Syllabus - Math 285 Version A
Ordinary Differential Equations and Boundary Value Problems

Text: Elementary Differential Equations with Boundary Value Problems, Edwards and Penny (1996)

Chapter 1: First Order Differential Equations (6 days)

1.1 Differential Equations and Mathematical Models

1.2 Integrals as General and Particular Solutions

1.3 Slope Fields and Solution Curves (emphasizing the importance of the existence and uniqueness theorem for the geometric structure of solution families)

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 days)

2.1 Population Models

2.3 Acceleration-Velocity Models

Chapter 3: Linear Equations of Higher Order (13 days)

3.1 Introduction: Second-Order Linear Equations (1)

3.2 General Theory of Linear Equations (including linear independence and Wronskians) (2)

3.3 Homogeneous Equations with Constant Coefficients (including the factorization of constant coefficient operators) (2)

3.4 Mechanical Vibrations (2)

3.5 Nonhomogeneous Equations: Undetermined Coefficients and Variation of Parameters (3)

3.6 Forced Oscillations and Resonance (1)

3.8 Endpoint Problems and Eigenvalues (2)

Chapter 9: Fourier Series (12 days)

9.1 Periodic Functions and Trigonometric Series (1)

9.2 General Fourier Series and Convergence (2)

9.3 Even-Odd Functions. Termwise Differentiation (1)

9.4 Applications of Fourier Series (2)

9.5 Heat Conduction and Separation of Variables (2)

9.6 Vibrating Strings and the One-dimensional Wave Equation (2)

9.7 Steady-state Temperature and Laplace's Equation (including the Dirichlet problem for a disk) (3)

Chapter 10: Eigenvalues and Boundary Value Problems (5 days)

10.1 Sturm-Liouville Problems and Eigenfunction Expansions (2)

10.2 Application of Eigenfunction Series (2)

10.3 Steady Periodic Solutions and Natural Frequencies (1)

Exams: 3 days

Total: 44 days