How To Find Critical Numbers Of A Fraction. Conclusion the critical points of this function are x=4, x=8/7,x=0 See the context for explanation of.
First, we find the derivative of the function to be. The value of c are critical numbers. Reduce the fraction to lowest terms, if possible.
3.) Plug The Values Obtained From Step 2 Into F (X) To Test Whether Or Not The Function Exists For The Values Found In Step 2.
Learn about the definition of critical numbers, how to locate them on the graph, and how to solve their values from the given equation. Therefore we set 5x^(1/5)=0 and solve. Set the derivative to 0 and simplify it for “x”.
Note That We Require That F (C) F ( C) Exists In Order For X = C X = C To Actually Be A Critical Point.
This is an important, and often overlooked, point. If any individual factor on the left side of the equation is equal to 0 0, the entire expression will be equal to 0 0. Then find any relative extrema.
Find The Critical Numbers Of The Function 4X^2 + 8X.
Find the critical value (s) of the function. Critical points are defined as points where either f ′ ( x) = 0 or f ′ ( x) is undefined. Plug any critical numbers you found in step 2 into your original function to check that they are in the domain of the original function.
Steps For Finding The Critical Points Of A Given Function F (X):
5x^(1/5)=0 x=0 therefore, the derivative is not defined at x=0. To find the critical values of a function, we must set the derivate equal to 0. 1.) take derivative of f (x) to get f ‘ (x) 2.) find x values where f ‘ (x) = 0 and/or where f ‘ (x) is undefined.
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The critical points of the function calculator of a single real variable f(x) is the value of x in the region of f, which is not differentiable, or its derivative is 0 (f’ (x) = 0). Use the sum and difference rules to distribute d d x throughout each term. Instead of this complicated process, you can find the critical point of the function given within a.


How many numbers are there? Some may say that numbers go up to infinity. But how many numbers do we use in day to day life? Maybe more then we realise.
While learning numbers in my Introductory BSL course I learnt numbers 1-100. I have 4 videos below. Each showing the different number signs. Breaking learning into manageable chunks.
This first video is the number sign itself:
Next up is the numbers 1-10. There are 3 systems of signing in regards to the numbers 6-10. These systems are variations of signs that have evolved in different parts of the world. I have learnt system 1 during this course. Although, it is good to be aware of each system.
As with numbers 6-10, numbers 11-20 also have 3 systems types for the signs in different parts of the country. Again, I’ve learnt system 1, shown in my video.
The next video is showing the numbers going up in 10s. From the above videos of 1-20, it’s easy to learn the numbers in between. For example, 27 is signing the number 2 and 7.


Objective: Explore the underlying mathematical principles that form the basis of cryptographic algorithms.
Introduction to Mathematical Foundations
- Purpose: Understanding the mathematics behind cryptography provides insight into how and why cryptographic methods are secure.
- Key Areas: Focus on number theory and algebra, which are crucial in understanding the algorithms used in cryptography.
Key Concepts and Theories
- Modular Arithmetic:
- Fundamental to many cryptographic algorithms.
- Involves arithmetic with a wrap-around feature at a certain value, known as the modulus.
- Prime Numbers and Factoring:
- The difficulty of factoring large prime numbers forms the basis of algorithms like RSA.
- Prime numbers are used because their properties make the factoring problem hard.
- Elliptic Curves:
- Used in algorithms like ECC (Elliptic Curve Cryptography).
- Involves points on a curve and the mathematics of their relationships.
- Discrete Logarithms:
- The discrete logarithm problem is a hard problem used in cryptographic algorithms, including Diffie-Hellman and some forms of ECC.
Hands-on Exercise: Exploring Modular Arithmetic
- Activity: Solve basic problems using modular arithmetic.
- Objective: Gain practical experience with the concept of modulus as used in cryptography.
- Algorithm Design: Understanding these concepts is essential for developing or analyzing cryptographic algorithms.
- Security Analysis: Helps in assessing the strength and vulnerabilities of cryptographic systems.
Further Reading and Resources
- “Introduction to Cryptography with Coding Theory” by Wade Trappe and Lawrence C. Washington.
- Online courses and resources on number theory and algebra in cryptography.


Mr Chen graduated from National Taipei University School of Statistics. He has profound understanding of mathematical statistics. He is excellent with grasping the global macro- economic development trends and using probability theory to establish mathematical models. He is proficient in collecting data of the observed systems and conducting quantitative analysis and summary.
Mr Chen has more than 10 years’ experience in the field of global securities and futures investment, as well as more than 10 years’ experience in the field of quantitative investment.
He founded YanChengXu trading team in 2010 and Yanqi Capital in 2013, managing onshore and offshore funds with a steady style.


Currently 4th Grade is teamed up with Visual Arts in Integration Studio. We are focusing on two major projects that integrate visual arts, science, social studies, and ELA skills.
4th Grade IS Exhibit - April 2, 2015 at 2pm in the CEA Cafe: You are invited!
Science, Social Studies, ELA and Visual Art merge in this Integrated Art Exhibit, presented by Mrs. O'clair's and Mrs. Ferrito's 4th grade students, with Mrs. Brownlee. The presentation begins at 2pm on Thursday, April 2, 2015 at 2pm in the CEA Cafe.
5th Grade: COMING SOON! (Beginning after Spring Break)
Past Integration Studio:
3rd Grade presented their 3D building design project, focusing on the mathematical concepts of area and perimeter at the end of January.
2nd Grade presented: Math, Myths and Mosaics: A Storytelling and Art Exhibit just prior to the winter break in December, and also attended a field trip the ColorBlind exhibit at the Arts Council.
1st Grade presented their exhibit: Kandinsky does Math in October, combining counting in sets and groups with ELA and visual arts.
Congratulations to all students for their hard work!


Engineering students are often required to perform complex calculations as part of their coursework or projects. While a traditional calculator can suffice for basic calculations, more advanced calculations may require specialized software or tools. Fortunately, there are several free engineering calculators available that can help students tackle complex calculations with ease. In this article, we will explore some of the best free engineering calculators that can assist students in their studies.
Table of Contents
Free Engineering Calculators for Students
There are several free engineering calculators available online that are essential tools for students.
offers new engineering calculators for conductor resistance, inductance, and capacitance for engineers, scientists, and students for free on their website. These online calculators accurately compute conductor electrical properties, providing resistance, inductance, and capacitance values for numerous conductor configurations. EMI Software LLC created these new online calculators because existing websites use overly simplified models and equations that don’t accurately account for skin effect and proximity effect, characteristics that are important at high frequencies and for closely spaced conductors. There are similar calculators online, but none with the accuracy of these new calculators.
Calculator is an online resource that offers free engineering calculators for engineers and students worldwide. The website features more than a few hundred calculators that cover various fields, including electrical engineering, mechanical engineering, civil engineering, physics, math, and many others. Engineers and students can use these calculators to access basic and advanced mathematical functions useful for their work. Other online resources, such as and , also offer free engineering calculators that cover various fields and formulas. When choosing an engineering calculator, it is important to consider factors such as the type of calculations needed, the level of accuracy required, and the ease of use of the calculator.
is an online engineering calculator resource that offers hundreds of calculators to help students and engineers across various fields, including electrical engineering, mechanical engineering, civil engineering, physics, math, and many others. CalcTown offers different engineering calculators for engineering students and professionals. Engineers and students can use these calculators to access basic and advanced mathematical functions useful for their work. Other online resources, such as Calculator and , also offer free engineering calculators that cover various fields and formulas. When choosing an engineering calculator, it is important to consider factors such as the type of calculations needed, the level of accuracy required, and the ease of use of the calculator.
is a computational knowledge engine developed by that answers factual queries by computing answers from externally sourced data. WolframAlpha can parse mathematical symbolism and respond with numerical and statistical results. WolframAlpha is available as an app on Google Play and the , and users can manage their Wolfram|Alpha Pro subscription by visiting the store. WolframAlpha is written in the , a general multi-paradigm programming language, and implemented in Mathematica, which is proprietary and not commonly used by developers.
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In conclusion, engineering students can benefit greatly from utilizing free engineering calculators to streamline their calculations and improve their efficiency. From structural design to thermodynamics, there are specialized calculators available for a wide range of engineering disciplines. By utilizing these free tools, students can focus on understanding the concepts behind their calculations rather than spending time on tedious computations. With the right engineering calculator, students can gain a competitive edge and excel in their studies.


the sum of three numbers in an arithmetic progression is 15 and their product is 105. Find the numbers An exam has a weightage of 30%. If a student has a. We can put what Gauss discovered into an easy-to-use formula, which is: (n / 2) (first number + last number) = sum, where n is the number of integers. Let's use the example of adding the numbers 1.
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This section covers the n-body gravity problem. I applied the Parker-Sochacki method to the 2-body, 3-body, and n-body gravity problem discussing what happens when you adjust the accuracy of the method. I also have a section where I compare different numerical integrators for different particle simulations: Forward Euler, Semi-Implicit Euler, Velocity Verlet, Runge-Kutta 2 Midpoint, and Runge-Kutta 4th Order.
3-Body Parts 1 and 2:
N-Body Comparing Different Integrators:


I counted the coins in order, bronze, silver, gold. I scratched out the numbers on a brick in the wall above where the treasure chest was as I went, then did some quick calculations, and then divvied up.
I was short by a few gold.
I started from the gold this time, scratching the numbers into the wall, but the numbers were right, so I redid the division.
I was over by a few silver.
I would have recounted them yet again, but at this point the mimic tired of playing with me, and stopped pretending to be a wall.


