# TR 9:30-10:50 am, room 209 Rush. Instructor: Anatolii Grinshpan Current office hours:  TR 3:30-5 or by appointment, 270 Korman

Outline

Apr 3. Introduction. Classification of differential equations. Direction fields.

Apr 5. First order linear equations. Integrating factors.

Separable equations.   Homework example.

Problems: 1, 3, 13-15, 38 (2.1) and 1-8 (2.2).

Apr 10. Undetermined coefficients and variation of parameters for first order equations.

Problems:  5 (p. 16), 38 (p. 41), 1-15 (odds), 22, 27, 29 (pp. 75-77).

Apr 12. Quiz: solving first order ODE.

Existence and uniqueness of  solutions. Linear equations vs nonlinear equations.

Reading: p. 49 (homogeneous equations), p. 77 (Bernoulli equations).

Problems:  30-32 (pp. 49-50, no drawing necessary); 27, 29 (p. 77), in class examples.

Apr 19. Quiz: homogeneous and Bernoulli equations.

Problems: 1-7 (p. 88).

Apr 24. Population dynamics (continued). Exact equations.

Problems: 17, 22 (2.5), 1-13 (odds), 19, 32 (2.6).

Apr 26. Exact equations and integrating factors.

May 1.  Euler’s method. Difference equations.

Problems: 2, 4, 5, 8 (explained)  (2.9).

May 3. Test 1: Chapters 1& 2.  Sample. Exam answers.

May 8. Second order linear equations.

Case of constant coefficients: characteristic equation with distinct real roots.

Homogeneous equations: superposition principle. Wronskian determinant.

Problems: 1-7 (odds), 9-12, 28 (3.1); 1-9 (3.2).

May 10. Linear independence and Wronskian. Fundamental solutions.

Case of constant coefficients: characteristic equation with a repeated root.

Problems: 2-14 (evens), 18, 22 (3.5).

May 15. Quiz: 2nd order linear equations.

Abel’s formula. Reduction of order.

Simple harmonic oscillator.

May 17. Case of constant coefficients: characteristic equation with nonreal roots.

Nonhomogeneous equations: structure of solutions.

Method of undetermined coefficients.

Problems: 1-6, 17-19 (3.4), 23-25 (3.5), 1-3, 13, 15 (3.6).

May 22. Quiz: reduction of order, complex roots of characteristic equation.

The method of undetermined coefficients. Examples.

May 24. Variation of parameters. Higher order equations.

Linear equations with constant coefficients (order n).

Problems: 3, 1, 2, 5 (3.7), 7, 8, 12 (4.1), 11-14, 22, 37 (4.2).

May 29. Test 2: Sections 3.1-3.7, 4.1, 4.2. Sample. Exam answers.

May 31.  Undetermined coefficients and variation of parameters for higher order equations.

Problems: 1, 3, 5, 13, 14 (4.3) and 1, 3, 5, 13 (4.4).

June 5.

Problems: 1, 3, 5, 6, 7, 9 (6.1) and 1, 3, 5, 11-13 (6.2).

June 7.    Quiz: Laplace transform.

The Laplace Transform (continued).

Problems: examples from class.

June 11. Questions session (4 P.M. at the office).

June 12. Final exam, 8-10 A.M., Curtis 451.

Focus: homework, examples (textbook, class), midterms, samples, quizzes.

Material: everything that we have covered in class. Expect 6-8 questions with parts

(true/false + midterm type). You can use a one-sided sheet with formulas and theorem statements.