Topics and Assignments, day by day, to be updated after each class.

• 1. Week 1, Wed, Jan 18. Integration Review and 1.1, Introduction to D.E. Assignment: Print Integration Review Problems and do the integration. Review what you need to know from your calculus book. Then read 1.1 and do p. 5, 1-5 all, 8-10 all, 13-16 all.
• 2. Fri, Jan 20. 1.2, Solutions and Initial Value Problems. Assignment: p. 14, 1-11 odd, 14-18 all, 22, 23-27 odd. Learn the statement of Theorem 1.
  
  
• 3. Week 2, Mon, Jan 23. 2.1 The falling body with air resistance. 2.2 Separable differential equations. Assignment: Work through the falling body problem as done in class. Try doing it looking at notes as little as possible. Then p. 46, 7-29 odd, 31 a-c. Handouts relating to last week: Integration Review Answers. Also notes on initial value problems and 1.2 Theorem 1.
• 4. Wed, Jan 25. 2.3 Linear Differential Equations. Handout on the method. Assignment: p. 54, 1-21 odd, 25 (do the integration of part b on your graphing calculator), 35 (We will be doing more of this kind of problem later in the course). Handout on two 2.2 problems. Note on the falling body problem done in class Monday. The assumption throughout is that positive velocity is downward. That is why the terminal velocity (the C=0 line) is positive, why throwing an object upward is a negative initial condition, and why throwing an object downward is a positive initial condition.
• 5. Fri, Jan 27. 2.4 Exact Differential Equations. Assignment: p. 65, 1-9 all, 11-25 odd.
  
  
• 6. Week 3, Mon, Jan 30. Review Handout on Exam 1 Assignment:Do or do again p. 5, 2, 3, 5, 6; p. 14, 1, 11, 23-27 all; p. 48, 33; p. 81, 1-7 odd, 13. Review also all previously assigned problems. If you need help, see me Wednesday either before class (from about 8:30), after class, or between 12 and 1. You can also e-mail me questions on Tuesday or Thursday.
• 7. Wed, Feb 1. Review Additional review problems which can be done by methods covered in class. Answers to those problems.
• 8. Fri, Feb 3. Exam 1 on Integration, 1.1, 1.2, 2.1-2.4 .
  
  
• 9. Week 4, Mon, Feb 6. 4.1 Introduction to second order linear differential equations. Mass spring problem. p. 159, 1-7 odd, 8, 9.
• 10. Wed, Feb 8. 4.2. Second order homogeneous linear differential equations with constant coefficients. Handout outline of material covered in class. Assignment: p. 167, 1-7 odd, 13-25 odd, 27-29 using Definition 1 and also the Wronskian. If you have any questions about partial credit or adding of points on the exam see me.
• 11. Fri, Feb 10. 4.3. The complex case. Assignment: p.177, 1-23 odd, 24, 25, 28, 29, 32, 33, A: Use the Wronskian to show e^(r1 t) and te^(r1 t) are linearly independent., B: Use the Wronskian to show e^(alpha t)cos( beta t) and e^(alpha t) sin (beta t) are linearly independent.
  
  
• 12. Week 5, Mon, Feb 13. Maple demonstration and 4.3. Undetermined Coefficients. Handout on the method. Assignment: p. 186, 9, 11, 13, 14, 17, 18, 23. First handin homework assignment. Due in class Wednesday Mar 1. Handout showing how to use Maple to plot solutions of first order differential equations. Handout Maple worksheet approximately what was done in clase.
• 13. Wed, Feb 15. Class meets in the math department computer lab, Cushwa 1062, today.
• 14. Fri, Feb 17. 4.3 continued. Assignment: p. 186, 9, 11, 13, 14, 17, 18, 23. (Same assignment as given Monday.)
  
