# Calculus

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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

The AP Calculus BC Exam Exam Content In 1956, 386 students took what was then known as the AP Mathematics Exam. By 1969, still under the heading of AP Mathematics, it had become Calculus AB and Calculus BC. The Calculus BC exam covers the same differential and integral calculus topics that are included in the Calculus AB exam, plus additional topics in differential and integral calculus, and polynomial approximations and series. This is material that would be included in a two-semester calculus sequence at the college level. Because graphing calculator use is an integral part of the course, the exam contains questions that require students to use a graphing calculator. If students take the BC exam, they cannot take the AB exam in the same year because the exams share some questions. Multiple-Choice Questions For sample multiple-choice questions, refer to the Course Description. AP Calculus Course Description, Effective Fall 2012 (.pdf/2.28MB) Free-Response Questions AP Calculus Free-Response Question Collections

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). 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.) This is a much more condensed version of the ideas in the preceding article. Outline Sketch for the Applications of Integration Method (Click here for DVI version.) Max-Min Problems. f(x)

CALCULUS.ORG 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

THE CALCULUS PAGE PROBLEMS LIST Problems and Solutions Developed by : D. A. And brought to you by : Beginning Differential Calculus : Problems on the limit of a function as x approaches a fixed constant limit of a function as x approaches plus or minus infinity limit of a function using the precise epsilon/delta definition of limit limit of a function using l'Hopital's rule ... Beginning Integral Calculus : Problems using summation notation Problems on the limit definition of a definite integral Problems on u-substitution Problems on integrating exponential functions Problems on integrating trigonometric functions Problems on integration by parts Problems on integrating certain rational functions, resulting in logarithmic or inverse tangent functions Problems on integrating certain rational functions by partial fractions Problems on power substitution Problems on integration by trigonometric substitution ... Sequences and Infinite Series :

Calculus Online Book Calculus, Contemporary Calculus, Hoffman Contemporary Calculus Dale HoffmanBellevue Collegedhoffman@bellevuecollege.edu A free on-line calculus text Many of these materials were developed for the Open Course Library Project of the Washington State Colleges as part of a Gates Foundation grant. The goal of this project was to create materials that would be FREE (on the web) to anyone who wanted to use or modify them (and not have to pay \$200 for a calculus book). They have been used by several thousand students. The textbook sections, in color, are available free in pdf format at the bottom of this page. The links below are to pdf files. Chapter 0 -- Review and Preview Chapter 1 -- Functions, Graphs, Limits and Continuity Chapter 2 -- The Derivative Chapter 3 -- Derivatives and Graphs Chapter 4 -- The Integral Chapter 5 -- Applications of Definite Integrals Chapter 6 -- Introduction to Differential Equations Chapter 7 -- Inverse Trigonometric Functions Chapter 8 -- Improper Integrals and Integration Techniques

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. 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. For a straight line from point (x[1], y[1]) to (x[2], y[2]), the change in ‘x’ is (x[2] – x[1]), and the change in ‘y’ is (y[2] – y[1]). Pages: 1 2

Web-Based Study Guides The Mth 253-256 sequence forms the core mathematics sequence for engineering, mathematics, and some science majors at Oregon State University. These courses cover sequences and series, multivariable calculus, vector calculus, and differential equations and have a total enrollment each year of approximately 1000. The purpose of this project is to develop Web-based study guides for these courses that can be used by students currently enrolled in these courses and serve as a resource for the OSU community. Web-based study guides take advantage of the power of hypertext links. In a book topics are ordered linearly. Accessing the Study Guides The study guides can be accessed by clicking on the buttons above or on the links below. There are also calculator tutorials for the TI-85 and HP 38G. Questions and Comments Please see the copyright page for information on contacting the authors of these pages. Personnel The principal investigators for this project are Dennis Garity and Satish Reddy. Funding

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

MATH 151 – CALCULUS I Upon successful completion of Math& 151, the student should be able to:

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