Math 210 – Differential Equations, Winter 2017


Instructor: Anatolii Grinshpan
Office hours:  Tu 12-1 and Th 12-2, Learning Terrace.

Course information   Terrell’s notes   Academic calendar    Tutoring center  

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

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

              Domain of the solution. Isoclines. Separable equations. Homogeneous equations.

              Reading: Chapters 1, 2. Problems.

 

Week 2. Bernoulli’s equation. Population dynamics. Quiz 1 (Chapters 1, 2).

              A glimpse into PDE: transport equation.

              Reading: Chapters 3, 4. Problems.

 

Week 3. Existence and uniqueness of solutions. Leaking bucket. Quiz 2 (Chapters 3, 4).

              Newton’s cooling law. Integrating factors. Exact equations.

              Reading: Chapters 5-7. Problems.

 

Week 4. Picard’s iteration. Euler’s numerical method. Example. Reading: Chapter 8.

              Example from class. Midterm 1 (Chapters 1-8).

 

Week 5. Spring-mass oscillations. Homogeneous linear equations with constant coefficients. Characteristic roots.

              Reduction of order. Forced oscillations. Method of undetermined coefficients. Resonance.

              Reading: Chapters 9, 10. Problems.

 

Week 6. Superposition. Complex characteristic roots. Fundamental pairs of solutions. Example.

              Quiz 3 (Chapters 9, 10). Multiple spring-mass systems. Example. Boundary-value problems.

              Reading: Chapters 11, 12. Problems.

 

Week 7. Eigenvalues and eigenfunctions. One-dimensional heat equation. Steady-state solutions. The heat kernel.

              Quiz 4 (Chapters 11, 12). Product solutions and boundary-value problems for the heat equation.

              Reading: Chapters 13, 14. Problems.

 

Week 8. One-dimensional wave equation. Series solutions. Bessel’s equation.

              Quiz 5 (Chapters 13, 14). A drum model.

              Reading: Chapters 15, 16.

 

Week 9. Midterm 2 (Chapter 9-16).  Systems of linear equations with constant coefficients. 

              Two-dimensional case. Slope fields. Methods of solution. 

              Reading: Chapters 14, 15, 21. Problems.

 

Week 10. Classification of phase portraits. Phase portrait generator. Purely imaginary eigenvalues. 

                Quiz 6 (Chapters 21-23). Nonhomogeneous systems (mixing in multiple tanks).

 

Mar  20. Questions session: 12-2PM, Curtis 352A.

Mar  24. Office hours: 3-5PM, MRC.

Mar  25. Final exam (all lectures): 1-3PM, Randell 121.