1 edition of Mathematics and Computer Science II found in the catalog.
|Statement||edited by Brigitte Chauvin, Philippe Flajolet, Danièle Gardy, Abdelkader Mokkadem|
|Series||Trends in Mathematics, Trends in mathematics|
|Contributions||Flajolet, Philippe, Gardy, Danièle, Mokkadem, Abdelkader|
|The Physical Object|
|Format||[electronic resource] :|
|Pagination||1 online resource (XIII, 557 pages).|
|Number of Pages||557|
Mathematics course is an amalgamation of in-depth knowledge of geometry, trigonometry, calculus and other theories. It also explores related topics like Computer Science and Statistics. This degree course helps students in building a good foundation base for pursuing higher studies. Mathematics: Syllabus Description. CS Numerical Methods II or CS Numerical Analysis. 3. MATH Linear Algebra, or MATH Abstract Linear Algebra. level mathematics and computer science requirements: Students must select at least six level mathematics and computer science courses, including one from each of the following five groups.
Download Books & Notes For All Semesters in PDF – 1st, 2nd Full Form is Master of Science. The Course of Masters of Science (MSc) postgraduate level program offered in a majority of colleges and universities in India. MSc course content in classes is imparted through various means such as lectures, projects, workshops ( పుస్తకాలు), and directed : Daily Exams. Discrete Mathematics II: Set Theory for Computer Science Part IA Comp. Sci. Lecture Notes Glynn Winskel c Glynn Winskel Febru standing and analysis of the new ideas in Computer Science that you will meet. ented books below are those of Devlin, Nissanke and Stanat-McAllister.
The Bachelor of Science with a Major in Mathematics and Computer Science is designed for students who seek careers in computer science and/or computer related fields requiring a strong mathematical background. The program is flexible and provides the students with a well-rounded education. Calculus II: 4: Calculus III: 4: Computer Programming Course: 3: CS Computer Science I or sufficient score on Placement Exam: HU Research Sources and Skills: 1 *If Precalculus Algebra (3 hours) is completed to satisfy the Area III mathematics requirement, the student should complete Precalculus Trigonometry (3 hours) in addition to.
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This is a great maths book for first year Computer Science undergraduates. It assembles in a single text most of the basic mathematical tools required in the study of Computer Science, ranging from sets and relations, to combinatorics and probabilities, to trees and logic. you'll find more products in the shopping cart.
Total € View cart. Foundation Mathematics for Computer Science covers number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus, and reveals the names of the mathematicians behind such inventions.
During this journey, John Vince touches upon more esoteric topics such as quaternions, octonions, Grassmann /5(2). Mathematics for Computer Scientists 5 Introduction Introduction The aim of this book is to present some the basic mathematics that is needed by computer scientists.
The reader is not expected to be a mathematician and we hope will nd what follows useful. Just a word of warning. Unless you are one of the irritating minority math-ematics is Size: 2MB.
IIT-JEE main and advanced, CBSE Standard 12 Math Survival Guide-Differential Equations by Prof. Subhashish Chattopadhyay SKM Classes Bangalore Useful for PU-II AP-Maths IGCSE IB AP-Mathematics, State Board or High School exams, College Math exams and other free e-Book covers how.
CBSE NCERT Books for Class 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 PDF English & हिन्दी में, UP, MP, UPSC के लिए एनसीईआरटी. Mathematics books Need help in math. Delve into mathematical models and concepts, limit value or engineering mathematics and find the answers to all your questions.
It doesn't need to be that difficult. Our math books are for all study levels. Do not read mathematics.
Use lots of pen and paper. Read “mathematics books” and do mathematics. Exercises are must. Use as many methods as you can think of, certainly including the one which is recommended. Consult the Appendix after you work out the solution. Follow the comments, interpretations and suggested extensions.
Think. Get Size: 2MB. X= fx: 1 iii. x= fx: 2 x 10;xis an even integer getc. Note that the above expressions are certain rules that help in de ning the elements of the set X. In general, one writes X= fx: p(x)gor X= fxjp(x)gto denote the set of all elements x (variable) such that property p(x) Size: 1MB.
Blast Into Math. Applied Statistics. Integration and differential equations. Elementary Algebra Exercise Book I.
Principles of Insurance. Essential Engineering Mathematics. Mathematics for Computer Scientists. Introduction to Complex Numbers. Essential Mathematics for Engineers.
Quantitative Analysis. Mathematics Fundamentals. Applied Business. From books on mathematics and physics to books on technology and the environment, the Kindle Store's selection of ebooks in Math & Science has something for everyone.
Mathematics & Science eBooks Browse the Kindle book store to download and read about science and math books for kids and adults on any device.
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The MnC programme at IIT-BHU, Varanasi is likely to be the best for people who enjoy Mathematics and are further open to work in the field of Computer Science, as it has got equal portions of Mathematics and Computing.
At IIT Kharagpur, Mathematics and Computing is offered as an programme. IIT Guwahati offers a B. Tech programme in MnC. Mathematics has its own speciﬁc notion of “proof.” Deﬁnition. A mathematical proof of a proposition is a chain of logical deductions leading to the proposition from a base set of axioms.
The three key ideas in this deﬁnition are highlighted: proposition, logical de-duction, and axiom. These three ideas are explained in the following chapters. math and computer science. Also, areas in computer science such as artiﬁcial intelligence and databases often use notions from model theory and proof theory.
The title of this book is “Foundations of Mathematics”, and there are a number of philosophical questions about this subject. Whether or not you are interested in the. Computer Science II. This course note explains computer programming concepts includes object-oriented programming techniques: class methods, wrapper classes for primitive types, inheritance, abstract classes, events and listeners, packaging your code as a stand-alone program or an applet, interfaces, garbage collection, introduction to exceptions; structured programming techniques: switch.
This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, engineering, Business, and the sciences.
Besides reading the book, students are strongly encouraged to do all the File Size: 1MB. Calculus BC exam will receive course credit for MATH Calculus II.
COMPUTER SCIENCE: A student who scores a 4 or higher on the Computer Science A exam or a 3 or higher on the Computer Science AB exam will receive course credit for CSCI Foundations of Computer Science I.
In addition, a student scoring 4 or higher on the Computer. Several authors consider that mathematics is not a science because it does not rely on empirical evidence. Mathematics shares much in common with many fields in the physical sciences, notably the exploration of the logical consequences of assumptions.
Mathematics for Computer Science revised Monday 9th May,Eric Lehman Google Inc. F Thomson Leighton Department of Mathematics and CSAIL, MIT Akamai Technologies Albert R Meyer Massachusets Institute of Technology Creative CommonsEric. Throughout this book, the authors discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics, etc.
Some parts of these problems may be found useful for scholarly stimulation. ( views) Basics of Algebra and Analysis For Computer Science by Jean Gallier, Get this from a library! Mathematics and computer science II: fundamental contributions in the Netherlands since [Michiel Hazewinkel; J K Lenstra; Lambert Meertens; Centrum voor Wiskunde en Informatica (Amsterdam, Netherlands);].The goal of the book is to expose the reader to a wide range of basic problems, some of which emphasize analytic ability, some requiring programming techniques and others focusing on statistical data analysis.
In addition, it covers some areas which are outside the scope of mainstream financial mathematics textbooks.


