#### MATH 520 -- Ordinary differential equations Professor Matt Miller (miller@math.sc.edu) Section 1, TTh 12:30-1:45, LC 405

Text: Elementary Differential equations by Boyce and Diprima, 9th ed., 2008.

• Class topics and problems
You will observe that I assign homework BEFORE we talk about a topic. That is because I really want you to READ the material, and struggle a bit with the problems; then the class and my lecture, or the group work, will make more sense to you, and you will be in a better position to ask good questions. ATTEMPTING problems and seeing where you get stuck is much more useful (albeit painful) than churning through problems that you basically already know how to do!
• Jan. 10-12. Basic solution techniques. Read section 1.1; we will come back to it. What is the main idea? Go on to section 1.2. Do problems 1.2, #1a, 2a, 3, 7, 8, 12, 13. Read sections 2.1 and 2.2. The key ideas are separation of variables, integrating factors, and dependence on initial conditions. Do problems 2.1 #1, 4, 5, 6, 7, 15-17, 21-22, 25, 38. Do problems 2.2 #1-4, 9, 11, 13.
• Jan. 17-19.Existence and Uniqueness of solutions, second order equations We investigate the differences between linear and non-linear equations. Read sections 2.4 and 2.8. Do problems 2.4 #1, 2, 3, 13, 15. Skip over to section 3.1 and do problems 1, 2, 3, 5, 9, 10, 17. Look ahead to section 3.2 and problems 1, 2, 4, 7, 13, 14, 22, 23, 24, 25, and section 3.3 problems 1, 2, 3, 7, 8, 9, 17, 18. The solution techniques of these are all basically the same.
• Jan. 24-26. More on second order equations Read section 3.5 and do problems 1, 2, 13, 16. Read section 3.6 and do problems 1, 2, 5, 6, 9. Check out the complicated integration by parts problem here
• Jan. 30- Feb. 1. Autonomous equations in one variable. Read section 2.5 and do problems 1, 3, 7, 14, 16, 20. Here is the solution to problem 3.6 #1.
• Feb 7-9. Linear algebra, Test #1. Read section 7.1 and do problems 1-7. Read section 7.2 and do problems 22-26. Read section 7.3. Here, after many attempts to get signs straight, is my solution to problem 3.5 #2.
• Feb 14-16. Beginning of systems, more linear algebra. Read section 7.3 and work on problems #7-9, 13-18, 22
• Feb 21-23. Systems, cont. Read section 7.4 and work on problems #6, 7. Read section 7.5 and work on problems # 1, 3, 4, 5, 15, 16, 21, 22, 24-27, 29.
• Feb 28-March 3. Systems, cont. Read section 7.6 and work on problems #1, 2, 5, 9, 13, 15, 14, 15, 18, 25bcd and 28.
• March 20-22. Fundamental matrices and Repeated Roots. Read section 7.7 and work on problems #1-12. Read section 3.4 (through the summary on p. 170) and work on problems #1-10, 15-18. Also, read section 4.2 and look at problems from #11-36. (The hardest part of these problems could be factoring the characteristic polynomial.)
• March 27-29. Repeated eigenvalues. Read section 7.8 and work on problems #1-4 and 7-10.
• April 3-5. Nonhomogeneous Linear Systems. Read section 7.9 and work on problems #1-12.
• April 10-12. Phase Plane, and Locally Linear Systems. Read section 9.1 and work on problems #1-15. Read section 9.3 and work on problems #1-3 and 5-18. (See the Additional Resources at the bottom of this page.)
• Exams for Spring, 2012
• FIRST EXAM: Thurs, 9 Feb. (day 10) and the solution key. Be in class to know what will be covered!
• SECOND EXAM: Thurs, 15 March (day 18) and the solution key. The exams covers what we did from sections 7.1 to 7.6. Don't forget that in section 7.1 we had the assignement (in class) of problems #1, 2, 3, 4, 5, 6, 7.
• THIRD EXAM: Thurs, 12 April (day 26) and the solution key.
• FINAL EXAM: Tuesday, 1 May, 2:00 pm.