Math 262 – Differential Equations, Fall 2010

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

Syllabus    Academic calendar    Math resource center   MIT video lectures

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 1.  Superposition. Wronskian and fundamental pairs. Abel’s theorem.

 

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).