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The other day, I thought it would be fun to play with a little OpenGL cube-drawing code.
The idea came up after finishing the “Getting Started” section on Learn OpenGL (great tutorial, btw). You start with some super simple triangle stuff and build up to a few cubes spinning around. Oh, and a first person camera to check out your handy work. Basic, but a great start.
Before the tutorial, I had worked through part of the big red book to do some 2d tilemap stuff (instancing is great). However, this was my first step into the 3rd dimension.
Let’s talk about how I draw the cube
I already knew that there was a much better way to draw cubes than what Learn OpenGL presents. Instead of using 36 vertices (2 triangles per face * 3 vertices per triangle) I got it down to 24 using a simple, and not optimal, triangle strip.
Dammit, I wanted to do better than that. Naturally, I asked Google what the best way to draw a triangle was, and found this post. Nice.
You may have noticed the link to a paper on the subject. Now I have all the tools to draw the perfect cube! Kinda.
A few minutes later, I cut down my vertex buffer to only 14 vertices! But, could I go further?
Like an Obsessed Optimization Loon…
I wanted more. Martin, a friend of mine, is particularly good at figuring out interesting ways to draw stuff with computers. I went to him after figuring out that if I used the optimal number of vertices for a cube, I would need to satisfy this table:
id x y z -------------------- 0 -1 -1 -1 1 1 -1 -1 2 -1 1 -1 3 1 1 -1 4 1 1 1 5 1 -1 -1 6 1 -1 1 7 -1 -1 -1 8 -1 -1 1 9 -1 1 -1 10 -1 1 1 11 1 1 1 12 -1 -1 1 13 1 -1 1
These are the values I would need to calculate if I wanted to only pass in the center point and dimensions of the cube. This is where my brain started to melt.
Can you see the patterns? Well, Martin could. Like a scene from A Beautiful Mind, he worked out a crazy formula that would figure out the location of all 14 vertices.
This was exactly the sort of thing I was trying to figure out, but I would have never gotten far enough to be dangerous. Here is the crux of the shader code:
float3((int3(id | id2, (id1 ^ id2) ^ (id & id2), ~id & id2) & 1) ^ (vertex_id < 7 ? 0 : int3(1, 0, 1))) * 2.0f - 1.0f
I don’t know about you, but I’m digging it
I’m guessing at least half of you are yelling at me through your monitor. “It’s just a cube, moron! You don’t need these ‘premature optimizations‘ for such a simple task!” (by the way, here’s Knuth’s entire quote)
Programmers waste enormous amounts of time thinking about, or worrying about, the speed of noncritical parts of their programs, and these attempts at efficiency actually have a strong negative impact when debugging and maintenance are considered. We should forget about small efficiencies, say about 97% of the time: premature optimization is the root of all evil. Yet we should not pass up our opportunities in that critical 3%.
Eff that. This optimization was fun and I learned a shitload from two brilliant friends, brain-melting trial and error, and hacking away at my OpenGL code. In fact, this isn’t the only approach to making this cube as slick as possible. Jeroen has a few things to say about Karnaugh Maps and how programmers could benefit from bringing them over into the software world rather than leaving them for the electronics crew.
Don’t settle with doing things the boring way. Optimize your ass off if you enjoy it. That’s what I do: enjoy myself.


The Mechanics behind Card Counting at Blackjack
Although not illegal, the system of Card Counting in the game of blackjack is frowned upon by most casinos. This can see a player being banned from playing at their blackjack tables or even removed from the casino altogether. However it certainly is a good strategy for reducing the house advantage if you can play undetected. But how does it work?
The first thing most people think of when card counting in blackjack is mentioned is that it must rely on great memorisation techniques. This would mean that those of us with not great memories would not be able to consider learning this technique. Luckily though it is not based around having to learn how many Kings or two’s are being dealt.
When playing the game of blackjack the player has a better advantage when there are more ten value cards and Aces remaining (such as 10’s J’s, Q’s and K’s). This is because the player has a higher chance of being dealt a blackjack which has better odds of 2:1. There is also more chance of the dealer going over 21 and being bust. On the opposite side of the coin, with more smaller cards remaining there will be fewer blackjacks for the player and dealer has an increased chance of a good hand. So in principle the technique of card counting is just down to trying to keep track of the relation between high cards and low cards.
Assigning a Value to each Card
Here at Free Casino we are going to look at the Hi-Lo card counting strategy as it is the most common and widely used system. This system was first introduced by Harvey Dubner in 1963. This is the first step towards card counting where you allocate a new value to each of the cards as they are dealt. This is fairly straight forward as it it build around blocks/groups of cards.
The groups of cards and their value is as follows:
- Cards with normal face value of 2, 3, 4, 5 and 6 have an allocated value of +1
- Cards with a face value of 7, 8 and 9 have an allocated value of 0
- Cards with a face value of 10, Jack, Queen, King or Ace are allocated a value of -1
As the cards are dealt by the dealer you will simply be adding 1 or subtracting 1 or doing nothing dependant on where those cards fall into the groups above.
Keeping a Running Count
So as the game progresses and for subsequent games until the cards are shuffled you will be updating the ‘running count’ as each card is dealt. This includes both player and dealer cards. If as you progress the running count is increasing then the advantage in the game is moving more towards the player. However the opposite is true if the running count decreases which means the advantage to the casino is increasing.
This system of card counting would mean if you were playing with a single deck then you could already start to manage your betting more effectively as you watch the way the advantage is going. Unfortunately casinos in their attempt to reduce the chances of card counters winning and beating the house introduced multiple decks.
Therefore if you are playing blackjack where multiple decks are in use you will need to also monitor the ‘True Count’ also know as the count per deck.
Calculating the True Count
If you were just playing with a single deck and had a running count of +5 it means there are at least 5 extra 10’s and Aces within the remaining cards. This would give approximately a 2% advantage to the player. If though your +5 running count was against a game with 6 decks still remaining then this would indicate less than 1 extra high card remaining per deck.
This is why the true count has to come into play. At any point in the game it will tell you what your advantage is in a blackjack game with multiple decks. To find out your true count you would simply divide your running count by how many decks are left to be dealt.
Therefore as an example if you had a running count of +10 with 5 decks remaining the true count would be 10 divided by 5 which would give a value of 2. If your running count was +9 with 3 decks remaining then 9/3 would give a value of 3. If you therefore combine the basic strategy alongside the Hi-Lo card counting system you can use the information to place your bets to your advantage and increase the chances of making that big win.
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EducationVilla Julie College - BS, Elementary Education
ExperienceI fully believe that teaching is my calling. As a child, I set up a classroom for my dolls and taught them a variety of subjects. Since then, of course, I have received more instruction in the fine art of teaching, including a B.S. in Elementary Education from Stevenson University. After graduating, I taught third and fifth grade students in all academic subjects for years, and I became especially passionate about teaching core subjects like reading and math, which many young students struggle with. Although I left my position as an elementary school teacher to raise my children, I continue my teaching career in many different ways, including homeschooling my children, working with the Children's Ministry at my church, and now, working as a tutor. I believe that children learn better when they receive one-on-one instruction or work in small groups with the teacher. It is important to me, as a tutor, to get to know the children I teach and build a strong relationship with them, so that they can feel comfortable enough with me to ask questions and learn new concepts. I want to get to know the whole child I tutor, including their hobbies and after school activities, so I can determine which approach best helps them.
HobbiesReading, playing the piano, music, crocheting, embroidery, teaching
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Features of the sinusoidal current
The most desirable form of the curve for instantaneous values of alternating current and tension is the sinusoidal form.
In mathematics sinusoidal changes are considered as the simplest harmonious form of the batch process therefore calculation of chains of the sinusoidal current is rather simple and in such chains there are no undesirable by-effects.
For creation of the sinusoidal curve we will take some piece of OA (fig. 1) which length on the scale of creation is equal to the maximum value of sinusoidal size, is the vector of sinusoidal size.
For example, Im = OA x n = 10 and, scale n = 0,1 and/mm; OA = 10: 0,1 = 100 mm. In the rectangular coordinate system we will direct this vector at first on the horizontal axis — it will be the starting position of the vector at the time of time reference mark, i.e. at t = 0.
As in expression? alternating-current frequency enters, that the angular speed of the vector is usually called angular frequency.
When from the moment of the reference mark will some time of t1 pass then the vector of OA will turn on the corner? t1. From the vector head of OA which is in new situation we will lower the perpendicular on the horizontal axis. Length of this perpendicular will be OA x sin ? t1. At some next moment of t2 the vector forms the corner with the horizontal axis? t2, and length of the perpendicular lowered from its end will be, respectively, OA xsin t2. Later the quarter of the period from the moment of time reference mark, i.e. at the time of t3 = T/4 the vector of OA will become perpendicular to the horizontal axis, and perpendicular length
Now near the circle described by the end of the rotating vector we will construct the curve of dependence of the size OA x sin in rectangular system ? t from? t or from t is and the sinusoidal curve for the period from t = About to t = t3 will be.
At the time of t3 = T/4 sinusoidal size reaches the maximum value. In process of further rotation of the vector the size OA x sin ? t decreases (the moments of t4 and t5). At last, at the time of t6 = T/2, having described the arch equal? to radians, the vector will accept horizontal position. At the moment, when OA x sin ? t6 = OA x sin? =0", sinusoidal size passes through zero value.
At further rotation of the vector perpendicular of OA x sin ? we will consider t negative (the moments of t7, ts, ts). Respectively, we will build from the horizontal axis this site of the sinusoidal curve down.
If at the initial moment of t = 0 vector forms some corner with the horizontal axis and, then at the time of the reference mark sinusoidal size is not equal to zero, and matters OA x sin 0 (fig. 2). The corner and is called the initial phase angle, or initial phase. In this case length of the perpendicular lowered from OA vector head on the horizontal axis at the time of t will be:
OA x sin (? t + a),
according to it the sinusoidal curve at the initial moment will not pass through zero. Thus, generally it is desirable that alternating current changed in time according to expression
I = Im x sin (? t + a).
In this expression of i - the instantaneous value of current intensity, Im — the maximum value (amplitude). It is necessary for receiving the sinusoidal current that the EMF of alternating current generators was sinusoidal too,
here? - any initial phase of this EMF. If EMFs е and i current, belonging to the same chain, not at the same time pass through zero or maximum value, then they are dephased relatively each other (fig. 3). In the presence of phase shift of EMF in the chain it can be equal to zero, and current will pass in it still, or current can be equal to zero in the presence of considerable EMF,
Phase shift ф is measured by the difference of initial phases of sinusoidal sizes. In the case considered by us ф = ? - and, and EMF advances current on the phase. Respectively, vectors of Em and Im form the corner ф which remains invariable at their rotation.
Sinusoidal sizes, for example tension and current, match on the phase if their initial phases are identical; they are opposite on the phase if their phase shift ф = ±?. If one of sinusoidal sizes changes on the sinusoid, for example i = Im x sin ? t, and the second — on the cosinusoid, for example u = Um cos ? t, phase shift between them ф = ?/2 (to what there corresponds the quarter of the period), as
It must be kept in mind that the rotating vectors of alternating-current sizes significantly differ from vectors of the physical quantities (force, speed, magnetic induction, electric field intensity, etc.) having determinate direction in space.
The alternating-current vectors called also radius vectors represent only the convenient mathematical form of the image of the sizes changing in time sinusoidalno. Radius vectors, as well as space vectors, often briefly call equally vectors. Alternating-current vectors distinguish the point over the letter designating this or that sinusoidal size, for example ? m or? mTop


