Math 286. Differential Equations Plus
Syllabus for Instructors

Text: Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modelling, 4th Edition, Prentice-Hall, 2008

Chapter 1. First Order Differential Equations (6 lectures)

1.1 Differential Equations and Mathematical Models

1.2 Integrals as General and Particular Solutions

1.3 Slope Fields and Solution Curves

1.4 Separable Equations and Applications

1.5 Linear First-Order Equations

1.6 Substitution Methods and Exact Equations

Chapter 2. Mathematical Models and Numerical Methods (2 lectures)

2.1 Population Models

2.3 Acceleration-Velocity Models

Chapter 3. Linear Equations of Higher Order (13 lectures)

3.1 Introduction: Second-Order Linear Equations

3.2 General Solutions of Linear Equations

3.3 Homogeneous Equations with Constant Coefficients

3.4 Mechanical Vibrations

3.5 Nonhomogeneous Equations and Undetermined Coefficients

3.6 Forced Oscillations and Resonance

3.8 Endpoint Problems and Eigenvalues

Chapter 4. Introduction to Systems of Differential Equations (1 lecture)

4.1 First Order Systems and Applications

Chapter 5. Linear Systems of Differential Equations (13 lectures)

5.1 Matrices and Linear Systems

5.2 The Eigenvalue Method for Homogeneous Systems

5.3 Second-Order Systems and Mechanical Applications

5.4 Multiple Eigenvalue Solutions

5.5 Matrix Exponentials and Linear Systems

5.6 Nonhomogeneous Linear Systems

Chapter 9. Fourier Series Methods (12 lectures)

9.1 Periodic Functions and Trigonometric Series

9.2 General Fourier Series and Convergence

9.3 Fourier Sine and Cosine Series

9.4 Applications of Fourier Series

9.5 Heat Conduction and Separation of Variables

9.6 Vibrating Strings and the One-Dimensional Wave Equation

9.7 Steady-State Temperature and Laplace's Equation

Chapter 10. Eigenvalues and Boundary Value Problems (5 lectures)

10.1 Sturm-Liouville Problems and Eigenfunction Expansions

10.2 Applications of Eigenfunction Series

10.3 Steady Periodic Solutions and Natural Frequencies

Examinations, review and leeway (4 lectures)

Total: 56 lectures