Math 262 – Differential Equations


TR 9:30-10:50 am, room 309 Matheson

Instructor: Anatolii Grinshpan
Current office hours:  TR 11-12:30 or by appointment, 270 Korman

Course information.   Math resource center.   Academic Calendar.

Outline

Jan 9. Introduction. Classification of differential equations.

          Reading assignment: Chapter 1.

      

Jan 11. First order linear equations. Direction fields. Integrating factors.

            Reading assignment: 2.1, 2.2.

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

 

Jan 16. No class.

 

Jan 18. Methods for solving first order ODE:  equations with constant coefficients (page 12),

            undetermined coefficients (problem 5, page 16), integrating factors (2.1), variation of parameters

            (problem 38, page 41), separation of variables (2.2).

 

Jan 23. Quiz: methods of solving first order ODE.  

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

            Reading assignment: 2.4

            Problems: 1-15 (odds), 22, 27, 29.

 

Jan 25. Bernoulli equations. Population dynamics.

            Reading assignment: 2.5

            Problems: 1-7, 17, 22.

 

Jan 30. Homogeneous equations (page 49). Exact equations.

            Reading assignment: 2.6

            Problems: 1-13 (odds), 19, 32.

 

Feb 1.  Quiz: logistic and exact equations.

            Exact equations and integrating factors. Difference equations.

            Reading assignment: 2.7, 2.9

            Problems: 2 a), d),  20  (2.7);  2, 4, 5, 8 (2.9) 

 

Feb 6.   Logistic difference equation.

           

Feb 8.  Test 1. Answers.

 

Feb 13.  Second order linear equations. Constant coefficients: characteristic equation.

              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)

 

Feb 15.  Quiz: Section 3.1.

              Wronskian and linear independence. Abel’s formula. Fundamental solutions.

              Reading assignment: 3.4, 3.5

             

Feb. 20. Case of constant coefficients: repeated and complex roots.

              Problems:  1-6, 17-19 (3.4) and 2-14 (evens), 18, 22 (3.5)

 

Feb. 22. Quiz: Sections 3.4, 3.5.

              Methods for solving second order linear ODE: reduction of order,

              variation of parameters, undetermined coefficients.

              Reading assignment: 3.6, 3.7.

              Problems: 23-25, 31 (3.5), 1-3, 13, 15 (3.6), 1, 2, 5 (3.7).

 

Feb. 27. Variation of parameters. Higher order equations.

              Linear equations with constant coefficients (order n).

              Reading assignment: 4.1, 4.2.

              Problems: 3,  7, 8, 12 (4,1),  11-14, 22, 37 (4.2)

 

March 1. Quiz: Section 3.6. Methods for solving higher order ODE.            

               Reading assignment: 4.3, 4.4.

               Problems: 1, 3, 5, 13, 14 (4.3) and 1, 3, 5, 13 (4.5)

 

March 6. Test 2. Answers.

 

March 8. The Laplace Transform.

                Reading assignment: 6.1, 6.2, 6.3.

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

 

March 13. Quiz: Sections 6.1, 6.2.

                 The Laplace Transform (continued).

                 Reading assignment:  7.1-7.3

                 Problems: examples from class.

 

March 15. Systems of  first order ODE.

                 Analysis of  linear systems in 2 variables.

                 Examples from class (pages 123-128 of the preview).

 

A list of extra credit questions.

 

March 17. Office hours: 5-6+

 

March 19. Final Exam, 8-10 am, Matheson 308.