V této publikace autor uvádí a vysvětluje statistické metody a algoritmy vyvinuté pro bádání tajů molekulární evoluce, fylogeneze a fylogeografie pro srovnávací analýzy genetických dat. Publikace poskytuje vysvětlení složitých statistických modelů a zásad používaných v reálných analýzách dat. Odkazy na webové stránky obsahují ukázkové datové sady C a R programů, které implementují výpočetní algoritmy popsané v knize.
Autor: Ziheng Yang
|Nakladatel||Oxford University Press|
Presents and explains the statistical methods and computational algorithms developed in molecular evolution, phylogenetics and phylogeography for the comparative analysis of genetic sequence data
• Clear explanations of complex statistical models and principles, using examples of real data analysis and numerical calculations to illustrate the theory
• Web-based support material includes example data sets, C and R programs that implement computational algorithms discussed in the book, and a primer on probably and statistics
• Ideal graduate seminar course material with working problems at the end of each chapter
Studies of evolution at the molecular level have experienced phenomenal growth in the last few decades, due to rapid accumulation of genetic sequence data, improved computer hardware and software, and the development of sophisticated analytical methods. The flood of genomic data has generated an acute need for powerful statistical methods and efficient computational algorithms to enable their effective analysis and interpretation.
„ I think Molecular Evolution: A Statistical Approach would also work very well as a text for a graduate level course in statistical phylogenetics ... The exercises at the end of each chapterwould be useful for academics anting to use the book as a course textquestions cover an interesting range of problems that would get the class both thinking and programming." - Barbara R. Holland, Systematic Biology
Ziheng Yang, RA Fisher Professor of Statistical Genetics, Department of Genetics, Evolution and Environment, University College London
Ziheng Yang is currently RA Fisher Professor of Statistical Genetics in University College London. He obtained a Ph. D in agronomy in Beijing Agricultural University in 1992. Since then he held a few postdoctoral researcher positions in the UK and US. He joined UCL in 1997, first as a lecturer, then reader and professor. He teaches statistical genetics. He has published about 150 research papers and book chapters in molecular evolution, phylogenetics, population genetics, and computational biology. His program package paml is widely used in the molecular evolution community. He was elected a Fellow of the Royal Society in 2006.
|1: Models of nucleotide substitution||1|
|2: Models of amino acid and codon substitution||35|
|3: Phylogeny reconstruction: overview||70|
|4: Maximum likelihood methods||102|
|5: Comparison of phylogenetic methods and tests on trees||153|
|6: Bayesian theory||182|
|7: Bayesian computation (MCMC)||214|
|8: Bayesian phylogenetics||263|
|9: Coalescent theory and species trees||308|
|10: Molecular clock and estimation of species divergence times||361|
|11: Neutral and adaptive protein evolution||390|
|12: Simulating molecular evolution||418|


Sometimes a little math goes a long way to illustrate a point, especially online. Tinysheet, the world’s tiniest spreadsheet, just made sharing simple calculations even easier. You can now embed a Tinysheet on any web page you make, so your visitors can see and edit the sheet inline, and make a copy of their own, without ever leaving your site.
To try it out, create a Tinysheet and then click on the Share button, and choose “Embed.” Copy the code to your clipboard, then paste it to any web page that allows you to add an iframe to it.
Here are six useful Tinysheet calculators you can try out, copy, and reuse directly on this page.
What would splitting with roommates cost?
What’s the average?
How does compound interest accumulate over time?
What do subscriptions cost per year?
What’s this percent of that?
How tiny is Tinysheet?
Try embedding a Tinysheet today–and let us know what your favorite uses for Tinysheet are.


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Image by Antoine Dautry
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Encourage learning through math. Guide students through middle school, develop students through community learning experiences in and outside the classroom, instill strong character and foster long-term relationships with their peers. Ultimately, preparing the child and parents for High School.


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Classes at SA Bronx 1 and SA Hell’s Kitchen got a lot bigger (and a little taller) earlier this month, when forty-five educators from as far away as Louisiana, Tennessee, Arizona, and Israel saw Success Academy’s innovative math curriculum in action in our kindergarten and first grade classrooms.
As an elementary school math manager who helps develop and implement our curriculum, I was thrilled to have the opportunity to show off our approach to math to a group that included CEO’s, curriculum developers, and principals. All of these educators had launched conceptual math programs at their own schools, but wanted to learn how they could make them even more effective. They spent the morning watching our young mathematicians in action — and they were impressed by what they saw.
Too often, students develop an unnecessary fear of math that stems from teachers encouraging rote memorization and procedure over deep conceptual understanding and problem solving. Children understand math best when they understand why procedures or rules work, and discuss these reasons with their teachers and peers. At Success Academy, all math tasks are presented as realistic problems, since math is not just an academic subject, but a part of everyday life.
At Success Academy, all math tasks are presented as realistic problems, since math is not just an academic subject, but a part of everyday life.
Our visitors watched as a kindergarten scholar sat in his teacher’s chair and explained to the class how different number combinations could be put together to make the same total. The scholar made sure he had the attention of the class before he began and correctly fielded questions from the teacher as he described his strategy. In another class, when a fourth grade scholar got an answer wrong, the visitors were impressed by the teacher’s response — he didn’t move on to another student in order to find the right answer, but instead asked questions of the scholar and his classmates that helped the kids arrive at the correct conclusion.
After witnessing our math program in action, workshop attendees took a walk in the shoes of a Success Academy teacher — they studied student work to assess the level of kids’ understanding, and participated in a unit launch, where teachers plan their approach to upcoming lessons.
In the unit launch, I asked the attendees to complete one of the first grade–level problems: There is a double-decker bus with 10 seats on each level. If there are 13 people total on the bus, what are the different ways they could be seated? How many on the top and on the bottom?
Immediately, participants started listing combinations such as 13 and zero, 12 and one, or 11 and two — proud of their systematic approach. I grabbed a “math rack,” one of the tools our kids often use, and asked the participants to model their strategy.
I could practically see the light bulbs go on above their heads! They realized that they’d assigned more than 10 people to a space with only 10 seats, forcing the fictitious passengers to stand instead of getting a seat! They had totally disregarded the context of the story and jumped straight into procedures. This was the perfect example of why we believe deeply in our model of math education: We want scholars to understand that math exists within a real-life context (there were only ten seats on each level of the bus) — and there’s more to solving problems than simply applying a procedure.
This also demonstrated how important it is for teachers to solve problems themselves, before scholars tackle them. This ensures teachers anticipate the types of mistakes students might make and can proactively plan to address these issues.
Our team received positive feedback from the workshop. “Thank you for your transparency,” wrote one participant. “Definitely revitalized my love for math and excited to implement these takeaways in the future,” said another. Many participants said they couldn’t wait to try out what they learned at their own schools. Sharing our best practices with other school networks is at the heart of Success Academy. We want to ensure that as many students as possible benefit from our model — even when our teachers aren’t the ones delivering the instruction.


