConvert the problem to an equation using the percentage formula: P% * X = Y.P is 10%, X is 150, so the equation is 10% * 150 = Y.Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.More items…
What is 60 out of 100 as a percentage?
60%Therefore the fraction 60/100 as a percentage is 60%.
How do you find 75%?
How much is 15 percent off?Divide your original number by 20 (halve it then divide by 10).Multiply this new number by 3.Subtract the number from step 2 off of your original number.You’ve just found your percentage off!Jan 24, 2021
How do you find 30% of a number?
Once you have the decimal figure, multiply it by the number for which you seek to calculate the percentage; i.e., if you need to know 30 percent of 100, you convert 30 percent to a decimal (0.30) and multiply it by 100 (0.30 x 100, which equals 30).
What is percentage and its formula?
If we have to calculate percent of a number, divide the number by whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It represented by the symbol “%”….Percentage Chart.FractionsPercentage1/250%1/333.33%1/425%1/520%10 more rows
What number is 25 percent of 80?
20Percentage Calculator: What is 25 percent of 80? = 20.
What number of 15% is 80?
1212 is 15% of 80 .
How do you find 15% of a number?
15% is 10% + 5% (or 0.15 = 0.1 + 0.05, dividing each percent by 100). Thinking about it this way is useful for two reasons. First, it’s easy to multiply any number by 0.1; just move the decimal point left one digit. For example, 75.00 x 0.1 = 7.50, or 346.43 x 0.1 = 34.64 (close enough).
How do I work out a percentage of two numbers?
If you want to know what percent A is of B, you simple divide A by B, then take that number and move the decimal place two spaces to the right. That’s your percentage! To use the calculator, enter two numbers to calculate the percentage the first is of the second by clicking Calculate Percentage.
What is percentage of a number?
In mathematics, a percentage is a number or ratio that represents a fraction of 100. It is often denoted by the symbol “%” or simply as “percent” or “pct.” For example, 35% is equivalent to the decimal 0.35, or the fraction.
How do you calculate percentage manually?
You divide your percentage by 100. So, 40% would be 40 divided by 100 or . 40. Once you have the decimal version of your percentage, simply multiply it by the given number.
What is the formula for calculating percentage with example?
So 10% of 150 = 10/100 × 150 = 15. If you have to turn a percentage into a decimal, just divide by 100. For example, 25% = 25/100 = 0.25. To change a decimal into a percentage, multiply by 100.


Nada, naught, nil, zip, zilch, zero. Whatever you call it, it's hard to imagine the world without it.
Zero is the basis for all modern computing and engineering, including trigonometry, algebra, and binary code. So, pretty important.
But despite how integral it is to our lives now, there was once a time when zero never existed.
Today we are joined by statistician and author Timandra Harkness, who is going to take us back in time to the invention of zero as a mathematical concept. Tune in to find out how it was discovered, the impact it had, and if we could possibly imagine a world without it today.


Abacus is first calculating machine invented by human beings almost 3000 years ago. The purpose of abacus was to add, subtract, multiply, divide, large numbers. It may have originated in China or Egypt of Greece.
It was constructed by wooden frame and that frame is divided into two parts, the lower part is called earth and upper part is called heaven. Small rods are adjusted in frame and small beads are adjusted in it. Two beads are in heaven and 5 beads are in earth. For calculation the beads can be move to mid bar.
This is first true calculating machine and invented by Blaise Pascal in 1642. Pascal is French mathematician. In this machine, the numbers were entered by dialing series of numbered wheels and series of gears. The numbers 0 to 9 are assign in wheel. When the first wheel made a complete turn from 0 to 9. It automatically cause the second wheel to advanced to the next number and so on. Pascaline could add and subtract by the movement of wheels. This machine can not perform. multiplication and division that was its great limitation. To remove this limitation, another scientist Gottfried Wilhelm von Leibniz invented another calculating machine called stepped Reckoner in 1673. His machine can perform addition, subtraction, multiplication, division as well as square root.
Babbage and his Engine
Charles Babbage is called father of computer science because modern computers are based on his idea.Babbage was Professor of Mathematics at Cambridge University and started a small model of his “Differential Engine”. This machine gives accurate result up to 20 decimal places. This machine was never completed because of mechanical problems. The important concept of Babbage which is implemented in modern computer is concept of input, output, and storage. According to his concept, the data or information is given to machine from input device, after processing, or calculation the result is given from output device. The modern computers are also based on his concept.
Neumann and store program concept
In computer technology, John von Neumann add a new concept which play important role to develop more reliable, fast, secure, small sized computer. His suggestions are:
- Binary number system should be used in computer system. (this is not new concept but he suggest to use it)
- Computer instructions as well as data being manipulated could be stored internally (inside small and fast memory) in the machine.
The first machine that use Neumann store program concept is EDVAC (Electronic Delay Storage Automatic Computer) in 1952. In this system, when we input the data inside computer that data is stored inside computer and all related programs are also stored inside it. To process the data, computer takes data from memory and related instruction from fixed memory locations. Modern computer as well as calculator or any electronic programmable devices even a mobile system store instruction inside it before processing.
J. Presper Eckert and John W. Mauchly founded their own company in 1946 and start work to develop this computer. In 1951, first UNIVAC-1 was started to work in census. It stands for UNIversal Automatic Computer. This is a first commercially used electronic computer. This computer was more reliable, accurate and fast machine for data manipulation.


Weplay Fun with Curves
Inspired by sunflowers, the yellow blocks have a solid, hollow quarter or half circle patterns on it. Seniors create different shapes of 2D or 3D constructions. The exercise helps to inspire seniors’ imagination, keep their minds sharp and exercise their fine motor skills.Product Feature:
- Each side has a pattern of solid or hollow quarter/half circles in blue and yellow. The color combination is like sunflowers under the sky.
- 6 double-sided game cards are included for play-along or as inspirations of creations.
- The patterns on the Blocks can be assembled into big and small circles, semicircles, and quarters of a circle. Users could enhance their agility of hands and spatial recognition by flipping and assembling the Blocks.
- Seniors can practice their observation skills and find the solutions by imitating the examples on the cards.
- Age: 3y+
- Product Weight: 0.8 KG
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- Block × 16
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Geometry, the study of shapes, sizes, and properties, becomes an intriguing puzzle to solve with Vance Jackson’s top tutors. Our team is dedicated to unraveling the complexities of geometry through comprehensive guidance and personalized instruction.
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Vance Jackson’s top tutors are dedicated to unraveling the mysteries of geometry, making it an accessible and intriguing subject for all. Join us in exploring the fascinating world of shapes, angles, and spatial relationships, and become a geometry guru with confidence and skill.


Table of Contents
Jim Simons is not your average mathematician. He is the world’s wealthiest one, with a net worth of $24.6 billion according to Forbes. How did he achieve such a feat? By starting the “quant revolution” in the world of trading through his company Renaissance Technologies and the Medallion Fund. In this article, we’ll take a closer look at the secrets behind the Medallion Fund’s success.
Who is Jim Simons?
Before we delve into the Medallion Fund’s remarkable performance, let’s first look at Jim Simons’ background. Born in 1938, Simons began reading extensively at an early age. He enrolled at MIT in 1955 and was able to skip the first year of mathematics due to his exceptional high school curriculum. Simons’ passion for mathematics eventually led him to get his PhD in the field by the age of 23.
Simons began his career in stocks during his time at the University of California, Berkeley. He would wake up early each morning to watch prices flash by and make a few trades. He then worked as a code-breaker at a US intelligence unit targeting Soviet Russia. This experience taught him an important lesson in hiring people. The unit’s success was based on hiring individuals with creativity, ambition, and brainpower, rather than specific expertise or education.
In 1968, Simons published a mathematical paper titled “Minimal Varieties in Riemannian Manifolds.” This paper has been cited over 1700 times, a remarkable achievement for a paper on geometry. The same year, he was asked to build and lead a math department at Stony Brook University. Simons was an extroverted mathematician and a great leader. He realized that he wouldn’t solve the puzzle of trading alone, so he used his mathematical expertise to hire and get the best out of other mathematicians.
In 1978, Simons left academia to pursue new challenges in the world of trading. He called his first hedge fund “Monemetrics,” a play on words combining “money” and “econometrics.” He used math to analyze the financial markets and eventually renamed his company Renaissance Technologies in 1982. In 1988, the Medallion Fund was launched, and it has become the most successful hedge fund of all time in terms of its track record.
Medallion Fund’s Performance
The Medallion Fund has an impressive track record that has yet to be matched by any other hedge fund. Before fees, it has averaged a 62.9% return per year, and 37.2% net of fees, compared to the S&P 500’s 11%. Simons’ investment record is even better than Warren Buffett’s, achieved with a much smaller capital.
So, what is the secret behind the Medallion Fund’s success? The answer lies in its use of quant trading. The fund relies on mathematical models and algorithms to make trades, rather than human intuition. The algorithms have been developed by Simons’ team of mathematicians, including Elwyn Berlekamp, Leonard Baum, James Ax, and Henry Laufer, to name a few.
The Medallion Fund’s algorithms analyze vast amounts of data and execute trades within seconds. This speed and accuracy give the fund an edge over its competitors. The fund also uses leverage to increase its returns, making it a high-risk, high-reward investment.
Should You Abandon Value Investing for Quant Trading?
It’s not advisable to abandon value investing to become a day trading quant, but there is value in diversifying your investment portfolio. The Medallion Fund’s success is undeniable, but it’s worth noting that it’s not accessible to the average investor. The fund is only open to Renaissance Technologies’ employees, and even they have limited access to it.
Furthermore, quant trading is not a foolproof strategy. While it has worked well for the Medallion Fund, there have been instances where the market behaved in ways that the algorithms did not predict. For example, in 2007, the fund lost 5% due to the subprime mortgage crisis.
In conclusion, the Medallion Fund’s success is the result of Jim Simons’ pioneering work in the field of quant trading and his team’s expertise in developing and executing sophisticated mathematical models. While the average investor may not be able to invest in the Medallion Fund, there are still valuable lessons to be learned from its success, such as the importance of diversifying your portfolio and considering the potential benefits of incorporating quantitative strategies into your investment approach.
Further Reading and Sources:
To keep learning and advancing your career, we highly recommend these additional resources:


