# Syllabus Math 286

## 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: Sturm–Liouville Boundary Value Problems

Exams, review and leeway (6 lectures)

Total: 56 lectures

updated 8/15/17