List of Lecture topic, references in text and exercises


1.  Jan 21  Direction Fields and intro to differential equationsD: 
Sections 1.1, 1.2 1.3  Exercises: pg 7, 1-6, pg 8 11-20, pg 24 1-8.

2. Jan 23  Linear Equations:  section 2.1 page 16 3-5 page 39 1-6, 13,15, 17.

3. Jan 26  More on linear equations, examples: section 2.1 (again) section 2.3,
 page 40, 28,31 ; page 59-62 1,3, 8, 11, 13.

4. Jan 28 More on linear equations, section 2.3; page 59-62; 1,3,8,11,13. 

5. Jan 30:  Autonomous equations, section 2.5: pg 88 1-6, pg 89 15, 17.

6. Feb 2:   Linearizations:  See notes on Linearization.  As a exercise,
 find the linearizations at the critical (fixed) points in the exercies
 on page 88, 3-6.

7. Feb 4: First order difference equations, Section 2.9; page 129, 1 - 6.

8. Feb 6: More on first order difference equations; fixed points, periodic

 points and  linearizations.  page 129,  14, 15.

9. Feb 9  Review for exam

10.Feb 11  Discussion of the project

11. Feb 13  Chaos; intro to higher order ODE  Sections 3.1, 4.1 pg 142 1-16,
page230  11-20.

12. February 16; Basic solutions; 3.1 and 3.4 page 142 1-16.

13. February 18; More on complex numbers, sines and cosines. Section 3.4
Page 164, 1-16.

14. and 15. February 20-23; Complex functions; Spaces, Vector spaces,
linear independence,   basis, dimension, matrix, determinant, the vector
space of solutions of a  linear equation, basis of the vector space
of solutions = fundamental    set of solutions; sections 3.2; skip 3.3.
page 152 #27 page 222, #7-10.

15. February 25; Final discussion of bases for a vector space.

16. February 27; Undetermined coefficients; section 3.6; page 184-185:  1-18.

17. March 2; Springs, period, frequency, amplitude. Section 3.8; page 203 1-4.,
page 204 #24.

18. March 4, Resonances.  Section 3.9; page 214 1-4, page 215 # 15
page 216 18.,19

19. March 6  Linear systems of first order equations, some linear algebra,
basic idea of the solution method, 7.1, 7.2 page 372 1-17 page 373 22-24.

20. March 9  Solving systems of linear equations, eigenvalues
and eigenvectors 7.3  page 383 1-10; 384 15-24

21. March 11  Homogeneous equations with constant coefficients. 7.5 page
398 1-17.

22. March 13 Complex Eigenvalues. 7.6 page 410 1-8, 9, 10.

23. March 23  Stability of linear systems, 9.1 page 492-3 1-12 (classify
as a stable or unsablle node, stable or unstable spiral, or a saddle).
Guest lecture by Professor Lorenzo Sadun.

24. March 25  Review for Exam

25.  March 27 Exam given in lecture section

26.  March 30 Discussion of class projects

27.  April 1   Examples of systems and conservation laws.

28.  April 3   Enzyme reactions and some basic mechanics problems

29.  April 6  Autonomous systems and stability:  Section 9.2  Page 501-
502  1-4; 5-22.

30.  April 8:  Linearization near a fixed point:  Section 9.3 page 511, 1-4
page 511 5-16.

30. April 10:  More on linearization; the SIRS model, 9.4 and 9.5;
page 525, 1-6; page 534, 3-5.

31. April 13; Power series solutions; Chapter 5.2 page 2, 1-14.

32. April 15;  Two point boundary problems, 10.1,  14-20.

33. April 17; Orthogonal bases and Fourier series, 10.2  See problem 29
on page 587. 

34. April 20; Fourier series, 10.2 13-18.

35.April 22: Even  and odd functions, Cosine and Sine series 10.4;
page 600 15-22.

36. April 24;  The Fourier convergence theorems; the Hilbert space length
norm.  !0.3 page 592 # 17;  page 592 1-6; 

37. April 27: Separation of variables: 10.5.  page 610, 1-6, 7, 8.

37. April 29: Vibrations of a guitar string: 10.7 page 632, 1-8.

39. May 1: Harmonic functions in a circle: 10.8 page 643-645; page 646, 5-7.

40. May 4; Review for last midterm

41. May 6; Last midterm (in lecture)

42. May 8; Wrap up on  course material.