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New student-produced math videos
I wanted to share the latest in our student-produced video series.
Earlier today I uploaded our new math instructional videos, developed in collaboration with Dan Meder’s Video Production class and members of our Math Department. These join our collection of grammar non-negotiables, developed last year for language arts, and our pilot series of information skills videos, developed the year before.
The library’s role?
We get the ball rolling by identifying the learning need. We present the problem to students and teachers. We help our students and faculty develop a solution. We archive and share the knowledge (our students’ efforts) with the community.
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About Joyce Valenza
Joyce is an Assistant Professor of Teaching at Rutgers University School of Information and Communication, a technology writer, speaker, blogger and learner. Follow her on Twitter: @joycevalenza
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HobbiesI enjoy hiking and being outdoors. I enjoy studying and practicing music, primarily classical. I love reading, especially classical literature. I have been engaged in practicing programming, mostly C++. I also enjoy spending quality time with friends and family when my schedule allows.
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The IDL bindings for the low-level MAGMA routines are automatically generated wrappers for the standard LAPACK interface, but GPULib also offers a higher-level routine mimicking the
LA_ routines present in the IDL library. GPUINVERT is comparable to LA_INVERT, inverting a non-singular matrix in a single call:
dinverse = gpuInvert(da, lhs=dinverse)While these routines document their technique for performing their operations, they do not require much user knowledge of the underlying techniques used. More high-level routines similar to the
LA_are planned for future GPULib versions.
Calling the low-level routines directly in MAGMA requires more knowledge of the mathematical algorithms and a bit more cumbersome notation. For example, the following example shows how to call the MAGMA version of SGELS:
status = gpusgels((byte('N')), $ m, n, nrhs, $ da->_getHandle(), lda, $ db->_getHandle(), ldb, $ work, lwork, $ info)SGELS solves overdetermined or underdetermined real linear systems using a QR or LQ factorization of a matrix of full rank. This low-level operation has options for performing multiple solves in a call and operating on the transpose.
The calling syntax for the MAGMA routines is in the API documentation for GPULib as well as in
lib/magma_routines.h in the GPULib distribution.


Sudoku is a logic-based number-placement puzzle that normally consists of a 9x9 grid (of 81 squares) subdivided into nine 3 by 3 sub-grids. The individual squares in a grid are usually called cells, and sub-grids often called boxes, blocks, submatrices, regions, or sub-squares.
Sudoku rules are simple: each 3x3 block, each row, and each column has to contain all the numbers from 1 to 9 and each number should only appear once in each box, row, and column. The puzzle provides a partially completed grid, and the goal is to find the remaining entries. Puzzles should have a unique solution.
Usually, Sudoku puzzles are ranked according to the difficulty level. There is no standardized ranking system or metric. Ranking is usually based on the techniques required to generate a solution. While Easy Sudokus can be solved in less than 10 minutes, solving Hard puzzles requires some really difficult logic and may take well over one hour.
While the classic 9×9 Sudoku grid with 3 by 3 regions is by far the most common, there are numerous variations of the basic Sudoku format. Some of them change the size of the grid, add extra constrains, or replace squares by other shapes.


Estimation of parameter k(max) in fractal analysis of rat brain activity
Conference object (Published version)
MetadataShow full item record
We recorded electrocortical activity in anesthetized rats and constructed kmax new self-similar time series, applying Higuchi's algorithm. The aim of this study was to estimate value of the parameter k(max). in order to obtain fractal dimension values as an optimum measure of biosignal change. After our analysis, electrocortical activity recordings resulted in a family of curves f(k(max)). Three regions could be distinguished 2 <= k(max). < 8, with a U-shape; 8 <= k(max) <= 30, with a steeper quasilinear increase; and k(max) >= 30, with a smaller slope quasilinear increase. We suggest the optimum region for k(max): 8 < k(max) < 18, specifically k(max) = 8.
Source:Biophysics from Molecules to Brain: in Memory of Radoslav K. Andjus, 2005, 1048, null, -429


Linear least squares regression line calculator v1. The processor can essentially only perform addition, multiplication, division. The construction of a least-squares approximant usually requires that one have in hand a basis for the space from which the data are to be approximated. The best fitting curve has the least square error, i.e., Please note that , , and are unknown coefficients while all and are given. Theory. Approximating a dataset using a polynomial equation is useful when conducting engineering calculations as it allows results to be quickly updated when inputs change without the need for manual lookup of the dataset. Least-Squares Polynomial Approximation . Wolfram|alpha widgets: "regression calculator" free widget. The Least-Squares method is essentially an orthogonal projection from a Hilbert space onto a finite-dimensional vector subspace. The least squares method is the optimization method. Section 6.5 The Method of Least Squares ¶ permalink Objectives. Note: When using an expression input calculator, like the one that's available in Ubuntu, … In this section, we answer the following important question: Approximation problems on other intervals [a,b] can be accomplished using a lin-ear change of variable. The matrix has more rows than columns. Free alternative To The descriptive statistics view in Minitab and other paid statistics packages. FINDING THE LEAST SQUARES APPROXIMATION We solve the least squares approximation problem on only the interval [−1,1]. where p(t) is a polynomial, e.g., p(t) = a 0 + a 1 t+ a 2 t2: The problem can be viewed as solving the overdetermined system of equa-tions, 2 … Exponential Regression Calculator. Least Squares Optimization The following is a brief review of least squares optimization and constrained optimization techniques,which are widely usedto analyze and visualize data. The process of finding the equation that suits best for a set of data is called as exponential regression. Get the free "Solve Least Sq. Enter your data and it generates descriptive statistics and a histogram plot. In Correlation we study the linear correlation between two random variables x and y. The following figure plots the different solutions against the data points (solid: original problem, dashed: transformed problem. The hmx mixing calculation program | springerlink. Recipe: find a least-squares solution (two ways). Whoever helped develop this interface, thank you, and great job. As a result we should get a formula y=F(x), named the empirical formula (regression equation, function approximation), which allows us to calculate y for x's not present in the table. Least squares in Rn In this section we consider the following situation: Suppose that A is an m×n real matrix with m > n. If b Example problem: We want to understand how a calculator or computer can evaluate sinx for a given value x. i x i y i 1 0 1.0000 2 0.25 1.2480 3 0.50 1.6487 4 0.75 2.1170 5 1.00 2.7183 Soln: Let the quadratic polynomial be P 2(x) = a 2x2 +a 1x+a 0. 4 Least-Squares Approximation by QR Factorization 4.1 Formulation of Least-Squares Approximation Problems Least-squares problems arise, for instance, when one seeks to determine the relation between an independent variable, say time, and a measured dependent variable, say position or velocity of an object. Ask Question Asked 3 years, 6 months ago. Fit the data in the table using quadratic polynomial least squares method. Learn to turn a best-fit problem into a least-squares problem. Ax=b" widget for your website, blog, Wordpress, Blogger, or iGoogle. An online LSRL calculator to find the least squares regression line equation, slope and Y-intercept values. Approximation of a function consists in finding a function formula that best matches to a set of points e.g. mldivide, ("\") actually does that too.According to the documentation:. Linear Least Squares. And finally we do 20.73 / 7.41 and we get b = 2.8. Least-Squares Approximation by Natural Cubic Splines. b = the slope of the line The matrix A and vector b of the normal equation (7) are: A = 2 6 6 6 6 4 4.3 Least Squares Approximations It often happens that Ax Db has no solution. Maths reminder Find a local minimum - gradient algorithm When f : Rn −→R is differentiable, a vector xˆ satisfying ∇f(xˆ) = 0 and ∀x ∈Rn,f(xˆ) ≤f(x) can be found by the descent algorithm : given x 0, for each k : 1 select a direction d k such that ∇f(x k)>d k <0 2 select a step ρ k, such that x k+1 = x k + ρ kd k, satisﬁes (among other conditions) Least Squares Method & Matrix Multiplication. Curve Fitting Toolbox software uses the linear least-squares method to fit a linear model to data. Linear Least Squares Regression Line Calculator - v1.1: Enter at least two XY data pairs separated by spaces. obtained as measurement data. The Least-Squares Parabola: The least-squares parabola uses a second degree curve to approximate the given set of data, , , ..., , where . Then p is called the least squares approximation of v (in S) and the vector r = v−p is called the residual vector of v. 2. Least Squares Regression Line Calculator. A linear model is defined as an equation that is linear in the coefficients. 8.1 - Discrete Least Squares Approximation. One method of approaching linear analysis is the Least Squares Method, which minimizes the sum of the squared residuals. Basis functions themselves can be nonlinear with respect to x . The linear least squares problem is to ﬁnd a vector ~xwhich minimizes the ℓ2 norm of the residual, that is ~x= min z∈IRn k~b− A~zk 2 Vocabulary words: least-squares solution. Save time rekeying data - our tool lets you save and recycle data in other studies, even send it via email! Recall that the equation for a straight line is y = bx + a, where. As the example of the space of “natural” cubic splines illustrates, the explicit construction of a basis is not always straightforward. Example 4.1 The least squares approximation for otherwise unsolvable equations Linear Algebra: Least Squares Examples An example using the least squares solution to an unsolvable system ... You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Least squares regression line on the ti83 ti84 calculator youtube. The usual reason is: too many equations. Enter the number of data pairs, fill the X and Y data pair co-ordinates, the least squares regression line calculator will show you the result. The least squares solution is the central cross at the minimum; the solution for the logarithmically transformed equations is marked by a star. Thus, the empirical formula "smoothes" y values. We use the Least Squares Method to obtain parameters of F for the best fit. Least squares method, also called least squares approximation, in statistics, a method for estimating the true value of some quantity based on a consideration of errors in observations or measurements. 1. There are more equations than unknowns (m is greater than n). Example. Least squares approximation of continuous functions on [-1,1] using Legendre and Chebyshev polynomials. Residuals are the differences between the model fitted value and an observed value, or the predicted and actual values. Linear Least Squares Problem Let Az = b be an over-determined system where Ais m×nwith m>n. Enter the x and y values in the exponential regression calculator given here to find the exponential fit. Applied Formulas: Best linear equation through the data point dispersion: where: n: Number of matching XY data pairs (at least 2) a: Slope or tangent of the angle of the regression line: b: This regression calculator has proved extremely helpful in modelling the motors speed vs power response to come up with an approximate formula to use in a control algorithm. Find more Mathematics widgets in Wolfram|Alpha. Things to try: Change the function f(x) defined on the interval [ … Online calculator: function approximation with regression analysis. Method of Least Squares. Linear least squares fitting can be used if function being fitted is represented as linear combination of basis functions. Unless all Built by Analysts for Analysts! Least Squares Approximation with inner products. Learn examples of best-fit problems. If it is known that the measured quantity y (depended variable) is a linear function of x (independent variable), i.e. The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals made in the results of every single equation.. Picture: geometry of a least-squares solution. For example, f POL (see below), demonstrates that polynomial is actually linear function with respect to its coefficients c . Least Squares Approximation 1 Introduction In many applications we want to ﬁnd an approximation for a function, for example for differential equations. The least squares method is one of the methods for finding such a function. We now look at the line in the xy plane that best fits the data (x 1, y 1), …, (x n, y n). Least squares (LS)optimiza-tion problems are those in which the objective (error) function is a … The Linear Algebra View of Least-Squares Regression. The linear least squares method uses the ℓ2-norm. I am being vague, but they are essentially equivalent, and can be found in many books. The most common method to generate a polynomial equation from a given data set is the least squares method. Figure 1: Least squares polynomial approximation. When x = 3, b = 2 again, so we already know the three points don’t sit on a line and our model will be an approximation at best. If A is an m-by-n matrix with m ~= n and B is a column vector with m components, or a matrix with several such columns, then X = A\B is the solution in the least squares sense to the under- or overdetermined system of equations AX = B. For example, polynomials are linear but Gaussians are not. The n columns span a small part of m-dimensional space. The weird symbol sigma (∑) tells us to sum everything up:∑(x - ͞x)*(y - ͞y) -> 4.51+3.26+1.56+1.11+0.15+-0.01+0.76+3.28+0.88+0.17+5.06 = 20.73 ∑(x - ͞x)² -> 1.88+1.37+0.76+0.14+0.00+0.02+0.11+0.40+0.53+0.69+1.51 = 7.41.