These are the perfect little ladybugs for counting and colour sorting. Pair them with other toys in our pastel line up to practice color matching. Put the bugs into order from smallest to biggest. Or maybe do some addition and subtraction — the 4 dotted bug plus the 2 dotted bug equals the 6 dotted bug.
Draw a little background on paper, such as addition and subtraction signs — or draw the numbers and have your little one match up the dotted bug to the correct number. Or — have some imaginary play and have these bugs crawling around a little village. Use other wood toys in our lineup to make your little imaginary play setting.
Help your little one learn number recognition while practicing fine motor skills and sharpening color recognition. Your little one will love playing with these colored bugs! . This set pairs beautifully with other toys in our lineup. This set is good for colour sorting, shape identification, pincer grasp, counting, stacking, hand-eye coordination — the list goes on. Plus it is great for imaginary play.
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By A. M. Yaglom,I. M. Yaglom
Designed for complicated highschool scholars, undergraduates, graduate scholars, arithmetic academics, and any lover of mathematical demanding situations, this two-volume set deals a extensive spectrum of hard difficulties — starting from fairly uncomplicated to tremendous tough. certainly, a few rank top-of-the-line achievements of exceptional mathematicians.
Translated from a widely known Russian paintings entitled Non-Elementary difficulties in an user-friendly Exposition, the executive target of the e-book is to acquaint the readers with a number of new mathematical evidence, principles, and strategies. And whereas the vast majority of the issues characterize questions in larger ("non-elementary") arithmetic, so much may be solved with trouble-free arithmetic. in reality, for the main half, no wisdom of arithmetic past a superb highschool direction is required.
Volume One comprises a hundred difficulties, with unique strategies, all facing chance conception and combinatorial research. issues contain the illustration of integers as sums and items, combinatorial difficulties at the chessboard, geometric difficulties on combinatorial research, difficulties at the binomial coefficients, difficulties on computing possibilities, experiments with infinitely many attainable results, and experiments with a continuum of attainable outcomes.
Volume includes seventy four difficulties from a number of branches of arithmetic, facing such issues as issues and features, lattices of issues within the aircraft, topology, convex polygons, distribution of gadgets, nondecimal counting, conception of primes, and extra. In either volumes the statements of the issues are given first, through a bit giving whole ideas. solutions and tricks are given on the finish of the book.
Ideal as a textual content, for self-study, or as a operating source for a arithmetic membership, this wide-ranging compilation bargains 174 conscientiously selected difficulties that would try the mathematical acuity and problem-solving talents of just about any scholar, instructor, or mathematician.
Read or Download Challenging Mathematical Problems with Elementary Solutions, Vol. I: 001 (Dover Books on Mathematics) PDF
Best combinatorics books
Built from the authors’ classes at Syracuse collage and the U. S. Air strength study Laboratory, entry regulate, defense, and belief: A Logical process equips readers with an entry regulate good judgment they could use to specify and confirm their safeguard designs. in the course of the textual content, the authors use a unmarried entry regulate good judgment in keeping with an easy propositional modal common sense.
Bringing the cloth brand new to mirror glossy functions, Algebraic quantity conception, moment version has been thoroughly rewritten and reorganized to include a brand new kind, method, and presentation. This variation makes a speciality of indispensable domain names, beliefs, and distinct factorization within the first bankruptcy; box extensions within the moment bankruptcy; and sophistication teams within the 3rd bankruptcy.
This booklet presents a thrilling background of the invention of Ramsey conception, and includes new learn in addition to infrequent photos of the mathematicians who built this concept, together with Paul Erdös, B. L. van der Waerden, and Henry Baudet.
Filling a niche in literature, this self-contained ebook offers theoretical and application-oriented effects that let for a structural exploration of complicated networks. The paintings focuses not just on classical graph-theoretic tools, but in addition demonstrates the usefulness of structural graph concept as a device for fixing interdisciplinary difficulties.
- Combinatorial Aspects of Commutative Algebra and Algebraic Geometry: The Abel Symposium 2009: 6 (Abel Symposia)
- Algebra, Logic and Combinatorics: 3 (LTCC Advanced Mathematics Series)
- Oriented Matroids (Encyclopedia of Mathematics and its Applications)
- Parallel Processing of Discrete Problems (The IMA Volumes in Mathematics and its Applications)
Additional resources for Challenging Mathematical Problems with Elementary Solutions, Vol. I: 001 (Dover Books on Mathematics)
Challenging Mathematical Problems with Elementary Solutions, Vol. I: 001 (Dover Books on Mathematics) by A. M. Yaglom,I. M. Yaglom


On November 24th, 2015 Katherine Johnson was awarded the Presidential Medal of Freedom. Katherine was given this award for her work as a mathematician helping pave the way to human space flight. Her work with NASA began at the Langley Research Center where she was hired on a team that was nicknamed “computers who wear skirts” where she helped with research to get astronauts into orbit around the earth for the first time and also send astronauts to the moon. Katherine was so good at her job that even John Glenn refused to launch on his mission around the world until Katherine double checked the mathematics that the computers at the time already calculated.
From the Challenger Learning Center in Sacramento we would like to say thank you to Katherine Johnson for helping NASA be a leader in human space flight.
To learn more about Katherine Johnson and her impact on human space flight visit the NASA website here:


Listed below are definitely the topics in math
These are things that students learn one of the maximum. With these themes, they are aware they will be able to have a solid foundation in mathematics.
Arithmetic – amount makings and quantity measuring are one of the topics in math. Students can learn along with different values between between 2 amounts and also about accepting the product of just two amounts. One of the principal theories with this topic is division.
Algebra – Knowing just how exactly to convey that the relationships between 2 entities will be part of algebra. The two is one of those fundamentals and also the working of subtraction, addition, multiplication and division is still an integral portion with this area. It’s essential for students to perfect all the problems of algebra in order that they can remedy them when demanded. There are also various sorts of algebra like linear algebra, quadratic, harmonic and others.
Geometry – Geometry incorporates geometric forms including circles, lines, and polygons. In addition, there are straight lines, curved lines, cylinders, spheres, circles, etc.. Students should be able to understand simple shapes such as rectangles, squares, ovals, circles, etc..
Works – One of the main topics in mathematics acts. Features are related to surgeries and hence they are easy to grasp. Students should have the ability to utilize functions to see that they are able to change a single thing.
Logarithms – Logarithms really are one of the most essential topics in math. Students should be able to divide numerals in base 10 and need to be able to know the basics of logarithms like exponent and foundation. Students must also find a way to detect the root of a number in both the lower and upper bases.
Binary – Binary is just probably perhaps one of the most popular topics in math. Binary includes subtracting and adding amounts http://catalog.rpi.edu/preview_course_nopop.php?catoid=10&coid=16264 in binary. They need to be able to multiply and split by splitting their foundation in binary and then add their base.
Vertical equations – Pupils should understand just how exactly to fix linear equations. They ought to have the ability so as to determine things from 14, to create equations. A few samples of equations that are linear include x and x + y = z =y.
Trigonometry – An issue that is ordinarily taught in amount is trigonometry. Trigonometry consists of also areas, lengths, and angles. Students should be able to find the cosine and sine of the number.
Hyperbola and parabola – themes in math which are applied are amounts and groups. They’re applied in geometry. They aid in understanding that how the origins that are square and needs to be learnt entirely.
Quadratic specimens – Quadratic equations are common and persons need to be in a position to solve them with different strategies. However, it is perhaps not always essential to remedy it. Manners might be utilised to discover solutions with this topic.
You will find many other topics. There are topics to be learnt also it’s all up to the teacher to choose. Before educators start off teaching such topics, they really should know that regions of math students should be familiar with.


The authors of [21, 22] studied the quadratic electro-optic effects (QEOEs) and electro-absorption
(EA) process in InGaN/GaN cylinder quantum dots and CdSe-ZnS-CdSe nanoshell structures. They have found that the position of nonlinear susceptibility peak and its amplitude may be tuned by changing the nanostructure configuration. The obtained susceptibilities in these works are around and 10-15 esu, respectively. In reference , Quisinostat price self-focusing effects in wurtzite InGaN/GaN quantum dots are studied. The results of this paper show that the quantum dot size has an immense effect on the nonlinear optical properties of wurtzite InGaN/GaN quantum dots. Also, with decrease of the quantum dot size, the self-focusing effect increases. GS-1101 purchase In a recent paper ,
NSC 683864 mw we have shown that with the control of GaN/AlGaN spherical quantum dot parameters, different behaviors are obtained. For example, with the increase of well width, third-order susceptibility decreases. The aim of this study is to investigate our proposed GaN/AlGaN quantum dot nanostructure from quadratic electro-optic effect and electro-absorption process points of view. In this paper, we study third-order nonlinear susceptibility of GaN/AlGaN semiconductor quantum dot based on the effective mass approximation. The numerical results have shown that in the proposed structure, the third-order nonlinear susceptibilities near 2 to 5 orders of magnitudes are increased. The organization of this paper is as follows. In the ‘Methods’ section, the theoretical model and background are described. The ‘Results and discussion’ section is devoted to the numerical results and discussion. Summarization of numerical results is given in the last section. Methods In this section, theoretical model and mathematical background of the third-order nonlinear properties of a new GaN/AlGaN quantum dot nanostructure are presented. The geometry of a spherical centered defect quantum dot and potential distribution of this nanostructure are shown in Figure 1. We consider three Levetiracetam regions consisting of a spherical well (with radius a), an inner defect shell
(with thickness b - a), and an outer barrier (with radius b). The proposed spherical centered defect quantum dot can be performed by adjusting the aluminum mole fraction. Figure 1 Structure of the spherical quantum dot and related potential distribution. In this paper, the potential in the core region is supposed to be zero, and the potential difference between two materials is constant . There are various methods for investigating electronic structures of quantum dot systems [26–28]. The effective mass approximation is employed in this study. The time-independent Schrödinger equation of the electron in spherical coordinate can be written as . (1) where m i ∗ and V i (r) are effective mass and potential distribution in different regions.


