Copyright Kaplan AEC Education, 2008 Calculus and Differential Equations Outline Overview DIFFERENTIAL CALCULUS, p. 45 Definition of a Function Definition.

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Presentation transcript:

Copyright Kaplan AEC Education, 2008 Calculus and Differential Equations Outline Overview DIFFERENTIAL CALCULUS, p. 45 Definition of a Function Definition of a Derivative Some Relations Among Derivatives Table of Derivatives Slope of a Curve: Tangent and Normal

Copyright Kaplan AEC Education, 2008 Outline Overview Continued DIFFERENTIAL CALCULUS, p. 45 Maximum and Minimum Values of a Function Points of Inflection of a Curve Taylor and Maclaurin Series Evaluation of Indeterminate Forms Differential of a Function Functions of Several Variables, Partial Derivatives, and Differentials

Copyright Kaplan AEC Education, 2008 Outline Overview Continued INTEGRAL CALCULUS, p. 51 Definition of an Integral Fundamental Theorems on Integrals –Moment of Inertia –Center of Gravity –Work

Copyright Kaplan AEC Education, 2008 Outline Overview Continued DIFFERENTIAL EQUATIONS, p.53 Definitions Notation Equations of First Order and First Degree –Variables Separable –Linear Equation Second-Order Differential Equations

Copyright Kaplan AEC Education, 2008 Outline Overview Continued DIFFERENTIAL EQUATIONS, p. 53 Constant Coefficients –Variation of Parameters –Undetermined Coefficients Euler Equations Laplace Transform

Copyright Kaplan AEC Education, 2008 Basic Rules for Derivatives

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 The Chain Rule

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Maximum & Minimum Values of a Function

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Concavity & Points of Inflection

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Solution (continued)

Copyright Kaplan AEC Education, 2008 Differential Equations with Variables Separable

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Taylor Series

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Maclaurin Series

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Second Order Linear Equations

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Solution (continued)

Copyright Kaplan AEC Education, 2008 Euler Equations

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Method of Variation of Parameters

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Laplace Transforms

Copyright Kaplan AEC Education, 2008 Solution

Copyright Kaplan AEC Education, 2008 Convolution

Copyright Kaplan AEC Education, 2008 Solution