  
• 15. Week 6, Mon, Feb 20. 4.3 and 4.4 continued. A brief look at how numerical methods work to solve differential equations, as in Section 1.4. A Happy Half Hour With Maple Using Maple to help with the drudgery of 4.4 problem 16. Assignment: p. 186, 1-7 odd, 15, 19, 21, 27-31 odd. p. 192, 3, 5, 9, 11, 13, 19, 25, 27, 31-35 odd.
• 16. Wed, Feb 22. 4.6. Variation of Parameters. Handout on the method. A Happy Half Hour With Maple illustrating how Maple can be used to solve and graph a particular solution for problem 19. Assignment: p. 197, 1-11 odd, 15 hint: Use undetermined coefficients on the last two terms of f(t)., 19.
• 17. Fri, Feb 24. Review. Handout on Exam 2. Assignment: 4.6 p. 197, 2, 6. Chapter 4 Review p. 230, 1, 3, 9, 13, 15, 20, 21-31 odd, Tech. writing exercises 1-3. Needed fact for problem 27: Two linearly independent solutions to the homogeneous equations are y ₁ = x , y ₂ = x^-2. A Quality Quarter Hour with Maple checking an answer to review problem 30. Handout listing some of the theory of Chapter 4. Some of this was proved, and some will be proved in Chapter 6.
  
  
• 18. Week 7, Mon, Feb 27. Review. A Quality Quarter Hour with Maple solving Section 4.6 problem 10, by variation of parameters with Maple doing the algebra and integration, as partially done at the end of class today.
• 19. Wed, Mar 1. Exam 2 on 4.1-4.6.
• 20. Fri, Mar 3. 6.1 Theory of Linear Differential Equations. Assignment: p. 324, 1, 3, 5. Find the Wronskian in 15, 17. Maple worksheet illustrating how to find formulas of solutions of differential equations and initial value problems. Second homework assignment. Due in class Friday, March 24. See revision posted Mar. 6.
  
  
• 21. Week 8, Mon, Mar 6. 6.1 continued. Additional assignment: p. 324, Finish 15 and 17. Do 19, 21, 23, 26. Exam 2 Problem 4 solution done the hard way, by variation of parameters. Slightly revised Second homework assignment. Due date changed to Monday, March 27.
• 22. Wed, Mar 8. Finish 6.1. Start 6.2, the constant coefficient case. Outline Handout of the theory of Sections 6.1 and 6.2.
• 23. Fri, Mar 10. Finish 6.2. In class oral quiz on some topics of 6.1 (not for credit). Outline Handout about Cauchy Euler equations. Assignment: Section 6.2, p. 331, 1-21 odd.
  
  Spring Break Week
  
  
• 24. Week 9, Mon, Mar 20. Cauchy Euler Equations. Start 6.3 and 6.4. Assignment: Section 4.3 p. 179 41, 43, Section 6.2 p. 332 31 a-c. Also verify with Maple that the solution sets obtained for second order CE equations are fundamental sets of solutions. Do for all three cases. Notes on the solutions to homework 1, which will be returned Wednesday.
• 25. Wed, Mar 22. 6.1 Theory of Non-homogeneous Equations. 6.4. Variation of parameters. Assignment: Be able to prove the main theorem about non-homogeneous equations. Third homework assignment. Finding solutions of higher order non-homogeneous equations by variation of parameters, using Maple. This homework is to be done individually. Due Monday April 10. Handout example of a third order Cauchy Euler non homogeneous de solved by Maple (Text Example 1 Section 6.4).
• 26. Fri, Mar 24. 9.3 Preparation for Systems of Differential Equations. Some matrix concepts and calculations. Assignment: Do by hand 1, 3, 5. Do by machine 9, 11, 13, 16, 17. Do by hand 27, 29. Do by machine 33, 35, 37. ("Machine" means Maple or calculator.) Maple Examples of simple matrix calculations. Tentative Review Notes for Exam 3.
  
  Who should be better than differential equations students at integration? The first annual YSU integration Bee, run by Dr. Spalsbury, will be held Tuesday April 25. Click here for more information and registration.
  
  
• 27. Week 10, Mon, Mar 27. Finish review of matrices. Outline of review of matrices as presented in class. Assignment: Be able to do matrix calculations by using Maple (see handout posted Mar 24) and by using your calculator. Do problems A and B of today's handout. Section 9.2, p. 512, Do by machine, 1-7 odd. Homework 2 due but will be accepted Wednesday.
• 28. Wed, Mar 29. 9.1 etc. Intro to Systems of Differential Equatins. Assignment: Section 5.1, p. 251. Set up the system of equations but do not solve: 31, 33. Section 9.1 p. 507, 1-13 odd.
• Last day for W, March 30. (Changed from March 24 on 1/30/06)
• 29. Fri, Mar 31. Review Exam notes, finished form Assignment. Go over questions and problems on review handout. Do text review problems: Ch 5 p. 304, 7; Ch 6 p. 344, 1-6 all, 9, 10. Review all assigned problems from Chapter 9 sections 1-3.
  
