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.