Audrey joined Pathfinder in 1998. Prior to joining Pathfinder, Audrey dedicated many years to mathematics education, primarily in Pennsylvania and New Jersey. An avid chef, gardener and thespian, Audrey brings a wealth of knowledge and experience to Pathfinder’s classrooms. She has two daughters: Emily, a Pathfinder alumna and graduate of the University of Michigan - now attending Washington University for her MFA, and Anna, an eighth grader at Pathfinder. When not visiting Emily, the family enjoys living on the beautiful shore of Crystal Lake with their pet snakes Lilly and Xander as well as two tortoises Little So and So and Atlas.
Education and Credentials
B.S. in Psychology, Temple University
6-12 Math Certification
Four-time speaker at the National Council of Teachers of Mathematics Conference


Engineering mathematics evolved significantly over 150 years span starting with Newton and continuing with many others. This spanned from the fact that developing calculus was a major leap and that allowed all sorts of new mathematical ideas to arrive. Then, calculating these complex mathematics that were iterative in nature was slow, so it wasn’t practical to solve too many problems even though the math to do so existed.
Then along came computers which automated the iterative nature of these problems at rates millions (as a low estimation) of times faster than they can be done by hand. Currently, we are probably pushing the limits of accuracy that our current models can hope to achieve by brute forcing small and smaller iterations.
The next step from today isn’t a little improvement or further step along the current curve, it’s a quantum leap. The next step is the invention of the next calculus. We’re all waiting for the next quantum leap to show up. While we can’t be sure on the timeline for the next revolutionary idea in mathematics, we can be sure that there are all sorts of industries out there that are waiting for someone to show them their quantum leap. It might as well be you.


I assume that you are not using symbolic variables. For 2D plotting in matlab you need two equal size vectors, one per axis, so you need to create a x-axis vector and y-axis vector.If I have a function with steps that I want to sample regularly, interp1 complains about not strictly monotonic data. However, a step in the data is being interpreted as being defined up to the next time point, interpolation (at least table lookup) is well defined.Download coding: ----- clc; clear all; close all; num=; den=[1 2 9]; sys=tf(num,den) step(sys,0:.01:10); title('step response o...The unit step function is known to MATLAB as heaviside, with the slight difference that heaviside(0)=1/2. Example Define a symbolic MATLAB function which is equal to if and is equal to if This is Boyce and DiPrima, Section 10.2 #19. Optimization Toolbox solvers. • Multiobjectiveminimizers. This group of solvers attempts to either minimize the maximum value of a set of functions (fminimax), or to find a location where a collection o f functions is below some prespecified values (fgoalattain). Where t is a time vector. If no results on the left-hand side are supplied by you, the step function will automatically produce a graphical plot of the step response. If, however, you use the following format: [y, x, t] = step(NUM, DEN, t); Then MATLAB will not produce a plot automatically, and you will have to produce one yourself.Dec 04, 2012 · how to use heaviside step function?. Learn more about heaviside What Is the Function of the Linspace in MATLAB? The "linspace" function in MATLAB creates a vector of values that are linearly spaced between two endpoints. The function requires two inputs for the endpoints of the output vector, and it also accepts a third, optional input to specify the number of points to include between the endpoints. What I want is that for the input t, when t is >= 0 the value of the function is 1, and for everything else 0 and then plot the results.The unit step function is level in all places except for a discontinuity at t = 0. For this reason, the derivative of the unit step function is 0 at all points t, except where t = 0. Where t = 0, the derivative of the unit step function is infinite. The derivative of a unit step function is called an impulse function. Get the inside view on MATLAB and Simulink Insights and information from the engineers who design, build and support MathWorks products Subscribe to All Blogs Meet the Bloggers MATLAB provides built-in functions for unit step function u(t) and unit impulse function δ(t). The unit step function is called Heaviside or stepfun, while the impulse function is Dirac. Matlab Multithreading, EASY: making a multithreaded matlab program in five minutes:matlab is excellent, it makes it very easy to do things that would be very compicated and annoying in lower level languages (e.g. c++). The main large flaw of matlab is that it does not _inhere... How to plot the step function u(t) in matlab using the heaviside command.Function Design Pattern . A function in Matlab is always written using the same (starting) syntax. This syntax can be captured in a "Design Pattern". Your job is to learn this pattern for future use (and tests). When learning, you can refer here for help. Vector Functions¶ Matlab makes it easy to create vectors and matrices. The real power of Matlab is the ease in which you can manipulate your vectors and matrices. Here we assume that you know the basics of defining and manipulating vectors and matrices. ectorizationV optimization unlocks MATLAB's processing power and can result in signi cant speed gains. On the downside, there is no step by step list to vectorization. Good vectorization requires knowledge of MATLAB's aailablev vector functions, strong understanding of the computation to be optimized, and That yn plus 1 is yn plus h times the function f evaluated at t sub n and y sub n. This is Euler's method. We're now ready for our first MATLAB program, ODE1. It's called ODE1 because it's our first program and because it evaluates the function f that defines the differential equation once per step. There are five input arguments. The first is ... Sep 07, 2009 · Relational operators produce either a zero (false) or a one (true). You can use this to construct the unit step function using u(x) = x>=0. You could try doing this with anonymous functions: Create a transfer function model. Create an option set for step to specify input offset and step amplitude level. Calculate the step response using the specified options. Add Code to a MATLAB Function Block Programmatically. This example shows how to programmatically add a MATLAB Function block to a model and populate the block with MATLAB code. If you already have MATLAB code and do not want to add it to a MATLAB Function block manually, this workflow can be convenient.you can just enter the name of the function in the search, and a page with a good number of examples usually comes up. It is more challenging to find out how to do something, but most of the functions you need can be found by clicking on the MATLAB link on the main page and then following the menus that come up on subsequent pages. How to plot the step function u(t) in matlab using the heaviside command.step function using matlab :D hey guyzzzz i got a problem with this matlab program ...um a beginner in using matlab :D...and my professor insists to solve the attached problem with matlab without using "if statement" and in one line command and to plot the current versus the energy...may anyone help plz :DSmoothstep is a family of sigmoid-like interpolation and clamping functions commonly used in computer graphics and video game engines.. The function depends on three parameters, the input x, the "left edge" and the "right edge", with the left edge being assumed smaller than the right edge.The function receives a real number x as an argument and returns 0 if x is less than or equal to the left ...Step 2: Coding it in Now that you have everything in rst order form, you will need the following commands in your main code: [t,x] = ode45(@fname, tspan, xinit, options) fname is the name of the function M le used to evaluate the right-hand-side function in Eq. (1). This is the function where we will input the system of rst For more information on those topics see one of our tutorials on vectors (Introduction to Vectors in Matlab), matrices (Introduction to Matrices in Matlab), vector operations (Vector Functions), loops (Loops), or plotting (Plotting). In this tutorial we will introduce the basic operations for creating executable files. I am trying to use template matching for the first time. From this MATLAB documentation, it seems like step(H,I,T) will do the trick. I don't note what H is though. At the bottom it says briefly: H specifies the System object on which to run this step method. Figure 1: The Heaviside step function. Note how it doesn’t matter how close we get to x = 0 the function looks exactly the same. The Heaviside step function H(x), sometimes called the Heaviside theta function, appears in many places in physics, see  for a brief discussion. Simply put, it is a function whose value is zero for x < 0 and one ... MATLAB Functions What is a MATLAB function? A MATLAB "function" is a MATLAB program that performs a sequence of operations specified in a text file (called an m-file because it must be saved with a file extension of *.m). A function accepts one or more MATLAB variables as inputs, operates on them in some way, and thenLab Manual MatLab Signal Processing matlab code unit step function unit step function in matlab unit step function using matlab Leave a comment Post navigation You can search the post here : Jun 29, 2018 · The Heaviside step function is the function that returns H(x)=0 for x<0, and H(x)=1 for x>0. The value on 0 is usually set to 1/2, 1 or even 0. H(x)=1/2 more logical when you define H as a limite of sequence of functions.


