Math 210 – Differential Equations, Winter 2016 Instructor: Anatolii Grinshpan
Office hours:  Tu 12-1 and Th 12-2, Korman 249.

Week 1. First-order equations. Slope field. Slope field plotter. Phase line.

Stationary solutions.  Banker’s equation. A gallery of  equations.

Reading and exercises: Chapters 1, 2. Problems.

Week 2. Quiz 1 (Chapters 1, 2). A glimpse into PDE: transport equation.

Population dynamics. Existence and uniqueness of solutions. Leaking bucket.

Reading and exercises: Chapters 3-5. Problems.

Week 3. Quiz 2 (Chapters 3, 4). Newton’s law of cooling. Integrating factors. Exact equations.

Reading and exercises: Chapters 5-7. Problems.

Week 4.  Euler’s numerical method. Example. Reading and exercises: Chapter 8.

Quiz 3 (Chapters 7, 8). Spring-mass oscillations. About Babylonian astronomers.

Week 5.  Midterm 1 (Chapters 1-8). Spring-mass oscillations. Homogeneous second-order linear equations.

Space of solutions. Forced oscillations. Method of undetermined coefficients.

Reading and exercises: Chapters 9, 10. Problems.

Week 6.  Linear equations with constant coefficients. Complex numbers. Complex and repeated characteristic values.

Reduction of order. Resonance. Example. Quiz 4 (Chapters 9, 10). Multiple spring-mass systems.

Reading and exercises: Chapters 11, 12. Problems.

Week 7.  Multiple spring-mass systems. Boundary-value problems. Eigenvalues and eigenfunctions.

Quiz 5 (Chapters 11, 12). One-dimensional heat equation. Heat kernel.

Reading and exercises: Chapters 13, 14. Problems.

Week 8.  Product solutions. Boundary-value problems for the heat equation.

Quiz 6 (Chapters 13, 14). One-dimensional wave equation. A drum model. Bessel’s equation. Series solutions.

Reading and exercises: Chapters 15, 16.

Week 9.  Midterm 2 (Chapters 9-16). Systems of linear equations with constant coefficients. Two-dimensional case. Slope fields.

Methods of solution. Phase portrait. Reading and exercises: Chapters 14, 15, 21 (and 16-20 on Linear Algebra).

Week 10.  Classification of phase portraits. Purely imaginary eigenvalues. Quiz 7 (Chapters 21-23).

Nonhomogeneous systems (mixing in multiple tanks). Nonlinear systems (predator-prey).

3D systems (helical orbits, Lorenz attractor, Dzhanibekov effect).

Reading and exercises: Chapters 22-25.

Mar 11.    Discussion session: 4:10-5:30+, Lebow 241.

Mar 15.    Final exam (all lectures): 1-3 PM, Lebow 135. 