See also: Mn, Mw, Mz
|Top Previous Next|
By using a probability distribution function (PDF) a distribution can be generated based on user input of number of pseudo components, Mn, Mw, Mz and the minimum and maximum molar mass of pseudo component.
3 different models are currently implemented.
I recommend using the Gamma function.
To use the function use either the Distribution wizard or the calculation wizard.
This function is defined in C# as:
public Object[,] Distribution(string Model, int Size, double MolarmassMinimum, double MolarmassMaximum, [In, Optional] object Mn, [In, Optional] object Mw, [In, Optional] object Mz, [In, Optional] object AdvVLXE, [In, Optional] object AdvUser)
Below is a screen dump where 100 pseudo components has been generated


Welcome to my page! I am so excited to begin another year here at Moore West. A little about myself; I grew up in Norman. My husband and I have lived in Moore for the past 9 years and we love it! We have two daughters. Josie Kate is 3 years old and Elliot Olivia was born on the last day of school last year! I graduated from the University of Oklahoma with a Bachelor of Science degree in Mathematics Education.
I believe all students learn in different ways, so we will be incorporating many different activities and teaching styles into our classroom. If you have any questions or concerns, please do not hesitate to contact me using the information below.


Based on the volume of questions that we field from our customers, deciding how to price out a set of flower pots is one of the more difficult tasks facing garden center management today.
There are a lot of approaches to accomplishing this task, and different solutions will often work for different garden centers, or even for different products within the same garden center. In many ways, pricing planters is more of an art than a science, but there are some basic concepts that will help to get you started, and at least one rule that you should never break:
- The biggest key to successfully pricing your pots is to make sure that the prices for each piece are proportionally and logically related to the actual size and scale of each pot included in the set. The easiest way to do this is to use a simple formula to establish ballpark prices. We use the following to power the Unit Price Calculator on our website – Please note that the steps below will work either before or after your margin calculations:
- Each pot in the set is assigned a numerical value, with 1 being the smallest pot, 2 being the 2nd smallest, 3 being the 3rd smallest, and so forth.
- These numerical unit values are then added together – a three-pot set would have a total unit count of 6, for example (1+2+3=6). Similarly, a four-pot set would total 10 units (1+2+3+4=10).
- You then divide the cost of the set by the set’s total unit count – A three-pot set with a cost of $60.00 would be divided by 6 per the example above, resulting in a unit cost of $10.00.
- This unit cost is then multiplied by the total number of units assigned to an individual pot, so our $60.00 set with an individual unit cost of $10.00 results in per-pot benchmark prices of $10.00 (1 x $10.00), $20.00 (2 x $10.00), & $30.00 (3 x $10.00).
- If you don’t feel like doing the math by hand, we have an easy-to-use downloadable Excel calculator on our website.
Don’t be afraid to second-guess the results from the formula, as many times it will make sense to adjust the weighting of the prices – most often reducing the price of the smallest pot while adding to the cost of the largest pot(s), which tend to be less price-sensitive at retail.
One of the great things about the pottery category is that it offers a lot of opportunity for enhancing your margin dollars. It’s perfectly fine to raise your prices beyond what the formula dictates if you feel that a particular pot can support a higher price – If a pot looks like a $79.00 item to you, but the formula says that it should be a $59.00 pot, charge the higher price – you can always discount away from it if needed.
Finally, the only hard and fast rule in this process is that you should never, ever, simply divide the cost of a set by the number of pots in the set. This overly-simple solution always leads to retail prices that don’t make sense, as you wind up with large and small pots sitting on your shelves at the same price.


A few weeks ago, I introduced you to the concept of pro-forma portfolios, and explained how we use them to estimate our current portfolios’ position in terms of volatility and beta. There is an Italian saying that could be translated as “to trust is good, not to trust is better.” While the pro-forma portfolios give us the best possible ex-ante estimates of the amount of risk in the portfolios, these are by definition estimates and not reality, and we can only trust them so much. For this reason we have developed two very short-term measures of volatility and beta based on the actual daily portfolio returns, which we routinely compare to the pro-forma estimates to make sure the portfolios are in fact behaving as we expected. The first measure is called one-month time-weighted trailing volatility and starts with the calculation of the equal-weighted average of the portfolio’s daily volatility over trailing 5 days (1 week), 10 days (2 weeks) and 20 days (4 weeks). This number is then divided by the same average volatility calculated for the portfolio’s benchmark. The ratio gives us a measure of how volatile the portfolio is being relative to its benchmark:
Ratio = 1 (neutral): the portfolio is experiencing the same volatility as the benchmark;
Ratio > 1 (above neutral or aggressive): the portfolio is experiencing more volatility than the benchmark;
Ratio < 1 (below neutral or defensive): the portfolio is experiencing less volatility than the benchmark;
The other measure is called one-month time-weighted trailing beta and uses the same approach to calculate the beta of the portfolios versus their respective benchmarks. Both measures are based on 1 month (4 weeks) of data, but since they are the equal-weighted average of three overlapping time frames they give more weight to more recent data. Specifically, the trailing 5 days are accounted for 3 times, the previous 5 days are accounted for twice, and the previous 10 days are accounted for only once. Because of their short-term nature, these measures can be particularly volatile at times, which is why we introduced a one-month moving average to better gauge the direction of the trend. In the chart to the right, you can see that after a brief spike to nearly 1.2, the two measures have come back down to around 0.9, while the one-month moving average has just reached the Mendoza line of 1. This result is perfectly in line with our initial estimates based on pro-forma portfolios, which had indicated that our last trade would take us very close to neutral.
Copyright: albund / 123RF Stock Photo


