MTH 480: SYSTEMS OF ODES - Winter 2014
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General information
Assignments
Assignments and schedule
Policy on written assignments: For full credit, written assignments should be prepared in legible English and using correct and complete mathematical expressions.
Unless stated otherwise, the assignments must be prepared individually by each student. Group work is allowed, but no exchange of written materials is permitted.
Homework will be collected at the beginning of the class period when it is due.

Schedule

  1. 1/6/14: Introduction. Classification: order, scalar vs system, linearity, (non)autonomous ODE, (non)homogeneous ODE. [READ HSD 1.1-1.3]
    Review growth/decay/equilibrium models. Solution vs qualitative behavior.
    Slope fields and phase line.
    HW 1 due Friday 1/10/14 in class. Problems: [HSD] Chap.1/1,2ae
    problems page
  2. 1/8/14: Continue linear scalar ODE models. Sink, source, equilibrium. Worksheet 1.
  3. 1/10/14: Modeling clinic. Worksheet 2.
  4. 1/13/14: Review Existence/Uniqueness theory. Logistics model revisited and local linearizations. Another way to determine stability of equilibria from analysis of perturbations.
    Dependence on parameters. Bifurcations.
    HW 2 due Friday 1/17/14 in class. Problems: [HSD] Chap.1/3b,5,6,11,12
  5. 1/15/14: meet in Kidder 028 computer lab (underneath Math Learning Center). LAB1.html.
  6. 1/17/14: wrap up [HSD] Chapter 1 and stability analysis for scalar ODEs. [Go over x'=ax+sin(x)].
    Start systems of ODEs (linear, constant coefficients). When is the solution given by CeAt. How to construct exponential of a matrix ? What happens for matrices similar to diagonal matrices.
    Work on the linear algebra worksheet.
  7. 1/20/14: MLK Holiday (no class)
  8. 1/22/14: Clinic on linear algebra using the worksheet. Method of solving a linear, constant coefficient system of ODEs with a diagonalizable matrix. Read [HSD], Chapter 2.
    HW 3 due Monday 1/27/14 in class. Problems: [HSD] Chap.2/2,3.
  9. 1/24/14: Solution and qualitative analysis of a 2x2 linear system when the complete system of eigenvectors is available. Case of real distinct eigenvalues. Read [HSD], Chapter 3.
  10. 1/27/14: Continue 2x2. Case of complex eigenvalues, one zero eigenvalue, and of defective matrices.
  11. 1/29/14: meet in Kidder 028 computer lab. LAB2.html.
  12. 1/31/14: More on solving case 2x2.
    HW 4 due Friday 1/31/14 in class. Problems: [HSD] Chap.3/1, 2. (date due extended to Wednesday, 2/5/14).
  13. 2/3/14: Finish planar systems. Worksheet with systems in canonical form.
  14. 2/5/14: Classification of planar systems with determinant/trace plane. Continue worksheets, also non-canonical forms. (Read [HDE] Chapter 4.1-4.2).
    HW 5 due Friday 2/7/14 in class (dealyed to Monday, 2/10 due to campus closure). Problems: [HSD] Chap.2/5,7. Chap.3/5,16.
    Extra problems: Chap.3/9,10.
  15. 2/7/14: Review for exam.
    Due to campus closure, please proceed with individual review of material from Chapters 1-3 from the textbook. Use class notes, lab assignments, and worksheets for practice.
    Extra office hours: 17:00-18:00 CANCELLED (CAMPUS CLOSURE) I am offering extra office hours any time Monday 9:00am-noon en lie of extra Friday office hours.
  16. 2/10/14: MIDTERM in class.
  17. 2/12/14: Meet in computer lab. LAB3.html.
    "Snow day" extra credit worksheet due Friday, Feb. 14 (worth 5 points added to Midterm score).
  18. 2/14/14: Linear algebra and systems in n>2 dimensions [HSD Chapters 5-6]. Fundamental Theorem of Linear Algebra.
    HW 6 part a) due February 2/21/14. [RJ=Valentine's Day special]. Analyze the case from Strogatz paper (handout in class) with
    a11<0, a12>0, a21>0, a22>0. Answer the question: "can a cautious lover find true love with an eager-beaver" ?
  19. 2/17/14: Recap matrix exponential. Start nonlinear systems. Nullclines and equilibria. Qualitative behavior of a linearized system.
    HW 6 part b) due February 2/21/14. [HSD] Chap 7/1a,8. Chap. 8/1 abc for (i),(ii).
    Extra: Chap.7/2,9
  20. 2/19/14: [HSD 8.1] How to change variables to make a nonlinear system linear. What then ? Is it always possible ?
  21. 2/21/14: Examples. Change variables to polar coordinates. (Always possible ? How ?) Read [HSD 8.2-8.3]. Hartman-Groban Theorem.
  22. 2/24/14: Ideas of proof for Hartman-Groban theorem. Topologically conjugate systems (read [HSD] 4.2 for background)
    HW 7 due February 2/28/14. [HSD] Chap 8/1 (complete those parts not included in HW6; do not turn in). Turn in:
    1. Chap 8/2;
    2. Chap 8/8 for a=0.
    3. Use polar coordinates to discuss behavior of the system x'=-y +xy2, y'=x+y3.
    4. Complete problems 3.1, 3.2 from Lab 4.
  23. 2/26/14: Meet in computer lab for LAB4.html.
  24. 2/28/14: Wrap up local behavior of nonlinear systems. Worksheet and group work. Read [HSD] 8.4, Stable, asymptotically stable (=stable plus convergence of trajectories), and unstable equilibria (aka fixed points).
    HW (do not turn in): complete all the worksheet problems.
  25. 3/3/14: Global behavior of nonlinear systems.
    Special systems: conservative, Liapunov, gradient, and Hamiltonian.
  26. 3/5/14: Meet in computer lab for LAB5.html .
  27. 3/7/14: Continue examples of special systems. Exercises with Liapunov functions.
    HW 8 due March 3/12/14. [HSD] Chap 9/9,11; Chap 11/2.
    Extra practice (do not turn in): Chap. 9/1,6-8.
  28. 3/10/14: Modeling bio/eco systems and chemical reactions (loosely speaking, this material can be found in Chapters 10-11).
  29. 3/12/14: Meet in computer lab. Worksheet on BIFURCATIONS. (Group work is allowed, turn in the worksheet for credit).
  30. 3/14/14: REVIEW: recap global behavior of nonlinear systems.
  31. MONDAY 3/17/14: Help session 3:00-5:00 Kidd 356.