## Math 286. Differential Equations Plus

Syllabus for Instructors

**Text: Elementary Differential Equations and Boundary Value Problems. 10th Edition, Boyce & DiPrima, Wiley**

**Chapter 1: Introduction (3 lectures)**

1.1: Some Basic Mathematical Models; Direction Fields

1.2: Solutions of Some Differential Equations

1.3: Classification of Differential Equations

1.4: Historical Remarks (reading only)

**Chapter 2: First Order Differential Equations (7 lectures)**

2.1: Linear Equations; Method of Integrating Factors

2.2: Separable Equations

2.3: Modeling with First Order Equations (reading only)

2.4: Differences Between Linear and Nonlinear Equations

2.5: Autonomous Equations and Population Dynamics

2.7: Numerical Approximations: Euler's Method (time permitting)

2.8: The Existence and Uniqueness Theorem (time permitting) Miscellaneous Problems

**Chapter 3: Second Order Linear Equations (10 lectures)**

3.1: Homogeneous Equations with Constant Coefficients

3.2: Solutions of Linear Homogeneous Equations; the Wronskian

3.3: Complex Roots of the Characteristic Equations

3.4: Repeated Roots; Reduction of Order

3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients

3.6: Variation of Parameters

3.7: Mechanical and Electrical Vibrations

3.8: Forced Vibrations

**Chapter 4: Higher Order Linear Equations (3 lectures)**

4.1: General Theory of nth Order Linear Equations

4.2: Homogeneous Equations with Constant Coefficients

4.3: The Method of Undetermined Coefficients

4.4: The Method of Variation of Parameters (time permitting)

**Chapter 7: Systems of First Order Linear Equations (12 lectures)**

7.1: Introduction

7.2: Review of Matrices

7.3: Systems of Linear Algebraic Equations; Lin. Ind., Eigenvalues, Eigenvectors

7.4: Basic Theory of Systems of First Order Linear Equations

7.5: Homogeneous Linear Systems with constant Coefficients

7.6: Complex Eigenvalues

7.7: Fundamental Matrices

7.8: Repeated Eigenvalues

7.9: Nonhomogeneous Linear Systems

**Chapter 10: Partial Differential Equations and Fourier Series (13 lectures)**

10.1: Two-Point Boundary Value Problems

10.2: Fourier Series

10.3: The Fourier Convergence Theorem

10.4: Even and Odd Functions

10.5: Separation of Variables; Heat Conduction in a Rod

10.6: Other Heat Conduction Problems

10.7: The Wave Equation: Vibrations of an Elastic String

10.8: Laplace's Equation

**Chapter 11: Boundary Value Problems and Sturm-Liouville Theory (2 lectures)**

11.1: The Occurrence of Two-Point Boundary Value Problems

11.2: Sturmâ€“Liouville Boundary Value Problems

**Exams, review and leeway (6 lectures)**

**Total: 56 lectures **

updated 8/15/17

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