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Ivan has near 30 publications in Russian language, including the textbook "Methods of Forecasting" written in co-authorship with Sergey Svetunkov. The area of his scientific interests includes forecasting, statistical modelling, marketing analytics, time series analysis and application of complex valued models in business and economics. Ivan currently works in the field of theory of forecasting methods and their application to supply chain area. He focuses on state-space models and is also interested in time series analysis and econometrics.
The areas of his interests also include marketing analytics and marketing research.
For some more information about me see my Linkedin page , my twitter or my forecasting related website. The perfect candidate should not be scared of mathematics are you comfortable with linear algebra, probability theory, mathematical statistics and information theory? Recent searches. See all results for. Who we are What we do What we think Work with us Our locations.
Select your location Change. Local sites. Connect with us. In Transaction advisory services. Related topics Transaction advisory services. Valuation Justifying the value of assets and liabilities has grown more complex and critical for most businesses. Economic advisory EY helps you understand and improve overall economic strategy to identify opportunities and risks hidden within your data.
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This is the blog Mrs Jay Boyer used to share the learning of the children she taught from 2009 to 2012.
Thanks for sharing that information Edwina - I know that my basic facts get rusty if I don't brush them up every now and then too!Mrs Burt
That was so cool watching your slide show i beat you worked very hard on your maths.
Edwina i think you did a great job.I hope everyone will read your presentation.Also wish they get on the site. GREAT POST EDWINA YOU ARE A GREAT POSTER.
Awsome presentation on maths i thought you did great.
Hi Edwina I like your math matici that you did.
Hi Edwina I like the score you obtained. Congratulations on getting 100 percent. I'm also going to be working on maths magician and trying to get 100 percent. Good job!
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Wednesday, March 16, 2016
It's all about the data.
That's so obvious it seems silly to even comment on it in a page that's all about database design, doesn't it? But, every day, while addressing Access questions on my favorite Access forum, Utter Access, I run across questions can only be answered by looking at the specific data involved, not at the code used to manipulate it.
A recent example might help explain what I’m talking about. I’ve rephrased the question so as to avoid making it too easy to identify the source.
“My query raises a division by zero error. The query includes two calculated fields. The data is from three subqueries. The SQL for the final is shown below. How do I avoid the division by zero issue?”
Not picking on anyone, but the basic mathematician in me says “this ain’t a database question, it’s a math question. You avoid division by zero by not including zeros in the divisor.” But to the questioner, that simply hadn’t occurred, I guess. He or she was looking for “an Access solution” to the math problem.
There are, of course, two answers to this.
First, if records in the underlying tables have either Nulls or zeroes in one of the fields going into the calculation, then those values have to be resolved before you even START writing queries against that data. Exclude those records from the selection before you try to do any math on the remaining records.
There is, also in that sense, “an Access solution” to the question, "How do you handle Nulls and Zeroes in SQL so that they don’t blow up calculations?" The answers, of course, involve functions to convert Nulls and zeroes, as needed, when they appear. But that’s not the point of today’s comments.
Second, there is an even earlier, more fundamental, question to be addressed. If you are doing math (and a division by zero error definitely signals that math is being attempted), then you have to decide whether Null is valid for the data at hand, and whether Zero is valid for the data at hand. If so, then why do you then want to do math on either of those values, knowing that your calculation is not valid under any circumstances?
For example, if you want to calculate the average number of days between the date an order is placed and the date it is shipped, you have to decide, right at the beginning, if you want to try to include orders without a ship date. Those orders are still being processed and not yet shipped. I submit the answer to that one is obvious. You must exclude them because it’s only meaningful to ask about average processing days for orders that were actually processed and shipped. So, by the time you write that SQL with a division in it, there are no nulls to fret over.
Another example would have to do with calculating error rates in a manufacturing process. Let’s say you want to calculate a percentage of errors detected in Quality Control versus errors reported by customers after products are delivered. Unfortunately, if the calculation is QA Errors divided by Customer Reported Errors, it’s entirely possible (and one would have to hope, likely) to have one or more errors found in QA and Zero reported by customers for a particular product. See what’s going to happen there? Yup, a divide by Zero error.
The answer to that one is equally obvious, I think. You don’t do the arithmetic that way in the first place. You come up with a more appropriate, mathematically valid, way to calculate this metric. And how you do that is as much a business rule as it is a math problem. Maybe the next approach might be, well, okay, lets SUM the QA and Customer Reported errors first and then divide the QA errors by that total to get a ratio of QA errors. Uh uh! If there are no errors of either sort, then you’re still dividing by Zero.
At this point, I will step in and acknowledge that there is an Access way to handle it, but you can only get there by understanding the math—and the business rule—behind it.
It's all about understanding your data first. After that, it's all just code.


With Divide With Circle Models Designer you can design fractions examples using circle models.
You can input the divisor and dividend for a division of fractions example. The dividend or divisor each must be less than 6. The quotient must be less than 21.
If you want just a whole number for for the divisor or the dividend, type in 0 (zero) for a numerator. If you do not want a whole number, type in 0 (zero) for the whole number. Do not type in 0 for the denominator.
The default example above pictures with circle models the division of 1 3/4 by 2/3. The algorithm below the image shows how the quotient 2 5/8 results from multiplying the dividend 1 3/4 by the reciprocal (inverse) of 2/3.
When dividing, you are asking how much of the divisor or how many divisors fit into the dividend. In the above example the divisor is smaller than the dividend. This image shows that the divisor 2/3 will fit into the dividend 2 5/8 times. The quotient picture changes from dark blue to light blue each time the divisor fits into the dividend. The small mark on the right of each quotient circle shows where the fraction starts to be drawn on the circle..
To help understand the picture, keep increasing the divisor by one. So the next picture will show the division of 1 3/4 by 1 2/3, giving a quotient of 1 1/20. When you increase the divisor to 2 2/3 you will get the quotient .21/32. Here, you can see that when the divisor is larger than the dividend, the quotient is less than 1. The quotient picture shows 21/32 of the divisor fits into the divident..
Uncheck the <EXPLAIN> check box to turn off the answer and the explanation. You can ask your learners to complete the number sentence.
Uncheck the <SHOW INPUT> check box to make the input dialog boxes work like a password input boxes, hiding the numbers you input. This will uncheck the <EXPLAIN> check box. With <EXPLAIN> and <SHOW INPUT> unchecked you can ask your learners to write a number sentence that explains the picture.
With <EXPLAIN> and <SHOW COLOR> unchecked you can ask your learners to complete the picture by shading the circles.
Start with a dividend of 2 1/4 and a divisor of 2/3. Notice how 3 3/8 divisor amounts fit into the dividend. Increase the dividend by 1 to get 2 1/4 divided by 1 2/3 giving a quotient of 1 7/20. Then increase the divisor to 2 2/3. This will result in a quotient smaller than one (27/32) , showing that the quotient is smaller than one when the divisor is larger than the dividend.
You can also demonstrate how as the divisor decreases the quotient increases. Try a Dividend of 2 2/3 and a divisor of 2 2/3. Notice that the divisor and dividend are the same size, resulting in a quotient of one. Decrease the divisor by 1/3 increments. For example, keep the dividend at 2 2/3 and change the divisor to 2 1/3, 2 0/3, 1 2/3, etc, and continue with this pattern. You will see the quotient increase.
Try 1 3/4 divided by 3 1/2. Notice that only half the divisor fits into the dividend.
Divide one(1) by 2/3. (Enter 1 for the whole number, 0 for the numerator and 1 for the denominator. Then enter 0 and 2/3 for the divisor. You will get 3/2 or 1 1/2 for the quotient. This shows that 1 divided by any fraction will give the reciprocal (inverse) of the fraction.
Think of the dividend as available pizza and the divisor as the amount of the available pizza that can fit into a take-out container. If there are 5 1/2 pizzas and the container can hold 3/4 pizza, you can fill 7 containers with one piece left over. The piece will fill 1/3 of a container, so you can fill 7 1/3 containers.
How do you explain what's really going on when you divide 1/2 by 2/3? This is hard to picture, but if you cover the dividend 1/2 by the divisor 2/3 only 3/4 of the divisor is needed to cover the dividend. If you cover 2/3 by 1/2 you will find it will take a whole 1/2 piece plus 1/3 of the 1/2 piece.
You may copy the screen by pressing <Print Screen> on the keyboard. This copies the screen into Windows Clipboard™. The screen can then be pasted into Windows Paint™ or your favorite imaging program. Windows Paint™ will allow you to crop, print, or save the image.
Windows 7 users can use the Snipping Tool™ to capture any part of the screen you wish. These images can be edited and saved in PNG, GIF(recommended) or JPEG formats.
To take a screen shot with the Ipad first press the Sleep/Wake button at the top right of the Ipad. While holding the Sleek/Wake button press and release the round Home button at the bottom of the screen. You should see a photo of the screen by going to the Home page and pressing the Photos icon.


