# 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

Outline

Jan 9. Introduction. Classification of differential equations.

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

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).

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

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

Problems: 1-7, 17, 22.

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

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

Exact equations and integrating factors. Difference equations.

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

Feb 6.   Logistic difference equation.

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

Homogeneous equations: superposition principle. Wronskian determinant.

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.

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.

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).

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

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

March 8. The Laplace Transform.

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).

Problems: examples from class.

March 15. Systems of  first order ODE.

Analysis of  linear systems in 2 variables.

A list of extra credit questions.

March 17. Office hours: 5-6+

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