MATHEMATICS 33B: DIFFERENTIAL EQUATIONS, Lecture 1
Instructor: James Ralston
Text: Polking et al., DIFFERENTIAL EQUATIONS, 2nd Edition
LECTURES
MWF 8 - 8:50 in Kinsey Pavilion 1220A (on south side of Knudsen Hall)
SECTIONS
262-223-201 Discussion 1a 8-8:50 Tues MS5117 Joseph Viola
262-223-202 Discussion 1b 8-8:50 Thurs MS5117 Joseph Viola
262-223-203 Discussion 1c 8-8:50 Tues MS5137 Eric Radke
262-223-204 Discussion 1d 8-8:50 Thurs MS5137 Eric Radke
OFFICE HOURS
J. Ralston: Mon. 9-10, 2-3, Wed. 9-10, 2-3, Thurs. 11-12 in MS5238.
E. Radke: Mon. 10:30-11:30 in MS 2963, Student Math Center Tues. 9-10.
J. Viola: Tues. 12:30-1:30 in MS 3975, Student Math Center Thurs. 9-10
Welcome to Mathematics 33B. This is the grand culmination of the calculus series! While it may not really be all that grand, I hope that it will reveal some of the things that you can do with calculus, and bring together many of the topics from the earlier quarters. Its main topic is differential equations. Differential equations describe all motion in the universe -- among other things.
The format of the course will be more or less standard: three lectures and one discussion section per week, two hour exams and seven quizzes (quizzes are 12-15 minutes long, given in discussion section), daily homework assignments but no homework handed in. Checking your homework will not be difficult, since Polking, Boggess and Arnold put the answers to all odd-numbered exercises in the back of the book. There is the inevitable question, "What happens if I miss an hour exam or a quiz?" There are no make-ups for missed hour exams, but your scores on the other hour exam and the final will be rescaled to partially offset the missed hour exam. Likewise there will be no make-ups for missed quizzes, but only the best six quiz scores will be counted. All exams are closed book, i.e. no notes, calculators or ... cell phones.
Grading Policy: Your grade in the course is determined by the sum of your scores on the final, the two hour exams and your best six quizzes (weighted 40%, 30% and 30% respectively). If you get 80% of the possible points, you are guaranteed an A or A-. If you get 50% of the possible points, you are guaranteed a C. However, if necessary, I will move the A-/B+ line down until 25% of the class gets A or A-. Likewise, if necessary, I will move the C/C- line down until only 15% of the class gets grades below C. The median grade in this class is usually B-. Figuring out this policy -- and its implications -- is the first exercise in the course.
Syllabus and Exercises: The exercises listed in the syllabus below are not to be handed in. You should certainly do them -- and as many more of the exercises in Polking as you have time for. It is a good idea to keep the exercises you do in a notebook. The problems on the quizzes will be closely related (in the eyes of the instructor) to the problems listed below. The references to " Sections" refer to the sub-chapters of the textbook. The quizzes are given in the weeks beginning with "Quiz X", and will usually be based on the homework from the preceding week.
Jan. 8. Section 2.1. Introduction: Differential equations and Solutions. Exercises: 6, 7, 8, 16.
Jan. 10. Section 2.2. Separable Equations. Exercises: 3, 7, 9, 13, 15, 17, 23, 27, 33.
Jan. 12. Section 2.4. Linear Equations. Exercises: 3, 9, 11, 15, 19, 22, 23 (solutions to 22 and 23 by J. Viola), 41, 43.
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Quiz I
Jan. 15. Martin Luther King Jr. Day
Tuesday Quiz and Solutions .
Jan. 17. Section 2.5. Mixing Problems. Exercises: 1, 5, 9, 11.
Thursday Quiz and Solutions .
Jan. 19. Section 2.6. Exact Differential Equations. Exercises: 5, 9, 13, 17, 23.
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Quiz II
Jan. 22. Section 2.6 continued. Exercises: 27, 29, 39( solution (J. Viola)), 43, 45.
Tuesday Quiz and Solutions .
Jan. 24. Section 2.7. Existence and Uniqueness of Solutions.Discussion of the problems (J. Viola). Exercises: 7, 9, 11, 29, 31. If you are curious about where Theorem 7.15 (on page 81) comes from, click here.
Thursday Quiz and Solutions .
Jan. 26. Section 2.9. Autonomous Equations and Stability. Exercises: 7, 8, 9, 10, 19, 21, 27, 29.
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Quiz III
Jan. 29. Section 3.1. Modeling Population Growth. Exercises: 7, 13, 17 .
Tuesday Quiz and Solutions .
Jan. 31. Section 3.3. Personal Finance. Exercises: 5, 7, 9 , 13, 15.
Thursday Quiz and Solutions .
Feb. 2. Review
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Feb. 5: Hour Exam I. Solutions
Feb. 7. Section 4.1. Second Order Equations. Exercises: 1, 3, 5, 7, 9, 17, 25, 27.
Feb. 9. Section 4.3. Linear, Homogeneous Equations with Constant Coefficients. Exercises: 3, 9, 15, 17, 25, 27, 29, 33.
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Quiz IV
Feb. 12. Section 4.5. The Method of Undetermined Coefficients for Inhomogeneous equations. For a more theoretical discussion of this method click here . Exercises: 1, 7, 13, 15, 19, 23, 25, 31.
Tuesday Quiz and Solutions .
Feb. 14 Section 4.6. Variation of Parameters. Exercises: 3, 5, 13.
Thursday Quiz and Solutions .
Feb. 16 Sections 4.4 and 4.7: Harmonic Motion. Exercises from 4.4: 17, 19. Exercises from 4.7: 3, 9, 13 , 19.
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Quiz V
Feb. 19 President's Day
Tuesday Quiz and Solutions .
Feb. 21. Section 9.1. Linear Systems. Exercises: 3, 7, 9, 53, 56.
Thursday Quiz and Solutions .
Feb. 23 Review
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Feb. 26. Hour Exam II Solutions
Feb. 28. Section 9.2. Planar Systems. Exercises: 3, 9, 15, 17, 23.
Mar. 2. Section 9.2 continued. Exercises: 28, 29, 33, 39, 59.
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Quiz VI
Mar. 5 Section 9.3. Phase Plane Potraits. Exercises: 7, 11, 13, 17, 19.
Mar. 7 Section 9.4. The Trace Determinant Plane. Exercises: 1, 5, 7, 9, 11, 13, 17.
Mar. 9 Section 10.1. Nonlinear Systems. Exercises: 3, 5,7.
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Quiz VII
Mar. 12 Section 9.5. Higher Dimensional Systems. Exercises: 3, 7, 11, 13, 19(the answer given at the back of the book for this one is obviously wrong), 21, 27, 53.
If you would like to see a proof that any set of nonzero eigenvectors belonging to distinct eigenvalues is linearly independent look here. This is the proof of part 1 of Theorem 5.1 in Secion 9.5. As Polking points out, it is just the proof of Proposition 2.4 in Section 9.2 generalized from 2 eigenvectors to n eigenvectors.
Tuesday Quiz and Solutions .
Mar. 14. Review.
Thursday Quiz and Solutions .
Mar. 16. Conclusion. Here's an Outline of the course which may be helpful.
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FINAL EXAMINATION: Thursday, March 22, 3-6PM.