There are two types of girls in the world: those who never learned the multiplication tables and those who know the book by heart Baldor's Algebra, such as Ana Paula Jiménez, Nuria Sydykova Méndez, Karla Rebeca Munguía Romero and Natalia del Carmen Jasso Vera, who participated in the European Women's Olympiad of Mathematics (EGMO).
The four girls of Mexican origin demonstrated their knowledge and passion for numbers, and obtained gold, silver, honorable mentions and the applause of an entire nation.
On April 7, the four young Mexicans named the name of Mexico when they won gold and silver in the Mathematics Olympiad.
The EGMO lasted six days in which, through mathematical problems, equations and calculations, the Aztecs competed against 160 girls of different nationalities and achieved the tenth place among 49 competing teams.
Ana Paula won the gold medal; Nuria and Karla Rebeca, silver; while Natalia del Carmen received an honorable mention for her performance.
When the news arrived in Mexico, various media and friends congratulated them and offered their unconditional support.


Deb Lombard has been bringing arts integration and dance programs into Sarasota County Schools for over two decades. One of her greatest joys is instilling the love of dance to students of all ages. And, for 30 years, she’s been doing just that.
Her career began at Syracuse University, where she
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Moving through Math: DANCING DIGITS! (Fluency)
There's no greater joy than watching students laugh as they work together to solve math problems and demonstrate place value with their bodies – in fact, it’s so fun, that they often forget they’re doing math! Through playful activities, students will explore digits along with the dance elements' shapes and levels. They’ll solve addition and subtraction problems using their bodies,...
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3 edition of Lectures in Differential Dynamics (Cbms Regional Conference Series in Mathematics) found in the catalog.
by Amer Mathematical Society
Written in English
|The Physical Object|
Abstract: This extensively revised and expanded edition of Lectures in Differentiable Dynamics, first published in , provides an authoritative exposition of the central results of this fundamental and rapidly developing mathematical subject, starting from simple engineering systems and proceeding to current research topics concerning differentiable flows on manifolds. Introduction to Dynamics of Structures 3 Washington University in St. Louis Undamped system Consider the behavior of the undamped system (c=0). From differential equations we know that the solution of a constant coefficient ordinary differential equation .
David Tong: Lectures on Classical Dynamics. This is a second course in classical mechanics, given to final year undergraduates. They were last updated in January Individual chapters and problem sheets are available below. The full set of lecture notes, weighing in at around pages, can be downloaded here: PostScript PDF. James Binney's Lecture Courses. Complex Numbers and Ordinary Differential Equations. Synopsis; Lecture notes; Problem sets: 1 2 3; Quantum Mechanics. Synopsis; Overhead slides; Book of the course; Videos of the lectures on Oxford podcasts; Problem sets: MT1 MT2 Christmas Vacation HT1 HT2 HT3 Easter Vacation all; Solutions to starred problems.
Lectures on analytic differential equations. Local Dynamics and Nonlocal Bifurcations. In these lectures various topics related to the second part of Hilbert’s 16th problem are discussed. Details about Lectures, Problems And Solutions For Ordinary Differential Equations (Second Edition): This unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1, examples.
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Lectures on Ordinary Differential Equations (Dover Books on Mathematics) Paperback – Octo this kind of theory was applied to dynamic systems such as population dynamics.) This book has all of the existence and uniqueness theory which is required for two important differential geometry applications.
The first is parallel Cited by: Download Lectures on Differential Equations Download free online book chm pdf. Applications of First Order Nonlinear Equations, One-Dimensional Dynamics, Second Order Linear Differential Equations, The General Solution of Homogeneous Equations, Existence of Many Fundamental Sets, Second Order Linear Homogeneous Equations with Constant.
Professor Arnold's Lectures on Partial Differential Equations is an ambitious, intensely personal effort to reconnect the subject with some of its roots in modeling physical processes. He does so in a lively lecture-style format, resulting in a book that would complement almost any course in PDEs.
/5(4). Dynamics by Prof. George Haller. This course reviews momentum and energy principles, and then covers the following topics: Hamilton's principle and Lagrange's equations; three-dimensional kinematics and dynamics of rigid bodies, steady motions and small deviations therefrom, gyroscopic effects, and causes of instability, free Lectures in Differential Dynamics book forced vibrations of lumped-parameter and continuous systems.
History of differentiable dynamics 2. Differentiable dynamics, definitions and examples 3. Basic problems of differentiable dynamics 4.
Comparison and contrast of topological and differentiable dynamics 5. Morse-Smale, Anosov hyperbolic and generic dynamical systems 6.
The principal results of differentiable dynamics. Series Title. These video lectures of Professor Arthur Mattuck teaching were recorded live in the Spring of and do not correspond precisely to the lectures taught in the Spring of This table (PDF) provides a correlation between the video and the lectures in the version of the course.
While not yet the book I’d eventually like to write, the result may already be helpful for people interested in the mathematics of classical mechanics. The chapters in this LATEX version are in the same order as the weekly lectures, but I’ve merged weeks together, and sometimes split them over chapter, to obtain a more textbook feel to File Size: KB.
This course is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics covered include kinematics, force-momentum formulation for systems of particles and rigid bodies in planar motion, work-energy concepts, virtual displacements and virtual work.
Students will also become familiar with the following topics: Lagrange's equations for systems of. $\begingroup$ I liked Logan's book on ODEs a lot, and think the PDE book is good too.
It does not overwhelm the reader as many other books do. It does not overwhelm the reader as many other books do. Because so many mathematical topics converge in ODEs and PDEs, it can be hard to find a good balance between clear explanation versus rigor.
History of differentiable dynamics Differentiable dynamics, definitions and examples Basic problems of differentiable dynamics Comparison and contrast of topological and differentiable dynamics Morse-Smale, Anosov hyperbolic and generic dynamical systems The principal results of differentiable dynamics Bibliography Appendix () References to.
LECTURES IN ELEMENTARY FLUID DYNAMICS: Physics, Mathematics and Applications J. McDonough Departments of Mechanical Engineering and Mathematics University of Kentucky, Lexington, KY c, File Size: 2MB. This course of 25 lectures, filmed at Cornell University in Springis intended for newcomers to nonlinear dynamics and chaos.
It closely follows. "This book provides an introductory text (in German) to basic partial differential equations, based on the author's lectures at Moscow University. Most of the standard themes are treated (see list below), but some unusual topics are covered as well.
This book is an expanded version of a Master Class on the symmetric bifurcation theory of differential equations given by the author at the University of Twente in The notes cover a wide range of recent results in the subject, and focus on the dynamics that can appear in the generic bifurcation theory of symmetric differential equations.
Lectures On Ordinary Differential Equations Hardcover – 21 Sept (When I was an undergraduate, this kind of theory was applied to dynamic systems such as population dynamics.) This book has all of the existence and uniqueness theory which is required for two important differential geometry applications.
The first is parallel transport for /5(3). 23 videos Play all Online Dynamics Course Jeff Hanson Mix Play all Mix - Jeff Hanson YouTube How To Master 5 Basic Cooking Skills - Gordon Ramsay - Duration: These Lectures provide a survey of the modern theory of differentiable dynamics as an abstraction of the qualitative theory of ordinary differential equations.
Historical and conceptual developments are emphasized as the theories of nonlinear mechanics, topological dynamics, and differential topol. This unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1, examples.
The initial draft was used to teach more t advanced undergraduate students in engineering, physics, economics, as well as applied : World Scientific Publishing Company.
This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems.
Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics. This book is a revised and more comprehensive version of Dynamics of Stochastic Systems. Part I provides an introduction to the topic.
Part I provides an introduction to the topic. Part II is devoted to the general theory of statistical analysis of dynamic systems with fluctuating parameters described by differential and integral equations.
Application of the preceding investigation to the integration of partial differential equations of the first order, and in particular, to the case of mechanics. The theorem on the third integral derived from two given integrals of differential equations of dynamics.
Pages Clebsch, : Hindustan Book Agency.These notes study the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the classical case of rational maps of the Riemann sphere.
They are based on introductory lectures given at Stony Brook during the Fall Term of These lectures are intended to introduce the reader to some key ideas in the field, and to form a basis for further study. The.A record of his lectures on Dynamics given in at Konigsberg, edited by A.
Clebsch, has been available in the original German. This is an English translation. It is not just a historical document; the modern reader can learn much about the subject directly from one of its great masters.


Variables, Data Types, and Operators
- Number: Used for numeric values, such as integers and floating-point numbers.
- String: Used for text values, such as words and phrases. Strings are surrounded by quotation marks, either single or double.
- Boolean: Used for values that can only be either “true” or “false.”
- Object: Used to store collections of data and methods. Objects can be created using object literals or object constructors.
- Array: Used to store ordered collections of data. Arrays are defined using square brackets and the values are separated by commas.
- Null: Used to represent an intentional non-value, such as when a variable is declared but has not yet been assigned a value.
- Undefined: Used to represent a variable that has been declared but has not yet been assigned a value.
- Arithmetic Operators: Used for performing mathematical operations, such as addition, subtraction, multiplication, and division.
- Comparison Operators: Used for comparing values, such as equal to, not equal to, greater than, less than, and more.
- Logical Operators: Used for combining conditions, such as and, or, and not.
- Assignment Operators: Used for assigning values to variables, such as equal (=), add and assign (+=), subtract and assign (-=), and more.