Applied CalculusI & II: Course Outline
Objective: Teach the concepts of calculus and analytic geometry and the applications of these concepts to the solution of engineering problems.
CalculusI
 Complex Numbers
 DeMoivre’s Theorem and its Applications
 Simple Cartesian Curves
 Functions and Graphs
 Symmetrical Properties
 Curve Tracing
 Limit and Continuity
 Differentiation of Functions
 Derivative as Slope of Tangent to a Curve and as Rate of Change
 Application to Tangent and Normal
 Linearization
 Maxima/Minima and Point of Inflexion
 Taylor and Maclaurin Expansions and their convergence
 Integral as Antiderivative
 Indefinite Integration of Simple Functions
Methods of Integration:
 Integration by Substitution
 Integration by Parts
 Integration by Partial Fractions
 Definite Integral as Limit of a Sum
 Application to Area
 Arc Length
 Volume and Surface of Revolution
 Complex Numbers
 DeMoivre’s Theorem and its Applications
 Simple Cartesian Curves
 Functions and Graphs
 Symmetrical Properties
 Curve Tracing
 Limit and Continuity
 Differentiation of Functions
 Derivative as Slope of Tangent to a Curve and as Rate of Change
 Application to Tangent and Normal
 Linearization
 Maxima/Minima and Point of Inflexion
 Taylor and Maclaurin Expansions and their convergence
 Integral as Antiderivative
 Indefinite Integration of Simple Functions.
Methods of Integration:
 Integration by Substitution
 Integration by Parts
 Integration by Partial Fractions
 Definite Integral as Limit of a Sum
 Application to Area
 Arc Length
 Volume and Surface of Revolution
CalculusII
 Functions of Several Variables
 Partial Differentiation
 Multiple Integrals
 Line Integrals
 Surface Integrals
 Green’s and Stoke’s Theorem
 Fourier series
 Periodic functions
 Functions of any period P = 2L
 Even functions
 Odd functions
 Half Range expansions
 Fourier Transform
 Laplace Transform
 ZTransform
Text Books

Calculus and Analytic Geometry byCall Number: 515.15 THOISBN: 020160700XPublication Date: 19920101

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EBooks

by: Frank Ayres Jr., PhD, Elliott Mendelson, PhD

by: Arthur W. Leissa, Mohamad S. Qatu,
ISBN: 9780071714792 
by: Warren C. Young, Richard G. Budynas, Ali M. Sadegh

by: Roland E. Best
ISBN: 9780071493758