Differential Equations Homepage

Assignments (Due Dates are listed at the beginning of the Assignments page)

Syllabus

Chapter coverage for First Edition will be Chapters 1-4, Chapter 6, approximately half of Chapter 7 and some topics from Chapter 8.
First edition information and table of contents listed directly below. Second edition table of contents and information listed below that.
First edition is sufficient, but Second Edition is acceptable. The two editions correlate closely.
Differences between First and Second Editions:

The Second Edition has consolidated Chapters 2 and 3 into Chapter 2, and Chapters 4 and 5 into Chapter 3.

Second Edition sections 3.11 - 3.13 correspond to Chapter 5 of the first edition and are not covered.

First Edition Chapter 6 is now Second Edition Chapter 4.

First Edition Chapter 7 is Second Edition Chapter 5

First Edition Chapter 8 is Second Edition Chapter 6.

Second Edition coverage will therefore be Chapters 1 - 4, excepting Sections 3.11 - 3.13; plus approximately half of Chapter 5 and some topics from Chapter 6.

Information and Table of Contents for First Edition:

Elementary Differential Equations
Werner E. Kohler, Virginia Polytechnic Institute & State University
Lee W. Johnson, Virginia Polytechnic Institute & State University

ISBN-10: 0201709260
ISBN-13: 9780201709261

Publisher: Pearson
Copyright: 2003
Format: Cloth; 760 pp
Published: 12/06/2002

1. Introduction to Differential Equations.

Examples of Differential Equations.

Direction Fields.

2. First Order Linear Differential Equations.

Existence and Uniqueness.

First Order Linear Homogeneous Differential Equations.

First Order Linear Nonhomogeneous Differential Equations.

Introduction to Mathematical Models.

Mixing Problems and Cooling Problems.

3. First Order Nonlinear Differential Equations.

Existence and Uniqueness.

Separable First Order Equations.

Exact Differential Equations.

Bernoulli Equations.

The Logistic Population Model.

One-Dimensional Motion with Air Resistance.

One-Dimensional Dynamics with Distance as the Independent Variable.

Euler's Method.

4. Second Order Linear Differential Equations.

Existence and Uniqueness.

The General Solution of Homogeneous Equations.

Fundamental Sets and Linear Independence.

Constant Coefficient Homogeneous Equations.

Real Repeated Roots; Reduction of Order.

Complex Roots.

Unforced Mechanical Vibrations.

The General Solution of the Linear Nonhomogeneous Equation.

The Method of Undetermined Coefficients.

The Method of Variation of Parameters.

Forced Mechanical Vibrations, Electrical Networks, and Resonance.

6. First Order Linear Systems.

The Calculus of Matrix Functions.

Existence and Uniqueness.

Homogeneous Linear Systems.

Fundamental Sets and Linear Independence.

Constant Coefficient Homogeneous Systems.
Complex Eigenvalues.

Repeated Eigenvalues.

Nonhomogeneous Linear Systems.

Euler's Method for Systems of Differential Equations.

Diagonalization.

Propagator Matrices, Functions of a Matrix and the Exponential Matrix.

7. Laplace Transforms.

The Laplace Transform.

Laplace Transform Pairs.

Review of Partial Fractions.

Solving Scalar Problems. Laplace Transforms of Periodic Functions.

Solving Systems of Differential Equations.

Convolution.

The Delta Function and Impulse Response.

8. Nonlinear Systems.

Existence and Uniqueness.

Equilibrium Solutions and Direction Fields.

Conservative Systems.

Stability.

Linearization and the Local Picture.

The Two-dimensional Linear System y1=Ay.

Predator-Prey Population Models.

Information and Table of Contents for Second Edition

Elementary Differential Equations Bound with IDE CD Package, 2/E
Werner E. Kohler, Virginia Polytechnic Institute & State University
Lee W. Johnson, Virginia Polytechnic Institute & State University

ISBN-10: 0321398491
ISBN-13: 9780321398499

Publisher: Pearson
Copyright: 2006
Format: Cloth Bound w/CD-ROM
Published: 09/28/2005
Status: Instock

Table of Contents

1: INTRODUCTION TO DIFFERENTIAL EQUATIONS

1.1    Examples of Differential Equations

1.2    Direction Fields

2: FIRST ORDER DIFFERENTIAL EQUATIONS

2.1   Introduction

2.2   First Order Linear Differential Equations

2.3   Introduction to Mathematical Models

2.4   Population Dynamics and Radioactive Decay

2.5    First Order Nonlinear Differential Equations

2.6    Separable First Order Equations

2.7    Exact Differential Equations

2.8    The Logistic Population Model

2.9    Applications to Mechanics

2.10 Euler�s Method

2.11 Review Exercises



3: SECOND AND HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

3.1    Introduction

3.2    The General Solution of Homogeneous Equations

3.3    Constant Coefficient Homogeneous Equations

3.4    Real Repeated Roots; Reduction of Order

3.5    Complex Roots

3.6    Unforced Mechanical Vibrations

3.7    The General Solution of a Linear Nonhomogeneous Equation

3.8    The Method of Undetermined Coefficients

3.9    The Method of Variation of Parameters

3.10 Forced Mechanical Vibrations, Electrical Networks, and Resonance

3.11 Higher Order Linear Homogeneous Differential Equations

3.12 Higher Order Homogeneous Constant Coefficient Differential Equations

3.13 Higher Order Linear Nonhomogeneous Differential Equations

3.14 Review Exercises

4: FIRST ORDER LINEAR SYSTEMS

4.1    Introduction

4.2    Existence and Uniqueness

4.3    Homogeneous Linear Systems

4.4    Constant Coefficient Homogeneous Systems and the Eigenvalue Problem

4.5    Real Eigenvalues and the Phase Plane

4.6    Complex Eigenvalues

4.7    Repeated Eigenvalues

4.8    Nonhomogeneous Linear Systems

4.9    Numerical Methods for Systems of Differential Equations

4.10 The Exponential Matrix and Diagonalization

4.11 Review Exercises



5: LAPLACE TRANSFORMS

5.1    Introduction

5.2    Laplace Transform Pairs

5.3    The Method of Partial Fractions

5.4    Laplace Transforms of Periodic Functions and System Transfer Functions

5.5    Solving Systems of Differential Equations

5.6    Convolution

5.7    The Delta Function and Impulse Response

6: NONLINEAR SYSTEMS

6.1    Introduction

6.2    Equilibrium Solutions and Direction Fields

6.3    Conservative Systems

6.4    Stability

6.5    Linearization and the Local Picture

6.6    Two-Dimensional Linear Systems

6.7    Predator-Prey Population Models