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MA 321

## Solution of first and second order equations by formal methods, linear equations are studied in detail. Systems of linear equations, series of solutions, Laplace transforms, eigenvalues are covered as well as elementary PDE by separation of variables.

Ma 321 Ordinary Differential Equations

3 semester hours

Prerequisite: MA 225 or equivalent.

Fr. MacDonnell B108 ex 7222

Text: A First Course in Differential Equations by Dennis Zill Ed. 6

## Sylabus for MA 321

ch1,2 Elementary Methods LDE I

Existence and Uniqueness

Variables Separable

First-Order Linear D E

Exact Differential equations

Homogeneous Functions

ch4 LDE II

Linear Independence and Wronskians

The Characteristic Equation

Homogeneous D E w Const Coef

The general solution

Homogeneous D E w Variable Coef

Cauchy-Euler D E

Reduction of Order ( Abel's formula)

Nonhomogeneous D E

The Method of Undetermined Coef

Linear Systems

The Method of Elimination

The Matrix Method

ch5 Boundary Value Problems

Solution of Boundary Value Problems

Eigenvalues and Eigenfunctions

ch6 Series Solutions L D E II

Solutions of Linear Hom D E by Taylor

Ordinary Points and Singular Points

Power-Series Solutions about an Ord Pt

ch7 The Laplace Transform

Properties of Laplace Transform

The Laplace Transform Applied to D E

# Elemetary PDE

Boundary Value Problems

## Suggested problems for homework

{using Zill}

Initial value 1.2 15/11-16

Seperating variables 2.1 35/1-34

Exact equations 2.2 42/1-30

Linear equations 2.3 51/1-30

Homogeneous functions 2.4 57/1-14

Wronskian 4.1 108/15-30

Abel 4.2 112/1-112

LDE w constant coef 4.3 119/1-28

Undetermined coef 4.4 130/1-32

Variation/parameters 4/6 146/1-24

Cauchy-Euler 4.7 153/1-22

Systems of lin equa 4.8 160/1-16

Systems of non-lin eq 4.9 166/1-8

Eigenvalues 5.2 198/9-14

Power series 6.1 222/15-24

PS about ordinary pts 6.2 229/1-14

Laplace transforms 7.1 266/19-38

Inverse transforms 7.2 272/1-22

Applications 7.5 301/1-13

Systems of DE 7.7 313/1-12

Partial diff eq # sheets

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