8 edition of Surface topology found in the catalog.
Includes bibliographical references and index
|Statement||P.A. Firby, C.F. Gardiner|
|Series||Mathematics and its applications, Mathematics and its applications (New York, N.Y.)|
|Contributions||Gardiner, Cyril F|
|LC Classifications||QA612 .F57 1991|
|The Physical Object|
|Pagination||220 p. :|
|Number of Pages||220|
|LC Control Number||91031346|
Yet there is no book exclusively devoted to isosurfaces. Isosurfaces: Geometry, Topology, and Algorithms represents the first book to focus on basic algorithms for isosurface construction. It also gives a rigorous mathematical perspective on some of the algorithms and results. General Topology book. Read 4 reviews from the world's largest community for readers. Among the best available reference introductions to general topolog /5.
To update your Surface with the latest drivers and firmware from the Download Center, select file name that matches your Surface model and version of Windows. For example, to update a Surface Book 2 with build of Wind choose Go to Download driver and firmware for Surface, choose Surface Book 2 then click Download on the next page. Choose file that matches your current OS Build and click Next. After downloading, run and install then Restart.
Algebraic Topology by NPTEL. This is a basic note in algebraic topology, it introduce the notion of fundamental groups, covering spaces, methods for computing fundamental groups using Seifert Van Kampen theorem and some applications such as the Brouwer’s fixed point theorem, Borsuk Ulam theorem, fundamental theorem of algebra. - Explore Makkon06's board "Hard Surface Topology", followed by people on Pinterest. See more ideas about Hard surface modeling, Modeling techniques and Modeling tips pins.
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Examines topology of recent compact surfaces through the development of simple ideas in plane geometry; Contains a wealth of applications and a variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean geometry.
Containing over diagrams, the approach allows for a straightforward treatment of its subject area. It is particularly attractive for its wealth of applications and variety of interactions with branches of mathematics, linked with surface topology, graph theory, group theory, vector field theory, and plane Euclidean and non-Euclidean : P A Firby, C F Gardiner.
If accepted, sections Surface (topology)#In general, Surface (mathematics)#In physics, and Surface (mathematics)#In computer science would be deleted. 26 April (UTC)fgnievinski We can probably work on fixing up the disambiguation page in main space, it can always be moved aside once Draft:Surface is ready.(Rated B-class, High-importance): Surface topology book.
The first really important result in topology grew out of Euler’s polyhedra formula and it was a complete classification of surfaces, which are Surface topology book two dimensional shapes like the surface of a sphere.
Topology I and II by Chris Wendl. This note describes the following topics: Metric spaces, Topological spaces, Products, sequential continuity and nets, Compactness, Tychonoff’s theorem and the separation axioms, Connectedness and local compactness, Paths, homotopy and the fundamental group, Retractions and homotopy equivalence, Van Kampen’s theorem, Normal subgroups, generators and.
A wide variety of topics are linked with surface topology, such as graph theory, group theory, vector field theory and plane Euclidean and non-Euclidean geometry. Each topic is treated from its beginnings, thus offering a bird's eye view of many branches of mathematics.
The author's introductions are presented in simple terms and, for those who Author: P. Firby. Cumulative and current firmware and drivers for the Surface Book. This firmware and driver package contains drivers for all of the components in the Surface Book, as well as updates to the system firmware that have been released via Windows Update.
These drivers and firmware are compatible with Wind including Enterprise versions. The Operating System: Windows Additional Physical Format: Online version: Firby, P.A., Surface topology.
New York: Ellis Horwood, (OCoLC) Material Type: Internet resource. Purchase Surface Topology - 3rd Edition. Print Book & E-Book. ISBNCOVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.
Topology of Surfaces. Authors: Kinsey, ine Free Preview. Buy this book eB99 the only topology an undergraduate might see is point-set topology at a fairly abstract level. The next course the average stu dent would take would be a graduate course in algebraic topology, and such courses are commonly very homological in nature.
Public users can however freely search the site and view the abstracts and keywords for each book and chapter. Please, subscribe or login to access full text content. If you think you should have access to this title, please contact your librarian. $\begingroup$ Hatcher's book is very well-written with a good combination of motivation, intuitive explanations, and rigorous details.
It would be worth a decent price, so it is very generous of Dr. Hatcher to provide the book for free download. But if you want an alternative, Greenberg and Harper's Algebraic Topology covers the theory in a straightforward and comprehensive manner.
A List of Recommended Books in Topology Allen Hatcher that are diﬃcult to learn due to the lack of a good book. The list was made in and is in need of updating. For the books that were still Someone should someday write a comprehensive exposition of topological surface theory.
A small fraction of the theory can be found inFile Size: 65KB. The fractal method incorporates fractal dimension which is an intrinsic property of multiscale roughness of surface characterization.
It is invariant with length scales and is closely linked to the concept of geometric self-similarity. The self-similarity or self-affinity of rough surfaces implies that as the unit of measurement is continuously decreased, the surface area of the rough surface.
Design, Size And Weight. Putting aside the inch version of the Surface Book 2 (a new size for this generation), there is very little difference in size between the old and the new models.
This book initially follows a two-semester first course in topology with emphasis on algebraic topology. It furthermore takes the reader to more advanced parts of algebraic topology as well as some applications: the shape of the universe, configuration spaces, digital image analysis, data analysi 5/5.
May 3, - Explore shawnspetch's board "Hard Surface Topology Reference" on Pinterest. See more ideas about Hard surface modeling, Modeling tips and Modeling techniques pins. CS Computational Topology Surface Topology Fall We will see another formal deﬁnition of orientability in the next lecture.
For now, orientability means that the surface has two sides. Escher establishes that the Mobius strip is one-sided by marching ants on the strip (c).
Note that¨ the boundary of the Mobius strip is a File Size: KB. Cumulative and current firmware and drivers for the Surface Book 2.
This firmware and driver package contains drivers for all of the components in the Surface Book 2, as well as updates to the system firmware that have been released via Windows Update.
These drivers and firmware are compatible with Wind including Enterprise versions. The Operating System: Windows. In mathematics, a surface is a geometrical shape; the most familiar examples arise as boundaries of solid objects in ordinary three-dimensional Euclidean space R3, such as spheres.
The exact definition of a surface may depend on the context. In algebraic geometry, a surface may cross itself, while, in topology and differential geometry, it may not.This is an expository account of two classical theorems in surface topology: Topological surfaces have unique smooth structures, and homeomorphisms of smooth surfaces are isotopic to diffeomorphisms.
With the torus trick, almost no point-set topology is needed for the proofs. "A short exposition of the Madsen-Weiss theorem". pdf file (43 pages.🖥 Ergonomic VESA docks for Surface  🖥 Original Poster 1 point 2 years ago edited 3 minutes ago This regkey fix from Microsoft comes in handy if you get odd behavior when docking and un-docking with multiple monitors.


