## Math 285. Differential Equations Syllabus for Instructors

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

Chapter 1: Introduction
1.1: Some Basic Mathematical Models; Direction Fields (1)
1.2: Solutions of Some Differential Equations (1)
1.3: Classification of Differential Equations (1)
1.4: Historical Remarks (Assign for reading only)

Chapter 2: First Order Differential Equations
2.1: Linear Equations; Method of Integrating Factors (2)
2.2: Separable Equations (1)
2.3: Modeling with First Order Equations (Optional?)
2.4: Differences Between Linear and Nonlinear Equations (1) (Cover Bernoulli equation in the problems)
2.5: Autonomous Equations and Population Dynamics (2)
2.6: Exact Equations and Integrating Factors (Optional. We de-emphasized this in the past)
2.7: Numerical Approximations: Euler's Method (Assign as reading)
2.8: The Existence and Uniqueness Theorem (This is the proof. Optional)
2.9: First Order Difference Equations (Skip)
2.M: Miscellaneous Problems (1) (Work through some reducible second order equations)

Chapter 3: Second Order Linear Equations
3.1: Homogeneous Equations with Constant Coefficients (1)
3.2: Solutions of Linear Homogeneous Equations; the Wronskian (1)
3.3: Complex Roots of the Characteristic Equations (1)
3.4: Repeated Roots; Reduction of Order (1)
3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients (1)
3.6: Variation of Parameters (1)
3.7: Mechanical and Electrical Vibrations (2)
3.8: Forced Vibrations (2)

Chapter 4: Higher Order Linear Equations
4.1: General Theory of nth Order Linear Equations (1)
4.2: Homogeneous Equations with Constant Coefficients (1)
4.3: The Method of Undetermined Coefficients (1)
4.4: The Method of Variation of Parameters (Optional)

Chapter 10: Partial Differential Equations and Fourier Series
10.1: Two-Point Boundary Value Problems (3)
10.2: Fourier Series (2)
10.3: The Fourier Convergence Theorem (1)
10.4: Even and Odd Functions (1)
10.5: Separation of Variables; Heat Conduction in a Rod (1)
10.6: Other Heat Conduction Problems (1)
10.7: The Wave Equation: Vibrations of an Elastic String (2)
10.8: Laplace's Equation (2)

Chapter 11: Boundary Value Problems and Sturm-Liouville Theory
11.1: The Occurrence of Two-Point Boundary Value Problems (1)
11.2: SturmÐLiouville Boundary Value Problems (1) (Skip the proofs)
11.3: Nonhomogeneous Boundary Value Problems (Skip)
11.4: Singular SturmÐLiouville Problems (Skip)
11.5: Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion (Skip)
11.6: Series of Orthogonal Functions: Mean Convergence (Skip)

Exams, review, and leeway (6 lectures)

Total: 44 lectures

updated 8/16/17