Calculus Integrals Math Sheet Definition of an IntegralReturn to Top The integral is a mathematical analysis applied to a function that results in the area bounded by the graph of the function, x axis, and limits of the integral. Integrals can be referred to as anti-derivatives, because the derivative of the integral of a function is equal to the function. PropertiesReturn to Top Common IntegralsReturn to Top Integration by SubstitutionReturn to Top Integration by PartsReturn to Top Integration by Trigonometric SubstitutionReturn to Top Trigonometric identities can be use with integration substitution to simplify integrals. First Trigonometric SubstitutionReturn to Top To take advantage of the property Substitute After substitution Second Trigonometric SubstitutionReturn to Top After substitute Third Trigonometric SubstitutionReturn to Top

Pauls Online Math Notes Lee Lady: Calculus for the Intelligent Person Teaching students how to use the concepts of the derivative and the integral is different from teaching them to understand the concepts. Understanding is certainly nice, and to some extent it's something that students feel a need for, but my main goal is for students to be able to use calculus in applications. This means, among other things, being able to have confidence in setting up formulas using derivatives and integrals. Abstract (in HTML). Article in PDF (Adobe Acrobat) format.DVI version of the article.Postscript version of the article.Slides for a brief talk on this article. These notes are an attempt to show how to express a given mathematical relationship in the form of an integral. However in practice, the evaluation of integrals has nothing to do with dividing areas into little vertical strips and taking Riemann sums. Further Notes on Applications of Integration (Click here for DVI version.) (Click here for postscript version.) (Click here for DVI version.) Max-Min Problems. f(x)

Dimensions Home A film for a wide audience! Nine chapters, two hours of maths, that take you gradually up to the fourth dimension. Mathematical vertigo guaranteed! Background information on every chapter: see "Details". Click on the image on the left to watch the trailer ! Free download and you can watch the films online! The film can also be ordered as a DVD. This film is being distributed under a Creative Commons license. Now with even more languages for the commentary and subtitles: Commentary in Arabic, English, French, German, Italian, Japanese, Spanish and Russian. Film produced by: Jos Leys (Graphics and animations) Étienne Ghys (Scenario and mathematics) Aurélien Alvarez (Realisation and post-production)

Differential Calculus Introduction: Simple Polynomial Equations | Decoded Science Polynomial Calculations: Image by blumik The Main Question in Differential Calculus “Differential calculus” is a big phrase but a very useful part of mathematics. Several previous articles have built a foundation, and now the first floor will be erected. The question that differential calculus asks is: What is the slope of a function at a given point? What Do “Slope” and “Function” Mean? To Define a Function: For this article, a function relates one variable to another; it is often written as “y = f(x)”. Again, for this article, the best way to think of a function is that it prescribes a line or curve graphed on a Cartesian plane. Three other necessary features of a function for calculus are “smooth” and “continuous” and “well defined”. A function: “y = x unless ‘x’ is negative; in that case y = -x” is not smooth. To Define Two Types of Slopes The “average slope” between two points is the vertical change divided by the horizontal change. The slope then is (y[2] – y[1])/(x[2] – x[1]). Pages: 1 2

Detexify LaTeX handwritten symbol recognition Want a Mac app? Lucky you. The Mac app is finally stable enough. See how it works on Vimeo. Download the latest version here. Restriction: In addition to the LaTeX command the unlicensed version will copy a reminder to purchase a license to the clipboard when you select a symbol. You can purchase a license here: Buy Detexify for Mac If you need help contact mail@danielkirs.ch. What is this? Anyone who works with LaTeX knows how time-consuming it can be to find a symbol in symbols-a4.pdf that you just can't memorize. How do I use it? Just draw the symbol you are looking for into the square area above and look what happens! My symbol isn't found! The symbol may not be trained enough or it is not yet in the list of supported symbols. I like this. You could spare some time training Detexify. The backend server is running on Digital Ocean (referral link) so you can also reduce my hosting costs by using that referral link. Why should I donate? Hosting of detexify costs some money. No. Yes.

