CATALOG DESCRIPTION:

1701.236 Mathematics for Engineering Analysis II

(Prerequisite: 1701.235 Math for Engineering Analysis I) 4 s.h.

This course is a continuation of Mathematics for Engineering Analysis I. Methods for solving second - order ordinary differential equations and systems of first - order equations are discussed, including the Laplace transform. Methods for solving partial differential equations are also studied. A computer algebra system such as Mathematica is required.
 

OBJECTIVES:

Students will demonstrate the ability to:

i. Solve higher order linear differential equation with constant coefficients.

ii. Use the methods of undetermined coefficients and variations of parameters to solve ordinary differential equations.

iii. Solve systems of differential equations.

iv. Use power series and Laplace transforms to solve ordinary differential equations.

v. Solve partial differential equations using the method of separation of variables.

vi. Use numerical methods to solve differential equations.
 
 

CONTENTS:

Second-Order Linear Differential Equations

Homogeneous Linear Equations

Homogeneous Equations with Constant Coefficients

Case of Complex Roots, Complex Exponential Function

Euler -Cauchy Equation

Nonhomogeneous Equations

Solution by Undetermined Coefficients

Solution by Variation of Parameters

Numerical Methods including Runge-Kutta

Higher Order Linear Differential Equations

Homogeneous Linear Equations

Homogeneous Equations with Constant Coefficients
 
 

System of Differential Equations

Introduction: Vectors, Matrices

Introductory Examples

Basic Concepts and Theory

Homogeneous Linear Systems with Constant Coefficients

Series Solutions of Differential Equations

Power Series Method

Laplace Transforms

Laplace Transform, Inverse Transform, Linearity

Transforms of Derivatives and Integrals

s-Shifting, t-Shifting, Unit Step Functions

Differentiation and Integration of Transforms

Partial Fractions: Systems of Differential Equations

Laplace Transforms: General Formulas

Table of Laplace Transforms

Partial Differential Equations

Basic Concepts

Modeling: Vibrating String, Wave Equations

Separation of Variables: Use of Fourier Series

D'Alembert's Solution of the Wave Equation
 
 

TEXT:

Nagle, Saff & Snider, FUNDAMENTALS OF DIFFERENTIAL EQUATIONS, Pearson/Addison Wesley 6th Ed

Kreyszig, Erwin, Advanced Engineering Mathematics, 8th edition, John Wiley & Sons, 1999 and accompanying Mathematica manual.