We will see two types of matrices in this chapter. The identity matrix or the inverse of a matrix are concepts that will be very useful in the next chapters. We will see at the end of this chapter that we can solve systems of linear equations by using the inverse matrix. So hang on!
2.3 Identity and Inverse Matrices
The identity matrix $\bs_n$ is a special matrix of shape ($n \times n$) that is filled with $0$ except the diagonal that is filled with 1.
A 3 by 3 identity matrix
An identity matrix can be created with the Numpy function eye() :
When ‘apply’ the identity matrix to a vector the result is this same vector:
You can think of a matrix as a way to transform objects in a $n$-dimensional space. It applies a linear transformation of the space. We can say that we apply a matrix to an element: this means that we do the dot product between this matrix and the element (more details about the dot product in 2.2). We will see this notion thoroughly in the next chapters but the identity matrix is a good first example. It is a particular example because the space doesn’t change when we apply the identity matrix to it.
The space doesn’t change when we apply the identity matrix to it
We saw that $\bs
For this example, we will use the Numpy function linalg.inv() to calculate the inverse of $\bs$. Let’s start by creating $\bs$:
Now we calculate its inverse:
We can check that $\bs
We will see that inverse of matrices can be very usefull, for instance to solve a set of linear equations. We must note however that non square matrices (matrices with more columns than rows or more rows than columns) don’t have inverse.
Sovling a system of linear equations
An introduction on system of linear equations can be found in 2.2.
The inverse matrix can be used to solve the equation $\bs
Since we know by definition that $\bs^<-1>\bs=\bs$, we have:
We saw that a vector is not changed when multiplied by the identity matrix. So we can write:
This is great! We can solve a set of linear equation just by computing the inverse of $\bs$ and apply this matrix to the vector of results $\bs$!
We will take a simple solvable example:
We will use the notation that we saw in 2.2:
Here, $x_1$ corresponds to $x$ and $x_2$ corresponds to $y$. So we have:
And the vector $\bs$ containing the solutions of individual equations is:
Under the matrix form, our systems becomes:
Let’s find the inverse of $\bs$:
Since we saw that
This is our solution!
This means that the point of coordinates (1, 2) is the solution and is at the intersection of the lines representing the equations. Let’s plot them to check this solution:
We can see that the solution (corresponding to the line crossing) is when $x=1$ and $y=2$. It confirms what we found with the matrix inversion!
BONUS: Coding tip — Draw an equation
To draw the equation with Matplotlib, we first need to create a vector with all the $x$ values. Actually, since this is a line, only two points would have been sufficient. But with more complex functions, the length of the vector $x$ corresponds to the sampling rate. So here we used the Numpy function arrange() (see the doc) to create a vector from $-10$ to $10$ (not included).
The first argument is the starting point and the second the ending point. You can add a third argument to specify the step:
Then we create a second vector $y$ that depends on the $x$ vector. Numpy will take each value of $x$ and apply the equation formula to it.
Finally, you just need to plot these vectors.
Some matrices are not invertible. They are called singular.
This introduces different cases according to the linear system because $\bs^<-1>$ exists only if the equation $\bs
Feel free to drop me an email or a comment. The syllabus of this series can be found in the introduction post. All the notebooks can be found on Github.
This content is part of a series following the chapter 2 on linear algebra from the Deep Learning Book by Goodfellow, I., Bengio, Y., and Courville, A. (2016). It aims to provide intuitions/drawings/python code on mathematical theories and is constructed as my understanding of these concepts. You can check the syllabus in the introduction post.
NumPy Inverse Matrix in Python
NumPy linalg.inv() function in Python is used to compute the (multiplicative) inverse of a matrix. The inverse of a matrix is that matrix which when multiplied with the original matrix, results in an identity matrix. In this article, I will explain how to use the NumPy inverse matrix to compute the inverse of the matrix array using this function.
1. Quick Examples of Inverse Matrix
If you are in a hurry, below are some quick examples of how to use Python NumPy inverse matrix.
2. Syntax of numpy.linalg.inv() Function
Following is the syntax to create numpy.linalg.inv() function.
2.1 Parameter of Inverse Matrix
Following are the parameters of the inverse matrix.
arr : This parameter represents the matrix to be inverted.
2.2 Return Value of Inverse Matrix
This function returns the inverse of the matrix array.
3. Usage of numpy.linalg.inv() Function
Using Python numpy.linalg.inv() function to the inverse of a matrix in simple mathematics can be defined as a matrix.
3.1 Use numpy.linalg.inv() Function
We can use a matrix as a rectangular arrangement of data or numbers, in other words, we can say that it is a rectangular array of data the horizontal entries in the matrix are called rows and the vertical entries are called columns. For the matrix inverse function, we need to use np.linalg.inv() function. This function will inverse the given matrix. Python NumPy provides an easy function to calculate the inverse of the matrix. The function helps the user to check numpy.linalg.inv() is available in the Python library.
4. Get the Inverse of a Matrix Using scipy.linalg.inv() Function
We can also use the scipy module to perform different scientific calculations using its functionalities. Using scipy.linalg.inv() function is used to return the inverse of a given square matrix in NumPy Python. It works the same way as the numpy.linalg.inv() function.
Yields the same output as above.
5. Inverse of a Matrix NumPy Two Multi-Dimensional Arrays
We can also use np.linalg.inv() function to compute the multiplicative inverse of a matrix of the two multi-dimensional arrays elementwise.
In this article, I have explained how to use the inverse matrix to compute the inverse of the matrix array with examples.
Linear Algebra and Numpy
I ‘d like to present the blog post on the linear algebra and how it benefits to Machine Learning and Deep Learning. so, the goal of this post is to help the beginners in the field of Machine learning and Deep learning. basically, we have a focus on the Numpy Library, who don’t know about the Numpy Library. it is a Python Package basically stands for Numerical Python. I can assume that you are familiar with the basic Python Programming. So, Let’s start.
What is Linear Algebra?
Linear algebra is a branch of mathematics that is widely used throughout science and engineering. Yet because linear algebra is a form of continuous rather than discrete mathematics, many computer scientists have little experience with it. A good understanding of linear algebra is essential for understanding and working with many machine learning algorithms, especially deep learning algorithms.
In this Module, we learn about Linear algebra topic called Matrix and their Operations i.e Vectors, Matrix Multiplication, determinant, trace and many more.
And learn how to implement these in the Programming way. so, for this, we will be using the Python Package called Numpy.
let's familiarise with numpy and their installation.
NumPy is the fundamental package for scientific computing with Python. adding support for large, multi-dimensional arrays and matrices, along with a large collection of high mathematics functions to operate on these arrays.
-> a powerful N-dimensional array object.
-> sophisticated (broadcasting) functions.
-> tools for integrating C/C++ and Fortran code.
-> useful linear algebra, Fourier transform, and random number capabilities.
Installation of Numpy —
Numpy Installation via pip
Numpy Installation for Anaconda Jupyter Notebook user
To use the Numpy library in the program all you need to do in to import it.
don't confuse with np it just a method of the renaming of module numpy into np.
Now, the system is set up for writing the programs and learn Mathematics with hands-on Implementation.
So, Take a cup of coffee, wear your headphones and enjoy coding.
Let’s familiarize with the basics of Numpy —
Basic of Numpy —
Note: an array can be referred to as a matrix.
a) Create an Array and Print an Array —
b) Finding the Number of array dimensions —
c) Finding the shape of an Array —
d) Reshaping of an Array —
e) Some Mathematical Operation —
f) Finding the mean, median, variance and standard deviation of an array:
Now, we come to the main part i.e. Linear Algebra and we first discuss the Vectors.
Vectors and vector spaces are fundamental to linear algebra, and they’re used in many machine learning models. Vectors describe spatial lines and planes, enabling you to perform calculations that explore relationships in multi-dimensional space.
What is Vector —
A vector is a numeric element that has both magnitude and direction. The magnitude represents a distance (for example, “2 miles”) and the direction indicates which way the vector is headed (for example, “East”). Vectors are defined by an n-dimensional coordinate that describes a point in space that can be connected by a line from an arbitrary origin.
Our vector can be written as v=(2,3), Run the below code in your cell to visualize the vector v (which remember is described by the coordinate (2,3)).
Make sure you install the matplotlib Python Package.
Calculating Magnitude —
Calculating the magnitude of the vector from its cartesian coordinates requires measuring the distance between the arbitrary starting point and the vector head point. For a two-dimensional vector, we’re actually just calculating the length of the hypotenuse in a right-angled triangle — so we could simply invoke Pythagorean theorem and calculate the square root of the sum of the squares of its components. So, here we can calculate the magnitude of a vector by two methods —
Code 1 (simple)-by using math module
Code 2 (By using linalg library provided by numpy) —
In Python, numpy provides a linear algebra library named linalg that makes it easier to work with vectors — you can use the norm function in the following code to calculate the magnitude of a vector.
the output is the same as above
Calculating Direction —
To calculate the direction, or amplitude, of a vector from its cartesian coordinates, you must employ a little trigonometry. We can get the angle of the vector by calculating the inverse tangent; sometimes known as the arctan (the tangent calculates an angle as a ratio — the inverse tangent, or tan-1, expresses this in degrees).
n any right-angled triangle, the tangent is calculated as the opposite over the adjacent. In a two dimensional vector, this is the y value over the x value, so for our v vector (2,3):
=> tan( ) = 3/2
=> = tan-1(3/2) = 56.309932474020215
Run the following Python code in your cell to confirm this:
and you will see the output —
tan = 1.5
inverse-tan = 56.309932474020215
There is an added complication, however, because if the value for x or y (or both) is negative, the orientation of the vector is not standard, and a calculator can give you the wrong tan-1 value from this method. To ensure you get the correct direction for your vector, use the following rules:
Both x and y is positive: Use the tan-1 value.
x is negative, y is positive: Add 180 to the tan-1 value.
Both x and y is negative: Add 180 to the tan-1 value.
x is positive, y is negative: Add 360 to the tan-1 value.
In the previous Python code, we used math.atan function to calculate the inverse tangent from a numeric tangent. The *numpy library includes a similar arctan function. When working with numpy arrays, you can also use the numpy.arctan2 function to return the inverse tangent of an array-based vector in radians, and you can use the numpy.degrees function to convert this to degrees. The arctan2 function automatically makes the necessary adjustment for negative x and y values.
Vector Addition —
So far, we’ve worked with one vector at a time. What happens when you need to add two vectors.
let's take an example —
v = (2,1)
s = (-3,1)
addition of v and s give (-1,2)
Run the cell below to create v and plot it together with s.
now, we add the v and s vectors
now, let see how this is looking like (Plotting)
here, the blue arrow is vector s, the red arrow is vector v and the green arrow is them summation.
Vector Multiplication —
Vector multiplication can be performed in three ways:
- Scalar Multiplication
- Dot Product Multiplication
- Cross Product Multiplication
Scalar Multiplication —
Let’s start with scalar multiplication — in other words, multiplying a vector by a single numeric value.
suppose I want to multiply vector v by 3, which I could write like this: w = 3v.
so, basically, value 3 multiply to all elements of the vector. for example —
=> v = (-1,1)
=> w = 3v
=> w = (-3,3)
let’s do it by running the code —
The same approach is taken for scalar division.
Try it for yourself — to calculate a new vector named b based on the following definition: b = v/2
code of this problem is here
Dot Product Multiplication —
To get a scalar product, we calculate the dot product. This takes a similar approach to multiply a vector by a scalar, except that it multiplies each component pair of the vectors and sums the results. To indicate that we are performing a dot product operation, we use the • operator:
So for vectors v (2,3) and s (-3,1), our calculation looks like this:
⃗ ⋅⃗ =(2⋅−3)+(3⋅1)=−6+3=−3
In Python, you can use the numpy. dot function to calculate the dot product of two vector arrays.
you will the same output as we calculated: -3
In Python 3.5 and later, we can also use the @ operator to calculate the dot product:
The Cosine Rule —
A useful property of vector dot product multiplication is that we can use it to calculate the cosine of the angle between two vectors.
Here’s that calculation in Python:
Match your output with theta = 105.25511870305779
Cross Product Multiplication —
To get the vector product of multiplying two vectors together, you must calculate the cross product. The result of this is a new vector that is at right angles to both the other vectors in 3D Euclidean space. This means that the cross-product only really makes sense when working with vectors that contain three components.
In Python, we can use the numpy.cross-function to calculate the cross product of two vector arrays:
The output of this code: [-8 5 1]
A matrix is an array of numbers that are arranged into rows and columns.
So, we already learn how to create a matrix(Array) and their basic operation in section Basic of Numpy. here, we learn more advanced of Matrix i.e Transpose, Inverse, Eigen Vector, etc. but before we start more advanced let’s do a simple program to create a matrix.
In Python, we can define a matrix as a 2-dimensional numpy.array, like this:
The output of this code is as you expect —
but we can also use numpy.matrix type, which is a specialist subclass of an array:
The output of this code is the same as np.array() give
There are some differences in behavior between array and matrix types — particularly with regards to multiplication (which we’ll explore later). You can use either, but most experienced Python programmers who need to work with both vectors and matrices tend to prefer the array type for consistency.
We also prefer an array.
Matrix Transposition —
You can transpose a matrix, that switches the orientation of its rows and columns. You indicate this with a superscript T, like this:
In Python, both numpy.array and numpy.matrix have a T function:
Matrix Multiplication —
To multiply two matrices together, you need to calculate the dot product of rows and columns. This means multiplying each of the elements in each row of the first matrix by each of the elements in each column of the second matrix and adding the results. We perform this operation by applying the RC rule — always multiplying Rows by Columns. For this to work, the number of columns in the first matrix must be the same as the number of rows in the second matrix so that the matrices are conformable for the dot product operation.
In Python, we can use numpy.dot function or the @ operator to multiply matrices and two-dimensional arrays.
As you can see both np.dot(A, B) and A@B give the same output. so, you can anyone for multiplication.
Now, here is one case where there is a difference in behavior between numpy.array and numpy.matrix, You can also use a regular multiplication operator with a matrix, but not with an array:
You can compare the output of this code with the upper one that both are same.
Now, you already read about the property of the matrices that commutative law is not applicable in matrix multiplication.so, let’s proof this one.
Analyze your output that commutative law is applicable or not.
The inverse of Matrix —
So, how do you calculate the inverse of a matrix? For a 2×2 matrix
1)Either we use the Gauss — Jordan method(row or column elementary operation)
2)you can follow this formula:
In Python, we can use numpy.linalg.inv function to get the inverse of a matrix in an array or matrix object:
Additionally, the matrix type has an I method that returns the inverse matrix:
For larger matrices, the process to calculate the inverse is more complex.
Steps to calculate the Inverse of a Matrix:
- Step 1: calculating the Matrix of Minors,
- Step 2: then turn that into the Matrix of Cofactors,
- Step 3: then the Adjugate(also called Adjoint), and
- Step 4: multiply that by 1/Determinant.
As you can see, this can get pretty complicated. But the program to calculate is not so complicated.
So, till now we have learned multiplication, Inverse of the matrices, etc.
Let’s done a problem to Solve the Systems of Equations with Matrices.
Can you do yourself?
here, is the problem —
you have to solve these equations with the help of Matrices.
Hint — your equation looks like this:
Problem code solution is here.
Matrices and vectors are used together to manipulate spatial dimensions. This has a lot of applications, including the mathematical generation of 3D computer graphics, geometric modeling, and the training and optimization of machine learning algorithms. We’re not going to cover the subject exhaustively here, but we’ll focus on a few key concepts that are useful to know when you plan to work with machine learning.
Linear Transformations —
We can manipulate a vector by multiplying it with a matrix. The matrix acts as a function that operates on an input vector to produce a vector output. Specifically, matrix multiplications of vectors are linear transformations that transform the input vector into the output vector.
for example, consider this matrix A and vector v:
We can define a transformation T like this: T( ⃗) = A ⃗
To perform this transformation, we simply calculate the dot product by applying the RC rule; multiplying each row of the matrix by the single column of the vector.
Here’s the calculation in Python:
In this case, both the input vector and the output vector have 2 components — in other words, the transformation takes a 2-dimensional vector and produces a new 2-dimensional vector; which we can indicate like this:
Note that the output vector may have a different number of dimensions from the input vector; so the matrix function might transform the vector from one space to another — or in notation:
Here it is in Python:
Transformations of Magnitude and Amplitude —
When we multiply a vector by a matrix, we transform it in at least one of the following two ways:
- Scale the length (magnitude) of the matrix to make it longer or shorter.
- Change the direction (amplitude) of the matrix.
For example, consider the following matrix and vector:
As before, we transform the vector v by multiplying it with the matrix A.
In this case, the resulting vector has changed in length (magnitude) but has not changed its direction (amplitude).
Let’s visualize that in Python:
The original vector v is shown in orange, and the transformed vector t is shown in blue — note that t has the same direction (amplitude) as v but a greater length (magnitude).
Now let’s use a different matrix to transform the vector v:
This time, the resulting vector has been changed to a different amplitude but has the same magnitude.
Now let’s see change the matrix one more time:
Now our resulting vector has been transformed into a new amplitude and magnitude — the transformation has affected both direction and scale.
Affine Transformations —
An Affine transformation multiplies a vector by a matrix and adds an offset vector, sometimes referred to as bias; like this:
This kind of transformation is actually the basis of linear regression, which is a core foundation for machine learning. The matrix defines the features, the first vector is the coefficients, and the bias vector is the intercept.
here’s an example of an Affine transformation in Python:
Eigenvectors and Eigenvalues —
So we can see that when you transform a vector using a matrix, we change its direction, length, or both. When the transformation only affects scale (in other words, the output vector has a different magnitude but the same amplitude as the input vector), the matrix multiplication for the transformation is the equivalent operation as some scalar multiplication of the vector.
For example, earlier we examined the following transformation that dot-multiplies a vector by a matrix:
We can achieve the same result by multiplying the vector by the scalar value 2:
The following python performs both of this calculation and shows the results, which are identical.
In cases like these, where a matrix transformation is the equivalent of a scalar-vector multiplication, the scalar-vector pairs that correspond to the matrix are known respectively as eigenvalues and eigenvectors. We generally indicate eigenvalues using the Greek letter lambda (λ), and the formula that defines eigenvalues and eigenvectors with respect to a transformation is:
Where the vector v is an eigenvector and the value λ is an eigenvalue for transformation T.
When the transformation T is represented as matrix multiplication, as in this case where the transformation is represented by matrix A:
where λ is a scalar value called the ‘eigenvalue’. This means that the linear transformation A on vector ⃗is completely defined by λ.
We can rewrite the equation as follows:
Where, I is the identity matrix of the same dimensions as A.
A matrix can have multiple eigenvector-eigenvalue pairs, and you can calculate them manually. However, it’s generally easier to use a tool or programming language. For example, in Python, you can use the linalg.eig function, which returns an array of eigenvalues and a matrix of the corresponding eigenvectors for the specified matrix.
Here’s an example that returns the eigenvalue and eigenvector pairs for the following matrix:
So there are two eigenvalue-eigenvector pairs for this matrix, as shown here:
Let’s verify that multiplying each eigenvalue-eigenvector pair corresponds to the dot-product of the eigenvector and the matrix. Here’s the first pair:
So far so good. Now let’s check the second pair:
So our eigenvalue-eigenvector scalar multiplications do indeed correspond to our matrix-eigenvector dot-product transformations.
Here’s the equivalent code in Python, using the eVals and eVecs variables you generated in the previous code cell:
The output of this code —
You can use the following code to visualize these transformations:
Similarly, can you examine the following matrix transformation:
Hint: you can achieve the same result by multiplying the vector by the scalar value 2.
The solution is here.
So we’ve learned a little about eigenvalues and eigenvectors, but you may be wondering what use they are. Well, one use for them is to help decompose transformation matrices.
Recall that previously we found that a matrix transformation of a vector changes its magnitude, amplitude, or both. Without getting too technical about it, we need to remember that vectors can exist in any spatial orientation, or basis; and the same transformation can be applied in different bases.
We can decompose a matrix using the following formula:
Where A is a transformation that can be applied to a vector in its current base, Q is a matrix of eigenvectors that defines a change of basis, and Λ is a matrix with eigenvalues on the diagonal that defines the same linear transformation as A in the base defined by Q.
Let’s look at these in some more detail. Consider this matrix:
Q is a matrix in which each column is an eigenvector of A; which as we’ve seen previously, we can calculate using Python:
So for matrix A, Q is the following matrix:
Λ is a matrix that contains the eigenvalues for A on the diagonal, with zeros in all other elements; so for a 2×2 matrix, Λ will look like this:
In our Python code, we’ve already used the linalg.eig function to return the array of eigenvalues for A into the variable l, so now we just need to format that as a matrix:
So Λ is the following matrix:
Now we just need to find Q-1, which is the inverse of Q:
The inverse of Q is:
So what does that mean? Well, it means that we can decompose the transformation of any vector multiplied by a matrix A into the separate operations QΛQ-1:
To prove this, let’s take vector v:
Our matrix transformation using A is:
So let’s show the results of that using Python:
And now, let’s do the same thing using the QΛQ-1 sequence of operations:
And you can see that the output of this code is the same as above.
So A and QΛQ-1 are equivalent.
If we view the intermediary stages of the decomposed transformation, you can see the transformation using A in the original base for v (orange to blue) and the transformation using Λ in the change of basis described by Q (red to magenta):
So from this visualization, it should be apparent that the transformation Av can be performed by changing the basis for v using Q (from orange to red in the above plot) applying the equivalent linear transformation in that base using Λ (red to magenta), and switching back to the original base using Q-1 (magenta to blue).
Rank of a Matrix-
The rank of a square matrix is the number of non-zero eigenvalues of the matrix. A full rank matrix has the same number of non-zero eigenvalues as the dimension of the matrix. A rank-deficient matrix has fewer non-zero eigenvalues as dimensions. The inverse of a rank deficient matrix is singular and so does not exist.
Consider the following matrix A:
Let’s find its eigenvalues (Λ):
This matrix has full rank. The dimensions of the matrix are 2. There are two non-zero eigenvalues.
Now consider this matrix:
Note that the second and third columns are just scalar multiples of the first column.
Let’s examine its eigenvalues:
Note that the matrix has only 1 non-zero eigenvalue. The other two eigenvalues are so extremely small as to be effectively zero. This is an example of a rank-deficient matrix; and as such, it has no inverse.
Inverse of a Square Full Rank Matrix —
We can calculate the inverse of a square full rank matrix by using the following formula:
Let’s apply this to matrix A:
Let’s find the matrices for Q, Λ-1, and Q-1:
Let’s calculate that in Python:
That gives us the result:
We can apply np.linalg.inv function directly to A to verify this:
This will give you the same A inverse value as above.
Let’s end this here! All the code of this discussion is here.
So, congrats you do it perfectly.
I know it a little bit longer. but Hope I have given some idea about Numpy and the Linear Algebra and how it Apply in the field like Machine Learning, Deep Learning, and Computer Vision.