  
• 30. Week 11, Mon, Apr 3. Review. Note on third homework assignment for those doing problem 9: Your answer will include unintegrated integrals of formulas involving g(x).
• 31. Wed, Apr 5. Exam 3 on 6.1, 2, 4; Cauchy Euler equations, and 9.1-9.3 and a little of 5.2.
• 32. Fri, Apr 7. 4.8 and 4.9, Mass-Spring systems. Start 9.4, Theory of Systems of Differential Equations. Homework 2 will be returned and discussed in connection with 4.8 and 4.9. Assignment: p. 219, 1, 3, 7. p. 227, 3, 7, 9.
  
  
• 33. Week 12, Mon, Apr 10.Continue 9.4. Assignment: p. 530: 1-23 odd, 26 (important), 27, 28, 32. Maple handout illlustrating the solution of initial value problems for homogeneous linear systems. Added 4/10/06, 12:25 pm. Change problem H from y^(4) + y^(3) = sec(x) to y^(4) - y^(3) = x cos(x). Due date for people doing problem H extended to Friday.
• 34. Wed, Apr 12. Continue 9.4. Writeup of most of class presentation of Section 9.4.. See also Maple handout posted April 10. Homework 3 due except for people doing problem H. Date changed 4/7/06
• 35. Fri, Apr 14. 9.4 and 9.5, Finding a Fundamental Matrix for Constant A. Assignment: Do by hand: p. 541, 1, 3, 5, 9.
  
  
• 36. Week 13, Mon, Apr 17. 9.5. Maple worksheet example of finding a fundamental matrix for real eigenvalues. Assignment: Use Maple to solve p. 541, 19, 21 with initial condition x(0)=col[4,5,6], 23 with initial condition x(1)= col[-2, -1, 0, 1], 25. Check everything using Maple. These are not to hand in, but problems like these will be on the take-home part of the next exam.
• 37. Wed, Apr 19. 9.6. Finding a fundamental matrix when eigenvalues are complex. Class example finding a real fundamental matrix from complex eigenvalues. checked and worked out by Maple. A coupled mass spring problem worked out in Maple. Assignment: Do by hand: 1, 5, 7. Do by Maple: 9, 11, 14. Check everything done by Maple. Not to turn in.
• 38. Fri, Apr 21. 9.7. Variation of parameters. Maple example of how to handle an integral in a function. Maple example of an initial value problem done by variation of parameters. Assignment: p. 556, Do by Maple 11, 13, 17, 19, 21. Review handout final version, for Exam 4. (Final version posted 3:18 pm April 21)
  
  
• 39. Week 14, Mon, Apr 24. 10.1-10.2. The one dimensional heat equation. Assigmnent for Friday: p. 587, 1-11 odd, 15, 17.
• 40. Wed, Apr 26. Exam 4, in-class portion. The take-home portion will be given out in class. Take Home Part of Exam in case you need it.
• 41. Fri, Apr 28. 10.1 and 10.2. Introduction to PDEs and Separation of variables. The one dimensional heat equation. Assignment: 10.2, p. 567, 9, 11, 12, 15, 17. Outline and application with graphs.
  
  
• 42. Week 15, Mon, May 1. Finish 10.2. Start 10.3-10.4 Fourier Series.Outline of the solution of the heat equation as done in class Friday. Example where the initial condition is a single sinusoid. Example where the initial condition is a sum of sinusoids. Outline of Fourier Series as presented in class. Maple worksheet verifying the claims made on the Fourier Series outline. Example of a Fourier series graphed in maple, and used as an initial condition of a heat problem.
• 43. Wed, May 3. Finish the treatment of Fourier Series, using the abstract approach on the outline posted above. Exam 4 take-home portion due in my mailbox 3:45 pm. Assignment: p. 611, 1-5 all, 7, 8, 11.
• 44. Fri, May 5. Review Notes on the Final Exam. Formulas to be given to you with the final exam.