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.
Sept 27. Existence and uniqueness. Euler’s method. Examples.
Homework 2: due Tuesday, October 5.
Oct 4. More on integrating factors. Logistic Equation. Phase line.
Oct 5. Implementation of Euler’s method.
Oct 11. No class (Columbus Day).
Oct 12. Linear equations: homogeneous and not. The structure of solutions.
Oct 18. Second-order linear equations. Case of constant coefficients.
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.
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.
Nov 15. A two-mass, three-spring system. Mixing in interconnected tanks.
Repeated eigenvalues, improper nodes.
Nov 16. MATLAB: phase portrait generator (script).
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.
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).