- Honorary Professor at University of KwaZulu-Natal, Durban, South Africa
- Plenary speaker at South Africa Gravity Society meeting 2023, South Africa
- China Top Cited Paper Awards 2022 IOP for our review paper Teleparallel theories of gravity: illuminating a fully invariant approach, link here
- Plenary speaker at Metric-Affine Frameworks for Gravity 2022 Tartu
- Invited speaker at the 10th Physics School Roberto A. Salmeron 2021 EFRAS
- Interview at Faculti on Modified teleparallel theories of gravity
- Interview at Faculti on Regular black holes in 4-dimensional Born-Infeld gravity
- Interview at Faculti on Chirality in the plane
- Plenary focused talk at Gravitex 2021 ; see here youtube for the recorded lecture
I am a Professor in the Department of Mathematics of University College London, and an Honorary Professor at the University of KwaZulu-Natal, Durban, South Africa. Since September 2023 I am the head of department of UCL Mathematics.
My main research interests are in theoretical physics and applied mathematics where I am interested in the mathematical foundations of General Relativity and Cosmology. In recent years I have developed a keen interest in continuum mechanics.
Initially I worked on exact solutions of the Einstein field equations, especially spherically symmetric solutions. I analysed the effects of the cosmological constant on such systems and thereby developed an interest in the cosmological constant and the dark energy problem. I analysed various dark matter models in the context of classical gravity, brane world models and Bose-Einstein condensates, and also worked on modified gravity. I was always intrigued by generalisations of general relativity where the manifold underlying the theory is for instance allowed to carry torsion as well as curvature, Einstein-Cartan theory. In recent years I have been working on dynamical system techniques in cosmology.
In continuum mechanics I am mainly interested elasticity with microrotations, also known as Cosserat elasticity or micropolar elasticity. This field shows some surprising similarities with general relativity, the equations are long and complicated, and are nonlinear. In particular I am interested in wave type solutions and other exact solutions that can be constructed in Cosserat elasticity.


