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

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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.
  • Additional Resources
  • Direction Field Plotter: This Java applet will display the phase portrait for any 2x2 system of differential equations. Specify the equation in the boxes below the graph and click New Function to see the field. To see the solution curves through a specific point, click on that point in the phase portrait. Click on lots of points if you wish. For some problems you will want to change the viewing window (see the boxes along the right edge of the window, and click Set Limits).
  • ODE PowerTool [HTML] [Maple Worksheet] , a collection of 35 Maple worksheets for an introductory course in differential equations. Lesson 21 contains the nice graphical views of linearized systems about equilibrium solutions. Lessons 11 and 13 are also quite appropriate for this course.

  • Created January 8, 2012, by Matthew Miller.
    Last modified on April 2, 2012, by Douglas Meade.