Math 262 – Differential Equations

TR 9:30-10:50 am, room 209 Rush.

Instructor: Anatolii Grinshpan
Current office hours:  TR 3:30-5 or by appointment, 270 Korman

Course information.   Math resource center.   Academic Calendar.

Outline

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

           First order linear equations with constant coefficients.

           Reading: Chapter 1.

 

Apr 5. First order linear equations. Integrating factors.

           Separable equations.   Homework example.

           Reading: 2.1, 2.2.

           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.

             Reading: 2.4

             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.

 

Apr 17. Homogeneous equations. Bernoulli 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.

             Population dynamics.

             Reading: 2.5

             Problems: 1-7 (p. 88).

 

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

             Reading: 2.6

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

 

Apr 26. Exact equations and integrating factors.

             Reading: 2.7, 2.9.

 

May 1.  Euler’s method. Difference equations.

             Reading: 2.9.

             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.

            Reading assignment: 3.1-3.3. 

            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.

              Reading: 3.5.

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

 

May 15. Quiz: 2nd order linear equations.

              Abel’s formula. Reduction of order.

              Simple harmonic oscillator.

              Reading: 3.4.

             

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

              Nonhomogeneous equations: structure of solutions.

              Method of undetermined coefficients.

              Reading: 3.6, 3.7

              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).

              Methods for solving higher order ODE.

              Reading: 4.1, 4.2.

              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.

               Reading: 4.3, 4.4.

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

 

June 5.    The Laplace Transform.

               Reading: 6.1, 6.2, 6.3.

               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.