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The Concise Oxford Dictionary of Mathematics by Christopher Clapham; James NicholsonAuthoritative and reliable, this A-Z provides jargon-free definitions for even the most technical mathematical terms. With over 3,000 entries ranging from Achilles paradox to zero matrix, it covers all commonly encountered terms and concepts from pure and applied mathematics and statistics, for example, linear algebra, optimisation, nonlinear equations, and differential equations. In addition, there are entries on major mathematicians and on topics of more general interest, such as fractals, game theory, and chaos. Usinggraphs, diagrams, and charts to render definitions as comprehensible as possible, entries are clear and accessible. Almost 200 new entries have been added to this edition, including terms such as arrow paradox, nested set, and symbolic logic. Useful appendices follow the A-Z dictionary and include lists of Nobel Prize winners and Fields' medallists, Greek letters, formulae, and tables of inequalities, moments of inertia, Roman numerals, a geometry summary, additional trigonometric values of special angles, and many more. This edition contains recommended web links, which are accessible and kept up to date via the Dictionary of Mathematics companion website. Fully revised and updated in line with curriculum and degree requirements, this dictionary is indispensablefor students and teachers of mathematics, and for anyone encountering mathematics in the workplace.Readership: Students and teachers of mathematics at school and university level, and those in the related fields of statistics and economics.
Publication Date: 2014-07-22
CRC Concise Encyclopedia of Mathematics by Eric W. WeissteinUpon publication, the first edition of the CRCConcise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the dedication of author Eric Weisstein to collecting, cataloging, and referencing mathematical facts, formulas, and definitions. He has now updated most of the original entries and expanded the Encyclopediato include 1000 additional pages of illustrated entries. The accessibility of the Encyclopediaalong with its broad coverage and economical price make it attractive to the widest possible range of readers and certainly a must for libraries, from the secondary to the professional and research levels. For mathematical definitions, formulas, figures, tabulations, and references, this is simply the most impressive compendium available.
Call Number: QA5 .W45 2003
Publication Date: 2002-12-12
The Princeton Companion to Mathematics by Timothy Gowers (Editor); June Barrow-Green (Editor); Imre Leader (Editor); June Barrow-Green (Editor)This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Edited by Timothy Gowers, a recipient of the Fields Medal, it presents nearly two hundred entries, written especially for this book by some of the world''s leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact of mathematics on other disciplines such as biology, finance, and music--and much, much more. Unparalleled in its depth of coverage, The Princeton Companion to Mathematics surveys the most active and exciting branches of pure mathematics. Accessible in style, this is an indispensable resource for undergraduate and graduate students in mathematics as well as for researchers and scholars seeking to understand areas outside their specialties. Features nearly 200 entries, organized thematically and written by an international team of distinguished contributors Presents major ideas and branches of pure mathematics in a clear, accessible style Defines and explains important mathematical concepts, methods, theorems, and open problems Introduces the language of mathematics and the goals of mathematical research Covers number theory, algebra, analysis, geometry, logic, probability, and more Traces the history and development of modern mathematics Profiles more than ninety-five mathematicians who influenced those working today Explores the influence of mathematics on other disciplines Includes bibliographies, cross-references, and a comprehensive index Contributors incude: Graham Allan, Noga Alon, George Andrews, Tom Archibald, Sir Michael Atiyah, David Aubin, Joan Bagaria, Keith Ball, June Barrow-Green, Alan Beardon, David D. Ben-Zvi, Vitaly Bergelson, Nicholas Bingham, B#65533;la Bollob#65533;s, Henk Bos, Bodil Branner, Martin R. Bridson, John P. Burgess, Kevin Buzzard, Peter J. Cameron, Jean-Luc Chabert, Eugenia Cheng, Clifford C. Cocks, Alain Connes, Leo Corry, Wolfgang Coy, Tony Crilly, Serafina Cuomo, Mihalis Dafermos, Partha Dasgupta, Ingrid Daubechies, Joseph W. Dauben, John W. Dawson Jr., Francois de Gandt, Persi Diaconis, Jordan S. Ellenberg, Lawrence C. Evans, Florence Fasanelli, Anita Burdman Feferman, Solomon Feferman, Charles Fefferman, Della Fenster, Jos#65533; Ferreir#65533;s, David Fisher, Terry Gannon, A. Gardiner, Charles C. Gillispie, Oded Goldreich, Catherine Goldstein, Fernando Q. Gouv#65533;a, Timothy Gowers, Andrew Granville, Ivor Grattan-Guinness, Jeremy Gray, Ben Green, Ian Grojnowski, Niccol#65533; Guicciardini, Michael Harris, Ulf Hashagen, Nigel Higson, Andrew Hodges, F. E. A. Johnson, Mark Joshi, Kiran S. Kedlaya, Frank Kelly, Sergiu Klainerman, Jon Kleinberg, Israel Kleiner, Jacek Klinowski, Eberhard Knobloch, J#65533;nos Koll#65533;r, T. W. K#65533;rner, Michael Krivelevich, Peter D. Lax, Imre Leader, Jean-Fran#65533;ois Le Gall, W. B. R. Lickorish, Martin W. Liebeck, Jesper L#65533;tzen, Des MacHale, Alan L. Mackay, Shahn Majid, Lech Maligranda, David Marker, Jean Mawhin, Barry Mazur, Dusa McDuff, Colin McLarty, Bojan Mohar, Peter M. Neumann, Catherine Nolan, James Norris, Brian Osserman, Richard S. Palais, Marco Panza, Karen Hunger Parshall, Gabriel P. Paternain, Jeanne Peiffer, Carl Pomerance, Helmut Pulte, Bruce Reed, Michael C. Reed, Adrian Rice, Eleanor Robson, Igor Rodnianski, John Roe, Mark Ronan, Edward Sandifer, Tilman Sauer, Norbert Schappacher, Andrzej Schinzel, Erhard Scholz, Reinhard Siegmund-Schultze, Gordon Slade, David J. Spiegelhalter, Jacqueline Stedall, Arild Stubhaug, Madhu Sudan, Terence Tao, Jamie Tappenden, C. H. Taubes, R#65533;diger Thiele, Burt Totaro, Lloyd N. Trefethen, Dirk van Dalen, Richard Weber, Dominic Welsh, Avi Wigderson, Herbert Wilf, David Wilkins, B. Yandell, Eric Zaslow, Doron Zeilberger
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Non-negative matrix factorization is a fast technique for generating embeddings from a dataset.
More concretely, given a matrix you can decompose it into two matrices that are approximattely
multiplicands of the matrix. I.e. given matrix
M, it finds matrices
B such that
M ≈ AB.
A very cool thing about embedding matrices is that the rows and columns that comprise these matrices naturally tend to fill with values that will multiply together to create the values in your data. More concretely again, if your dataset is pictures of faces, and embedding matrix will be composed of face-like images that will be added together in varying amounts to make the faces in the dataset.
So let’s make some faces.