Multivariable Calculus This is a textbook for a course in multivariable calculus. It has been used for the past few years here at Georgia Tech. The notes are available as Adobe Acrobat documents. If you do not have an Adobe Acrobat Reader, you may down-load a copy, free of charge, from Adobe. Title page and Table of Contents Table of Contents Chapter One - Euclidean Three Space 1.1 Introduction 1.2 Coordinates in Three-Space 1.3 Some Geometry 1.4 Some More Geometry--Level Sets Chapter Two - Vectors--Algebra and Geometry 2.1 Vectors 2.2 Scalar Product 2.3 Vector Product Chapter Three - Vector Functions 3.1 Relations and Functions 3.2 Vector Functions 3.3 Limits and Continuity Chapter Four - Derivatives 4.1 Derivatives 4.2 Geometry of Space Curves--Curvature 4.3 Geometry of Space Curves--Torsion 4.4 Motion Chapter Five - More Dimensions 5.1 The space Rn 5.2 Functions Chapter Six - Linear Functions and Matrices 6.1 Matrices 6.2 Matrix Algebra Chapter Twelve - Integration 12.1 Introduction 12.2 Two Dimensions

LaTeX Symbols From AoPSWiki This article will provide a short list of commonly used LaTeX symbols. Operators Relations Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an n between the \ and the word. To use other relations not listed here, such as =, >, and <, in LaTeX, you may just use the symbols on your keyboard. Greek Letters Headline text Arrows (For those of you who hate typing long strings of letters, \iff and \implies can be used in place of \Longleftrightarrow and \Longrightarrow respectively.) Dots Accents When applying accents to i and j, you can use \imath and \jmath to keep the dots from interfering with the accents: \tilde and \hat have wide versions that allow you to accent an expression: Others Command Symbols Some symbols are used in commands so they need to be treated in a special way. (Warning: Using \$ for will result in . European Language Symbols Bracketing Symbols (\frac{a}{x} )^2 the parentheses don't come out the right size: gives Examples

Differential Equations Differential Equations (Math 3301) Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations. I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from a Calculus or Algebra class or contained in other sections of the notes. A couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. Because I wanted to make this a fairly complete set of notes for anyone wanting to learn differential equations I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here. Here is a listing and brief description of the material in this set of notes. Basic Concepts

Octave GNU Octave is a high-level interpreted language, primarily intended for numerical computations. It provides capabilities for the numerical solution of linear and nonlinear problems, and for performing other numerical experiments. It also provides extensive graphics capabilities for data visualization and manipulation. Octave is normally used through its interactive command line interface, but it can also be used to write non-interactive programs. The Octave language is quite similar to Matlab so that most programs are easily portable. Octave is distributed under the terms of the GNU General Public License. March 7, 2014 — Octave 3.8.1 Released Version 3.8.1 is a bug fixing release and is now available for download. One of the biggest new features for the Octave 3.8.x release series is a graphical user interface. Given the length of time and the number of bug fixes and improvements since the last major release Octave, we also decided against delaying the release any longer.

Introduction to Scilab Terence Leung Ho Yin, Tsing Nam Kiu Table of Contents About Scilab Installing and Running Scilab Documentation and Help Scilab Basics Common Operators Common Functions Special Constants The Command Line Data Structures Strings Saving and Loading Variables Dealing with Matrices Entering Matrices Calculating Sums Subscripts The Colon Operator Simple Matrix Generation Concatenation Deleting Rows and Columns Matrix Inverse and Solving Linear Systems Entry-wise operations, Matrix Size The Programming Environment Creating Functions Flow Control Some Programming Tips Debugging Plotting Graphs 2D Graphs 3D Surfaces Scilab versus Matlab References 1. About Scilab Scilab is a freely distributed open source scientific software package, first developed by researchers from INRIA and ENPC, and now by the Scilab Consortium. an interpreter libraries of functions (Scilab procedures) libraries of Fortran and C routines For further information and documentation, visit the Scilab homepage: 2. scilex