Math 262 – Differential Equations, Fall 2010

Instructor: Anatolii Grinshpan
Office hours:  MTW 5-6, Korman 247, or by appointment, Korman 253.

Sept 20. Introduction to the course.  First order equations.

Sept 21. Separation of variables and integrating factors.

Homework 1: due Tuesday, September 28. (answers)

Sept 27. Existence and uniqueness. Euler’s method. Examples.

Sept 28. Introduction to MATLAB: Moler’s book, tutorial.

Sample scripts: linear spline, contour map and slope field.

Homework 2: due Tuesday, October 5.

Oct 4.  More on integrating factors. Logistic Equation. Phase line.

Oct 5.  Implementation of Euler’s method.

Homework extended: due Tuesday, October 12. (answers, script)

Oct 11. No class (Columbus Day).

Oct 12. Linear equations: homogeneous and not. The structure of solutions.

Mixing model. Homework 3: due Tuesday, October 19. (answers)

Oct 18. Second-order linear equations. Case of constant coefficients.

Oct 19. MATLAB scripts: eulerf, eulerp, numderiv.

Homework 4: due Monday, October 25. Sample test.

Oct 25. Second-order linear equations. Review.

Oct 26. Midterm 1 (lectures of September 20 – October 25).

Nov 2. Harmonic oscillator. The method of undetermined coefficients.

Homework 5: due Tuesday, November 9. (answers)

Nov 8. Two-dimensional homogeneous linear systems with constant coefficients.

Phase plane. Fixed points. Eigendirections. Examples.

Nov 9. More examples. Classification of phase portraits.

Purely imaginary eigenvalues, elliptic trajectories.

Homework 6: due Tuesday, November 16. (answers)

Nov 15.  A two-mass, three-spring system.  Mixing in interconnected tanks.

Repeated eigenvalues, improper nodes.

Nov 16.  MATLAB: phase portrait generator (script).

Matrix exponentials. Homework 7: due Monday, November 22. (answers)

Nov 22.  Matrix exponentials. Review. Sample test.

Nov 23.  Midterm 2 (lectures of  November 1-November 22).

Nov 29. Loose ends: nonhomogeneous systems, large systems, nonlinear systems.

The Runge-Kutta methods. Examples.

Nov 30. MATLAB: Runge-Kutta (scripts: function, plot). John Polking’s software.

Linear and nonlinear examples. Week 11 summary.

Dec 2.  Office hour: 6-7.

Dec 3. Office hour: 6-7.

Dec 6. Final Exam: 7-9 PM, Korman 245 (all lectures).