SAKURA-a Japanese leading ICT solution provider for education has created software that will easily introduce pupils to early learning of mathematics basics including; addition, division, multiplication, among others.
The software dubbed ‘Interactive mathematics software’ was revealed during the press briefing on May 10 at Japan International Cooperation Agency (JICA) – Kigali.
It is practical when a teacher installs classwork in the software and a computer converts them into images, voice and animations in form of numbers.
‘Interactive mathematics software’ has been created with the capacity to convert installed numbers into images, voices and being able to show working on computer screen or projector.
“This software is so interactive through images, voice and animations relating to the real world that allows the user, especially young learners, to explore mathematic concepts with fun,” Angelique Mukampongerwa, head teacher of Groupe Scolaire Kimironko II, said.
“We have 1200 pupils who are expected to benefit from the programme. Normally, majority of students doesn’t enjoy learning mathematics. They consider it a boring and complicated course, but we hope many will enjoy counting using animation,” Mukampongerwa added.
“The study of ‘interactive mathematics software’ is underway in public primary schools around Kigali City, but already applicable in Japan,” Jiro Makimoto, Interactive Mathematics software program advisor said.
The software is expected to be launched in next three years after Rwanda Education Board (REB) and SAKURA have finished thorough study about its applicability.
“Interactive Mathematics software aims at introducing mathematics basics to pupils who don’t enjoy attending lessons to blackboards, but can learn through entertainment by watching images and listening to voices,”Makimoto said.
According to Makimoto, Interactive mathematics software targets all public primary schools across the country in line with policy of “SMART Classroom.”
The software will be exhibited during upcoming Transform Africa Summit in Kigali next week.
Makimoto said that this software can be used in Kinyarwanda by changing its setting in language. It also has the capacity to give voices indicating whether the answer is right or wrong.
“We are still doing the survey for the effectiveness of this software, we haven’t known how many schools will benefit, but we are targeting all public schools,” Makimoto said.


Undergraduate Institution: University of Kansas
Undergraduate Institution: University of Pittsburgh
Photo Credit: People Pill
Dr. Georgia Caldwell Smith is one of the first Black women to earn a bachelor’s degree in math. She served as a professor at Spelman College, Lincoln University (Missouri) and Alabama State University, eventually serving as the chair of the Department of Mathematics at Spelman until her death. Her Ph.D. was awarded posthumously, as she her thesis was approved months before her passing. Dr. Smith was also a member of Phi Beta Kappa and Pi Mu Epsilon.


WJES Receives Don Cargill STEM Scholar Award
West Jackson Elementary School was selected as a 2024 Don Cargill STEM Scholar Award recipient. The Georgia Youth Science and Technology Center recognized WJES educators Kathleen Venable and Jessica Frazer for their outstanding effort to engage and improve student learning in STEM disciplines.
Both Ms. Venable and Ms. Frazer will receive $500 in grant money to further incorporate STEM and STEAM into their classroom instruction.
West Jackson Elementary School is a Georgia Science Technology Engineering Arts and Mathematics (STEAM) Certified School for the 2021-26 school years.


Texture analysis using local fractal dimension of complex networks GONCALVES, D. N. ; SILVA, L. A. ; ARAUJO, R. F. S. ; MACHADO, B. B. ; GONÇALVES, W. N. XI Workshop de Visão Computacional, 2015. p. 236-241
The texture analysis is one of the most important research areas in computer vision. Currently, complex network has emerged as an approach for representing images due to its flexibility for modeling several problems. Generally, the application of the complex network theory involves two steps: representing the structure of interest into a network and extracting measurements from it. Due to the large number of measurements, decide the appropriate measurements for a particular problem is a challenge. This paper proposes the fractal dimension of complex networks as a measurement for extracting relevant features from texture images. For this, an image is modeled as a network where each pixel is mapped into a vertex. By varying the radius of connection between vertices, the proposed method estimates the local fractal dimension for each vertex to form a histogram of dimensions. Results on two image databases show the effectiveness of the proposed method against tradditional texture methods.


About Catherine Meldrum
Catherine Meldrum grew up in Dickinson, TX and moved to Carrollton with her husband and two children in 1999. She graduated from Texas Woman’s University with a B.S. in Mathematics and a minor in Engineering. Catherine has been a Math teacher for ten years at a local high school where she was also a Math club sponsor for several years. As a mother and teacher, she knows the importance of ﬁnding great schools for your children. Catherine will work diligently to help you ﬁnd the best home for your real estate needs.


Storage Heaters are designed to be used using cheap overnight electricity often called Economy 7 or Economy 10, these are Tariff’s which offer 7 hours (or 10 hours on Economy 10) of cheap rate Electricity, which allows the storage heater to ‘charge’ with heat, which is then convected to warm the room outside of the cheap rate period.
For this reason, Storage Heaters are not suitable for use on a standard, single rate Electricity Tariffs as doing so will work out extremely expensive, and very ineffective.
So lets work out how much Storage Heaters cost to run.
First of all, find out just how much Electricity each storage heater actually consumes. This will be stamped on a metal panel or label on the side or bottom of the heater.
If you cannot find the label with the electricity rating on your Storage Heater, then you can often find out how much Electricity your storage heater uses by putting the manufacturers name and the storage heater model into Google. For example ‘Dimplex XL24N’ into Google will bring up a website which tells you that the XL24N Storage Heater consumes 2.55KW of Electricity.
In fact there are 4 popular sizes of storage heater. Starting off with the smaller models of 850W and 1750W which are suitable for Bathrooms, Porches, and background heating of hallways and small bedrooms. Then there is a 2.55KW model, which is suited for medium sized areas such as standard bedrooms, and finally a 3.4KW model, which is recommended for Lounges and Living areas.
When working out the electricity consumption of an Electrical Appliance, it is easier to the rating of the appliance in ‘Kilowatts’ often expressed as ‘KW’
1000 watts = 1kw, 2000 watts = 2kw, 3000 watts = 3kw – fractions of each kw are expressed in decimals, for example 3400 watts = 3.4kw, 2550 watts would be 2.55kw
To work out how much storage heaters will cost to run, you need to use a simple maths formula, as shown below
Storage Heater consumption in kw x number of hours run x electricity cost in pence
You can find out how much your Electricity costs, by looking at a recent electricity bill. On an Economy 7 tariff, there will be two electricity rates given, one will be a daytime (peak) rate, the other will be a night time (off peak) rate, the cheaper off-peak tariff is the one that your storage heaters will be using overnight. So we will use this in our maths example, in order to work out the cost of running each storage heater.
So, we know that Economy 7 runs the Storage Heaters for a total of 7 hours, every night, so we now have the number of hours to put into the equation.
So lets work out how much it would cost for a 3.4kw storage heater to charge with heat, during a typical 7 hour economy 7 period.
At the time of writing this blog, Off peak economy 7 electricity cost between 5p and 6p per unit (kwh) of electricity, so we will use 5.5p as our working example.
So using the simple formula:- running cost = kw X hours run X cost
3.4 (kw) x 7 (hours) x 5.5 (p) electricity cost = £130.9p
So to charge a 3.4kw storage heater with heat for the 7 hour economy 7 period at an electricity cost of 5.5 pence per unit would cost £130.9 per night to run that storage heater.
Using the same 5.5 pence economy 7 off peak rate, I have also given the example below for the running costs of the popular sizes of storage heaters.
Running costs of Popular Storage Heaters, based on an example off peak Electricity cost of 5.5 pence per unit (kw/h)
850w (0.85kw) Storage Heater = £0.327p per 7 hour period
1700w (1.7kw) Storage Heater = £0.654p per 7 hour period
2550w (2.55kw) Storage Heater = £1.249 per 7 hour period
3400w (3.4kw) Storage Heater = £1.309 per 7 hour period
Electricity costs can vary, so to work out an accurate figure for your own Storage Heater running costs, simply enter your own figures into the calculator below. Remember to use your ‘off peak’ electricity kw/h unit cost in the ‘cost per kw/h field’
(The calculator displays the cost figure in ‘$’ but the actual result will be the same in any currency, simply substitute the ‘$’ with your own local currency symbol)
Of course these are worst case figures, based on the storage heater warming from cold, and with any ‘input’ control set to its maximum setting. If you tend to use the input setting if your storage heaters on a lower number, then the storage heater will use less electricity than in our example above and cost slightly less to run, however this will mean that less heat is stored, and the room will cold cold earlier than if a higher input setting was selected.


|Home / Congratulations / Greeting faculty graduate telegram Mechanics and Applied Mathematics KazSU 1986 Tahir Baratov||Greeting faculty graduate telegram Mechanics and Applied Mathematics KazSU 1986 Tahir Baratov|
To rector of the Kazakh National University Al-Farabi,
Fax: 8 (727) 3773344
Dear Galymkair Mutanovich!
We, the former KazSU students, remember that on March 1 this year it marks 85 years since the birth of the outstanding scientist and organizer of science and education, academic Umirbek Arislanovich Dzholdasbekov. We are glad that the name of our Master and Rector will be awarded to Hall of Mechanics and Mathematics Faculty, they will be assigned scholarships. We see this as a manifestation of the continuity of generations, a strong educational motive for modern students.
Under your leadership, Galymkair Mutanovich, continuing the tradition of our Alma Mater and we graduates, thank you for this!
Taking this opportunity, I congratulate you and the teaching staff with a significant day in the history of the university and wish them further success in their work and study! I am sure that the matter of Umirbek Arislanovich in good hands and will live forever!
graduate of the Faculty of Mechanics
and Applied Mathematics
of KazSU, 1986 Takhir Baratov
London, United Kingdom.