Here is a list of lectures and some exercises from the book which you should be able to solve.Di not hand them in. Lecture 1: (Jan 19) Overview, discussion of differential equations, worked examples of first order linear equations with constant coefficients, both homogeneous and inhomogeneous. 2.1 exercises page 25-26 1, 2, 3-6(the first part without the computer), 2.4 page 55 1, 2 Lecture 2: (Jan 21) Using dfield to analyze differential equations. Separable equations. More examples. Chapter 2.1 (page 21- page 25 exercises 3-6, 10,11,12-15. Chapter 2.2: page 35, 1-12, 24,25,26. Lecture 3: Jan 21: General theory of linear equations. Chapter 2.4 pages 47 and 48, and page 41 of chapter 4.1. Exercises: page 55 1-5 (etc),12,13 page 145 1-8, 13-16. Chapters 2.3 and 2.6 will not be covered and chapters 2.7 and 2.8 will be covered only briefly. We want to get on to 2.9 and chapter 3. Lecture 4: Theoretical Concepts. Existence, uniqueness, time of existence, continuous dependence on initial data, stability. A brief survey of chapters 2.7, 2.8 and beginning of 2.9: Exercises page 86 #1-6, 27, 28 Lecture 5: Feb 2 Autonomous equations and stability. Chapter 2.9:Exercises page 100-101, 1-6,15-22. See the notes on linearization. Lecture 6: Feb 4 Population and mixing problems. Chaptesr 2.5 and 3.1 Page 62 1-9; page 1-7,10,12,13,16,18. You will have a guest lecturer, Orit Davidovich. Lecture 7: Feb 9: More 2.5 and 3.1. Review for exam. Exam: Feb 11 Lecture 8: Feb 16 Solving higher order equation with constant coefficients, complex numbers, Section 4.3. Exercises at the end of the chapter are all useful. although you do not have to know how to do 17-24. Numbers 37 and 38 are extra credit useful. You will have Orit as a guest lecturer again. Lecture 9:Feb 18 More on complex numbers and solutions. The exercises at the end of the chapter are all useful. Lecture 10: Feb 23 More on complex functions, Undetermined coefficients 4.3, 4.5 Exercises on page 172 are all useful Lecture 11: Feb 25 Forced vibrations and resonance, 4.7 Exercises page 186 16-19. Lecture 12: March 2 Vector spaces and vector spaces of solutions to differential equations; 4.1, 7.1 page 145 1-8, 13-16 22, 23, 24, 25 Lecture 13:March 4 Vectors and matrices 7.1, 7.2; page 283 27-54. Lecture 14: March 9 Solving linear equations, bases for a null space 7.3, 7.5 page 299 1-18 page 317 25-32. Lecture 15: March 11 Square matrices and determinants, 7.6 and 7.7 page 321 2, 4-11, 12-19 page 329 22-41. Lecture 16: March 23 Solving linear equations; eigenvectors and eigenvalues, 9.1, 9.2 and 9.5 page 376 1-12, 16-25, page 389 1-6. Lecture 17: March 25 More on eigenvalues and eigenvectors; solving linear equations in the complex case. (.2 390, 7-12, 15, 16-21. Lecture 18: Review for Exam Sections 4.1-4.5;sections 7.1-7.7 sections 9.1-9.2. Exam March 31 in your TA session. Lecture 19: April 1 Examples of systems, fixed points, pplane diagrams 8.1-8.4; page 352 1-6 (part ii). 7-11. page 359 1-10,18-21 Lecture 20: April 6 Stability of linear systems;linearization near a fixed point 9.3,9.7,10.1.page 401 1, 10-15, 16-22.page 468 1-8 (ii,iii), Lecture 21: April 8 Worked Examples: competition,preditor-prey and SIRS model, example 10.1.9,page 469, 21-27. Lecture 22: April 13 Power series solutions; 11.1,11.2,page 554, 1-20. Lecture 23: April 15 Orthogonal bases, Fourier series, formulas 12.1-12.2 page 604 1-16. Lecture 24: April 20 Even and Odd functions, sine and cosine series; 12.3 Lecture 25: April 22 Separation of Variables, 13.2-13.4 page 643, 5-8 page 653, #10,17 Lecture 26: April 27 Vibrations of a guitar string, 13.3 Lecture 27: April 29 Review for exam: sections 9.3,9.7,9.8, 10.1,10.2,10.4, 11.2, 12.1,12.2,12.3, 13.1-13.4(separation of variables and series solutions, no need to remember all the equations). Exam: May 4 Lecture 28: May 6 Wrap up of course Projects due: May 10 (late projects will not be graded until after the final). Final: May 13, 9-12