
Instructor: Anatolii Grinshpan
Office hours: MTW 56, 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. Secondorder linear equations. Case of constant coefficients.
Oct 19. MATLAB scripts: eulerf, eulerp, numderiv.
Homework 4: due Monday, October 25. Sample test.
Oct 25. Secondorder 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. Twodimensional 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 twomass, threespring 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 1November 22).
Nov 29. Loose ends: nonhomogeneous systems, large systems, nonlinear systems.
The RungeKutta methods. Examples.
Nov 30. MATLAB: RungeKutta (scripts: function, plot). John Polking’s software.
Linear and nonlinear examples. Week 11 summary.
Dec 2. Office hour: 67.
Dec 3. Office hour: 67.
Dec 6. Final Exam: 79 PM, Korman 245 (all lectures).