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

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


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



INTEGRAL CALCULUS, p. 51 • Definition of an Integral • Fundamental Theorems on Integrals

– Moment of Inertia– Center of Gravity– Work


Outline Overview ContinuedDIFFERENTIAL

EQUATIONS, p.53 • Definitions • Notation • Equations of First Order

and First Degree– Variables

Separable– Linear Equation

• Second-Order Differential Equations

0 00

'' )]([)0()()()()]([ pypLydxxyepexydxxyepyL xpxpxp



DIFFERENTIAL EQUATIONS, p. 53• Constant Coefficients

– Variation of Parameters– Undetermined Coefficients

• Euler Equations• Laplace Transform


Basic Rules for Derivatives


Solution


The Chain Rule


Solution


Maximum & Minimum Values of a Function


Solution


Concavity & Points of Inflection


Solution


Solution (continued)


Differential Equations with Variables Separable


Solution


Taylor Series


Solution


Maclaurin Series


Solution


Second Order Linear Equations


Solution


Solution (continued)


Euler Equations


Solution


Method of Variation of Parameters


Solution


Laplace Transforms


Solution


Convolution


Solution

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