MATHEMATICS 33B: DIFFERENTIAL EQUATIONS
Instructor: James Ralston
Text: Boyce and Diprima, ELEMENTARY DIFFERENTIAL EQUATIONS ..., either 7th or 8th edition.
LECTURES
MWF 9 - 9:50 in Franz 1260
SECTIONS
262-223-201 Discussion 1a 9-9:50 Tues MS6229 Nick Crawford
262-223-202 Discussion 1b 9-9:50 Thurs MS5217 Nick Crawford
262-223-203 Discussion 1c 9-9:50 Tues MS5233 Will Conley
262-223-204 Discussion 1d 9-9:50 Thurs MS6229 Will Conley
OFFICE HOURS
J. Ralston: Mon 2-3, Wed 10-11 and 2-3, Fri 11-12 in MS5238.
W. Conley: Mon 1-2 in MS6160. Also Wed 11-12 in the Student Math Center (MS3974)
N. Crawford: Mon 10-11 and Tues 10-11 in MS3973.
:
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. We will also spend some time in the middle of the course summing infinite sequences (see the syllabus below).
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 Boyce and DiPrima put the answers to all exercises in the back of the book. There is inevitably the 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.
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. 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 Boyce and DiPrima 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 Boyce and DiPrima. The problems are listed with their numbers from the 7th edition, but, where they have different numbers in the 8th edition, those are given in parenthesis. The quizzes are given in the weeks beginning with "Quiz X" in the left margin, and will usually be based on the homework from the preceding week.
Oct. 1. Section 2.1 Linear Equations with Variable Coefficients. Exercises: 13,15,25,26, 30,33 (= 13,15,27,28,33,36 in Edition 8).
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Oct. 4. Section 2.2 Separable Equations. Exercises: 3,5,6,12,13,20,27.
Oct. 6. Section 2.3 Modelling with First Order Equations. Exercises: 4,9, 15,20ab, 25a (= 4,9,13,19ab,25a in Edition 8).
Oct. 8. Section 2.3 Continued.
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Quiz 1
Oct. 11. Section 3.1 Second Order Equations. Exercises: 2,8,15,17,20,25.
Oct. 13. Section 3.2 Fundamental Solutions. Exercises: 7,9,12,14,15,21,22.
Oct. 15. Section 3.3 Linear Independence, Wronskian. Exercises: 1,4,7,12,13,19,24,26.
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Quiz 2 Tuesday Quiz, Thursday Quiz
Oct. 18. Sections 3.4 and 3.5 Complex and Repeated Roots. Exercises in Section 3.4: 5,7,9,16,17,19,21, and in Section 3.5: 1,7,14,16.
Oct. 20. Section 3.6 The Method of Undermined Coefficients Concise Version Exercises: 1,4,8 ,9,10,13.
Oct. 22. Section 3.7 Variation of Parameters. Exercises: 3,7,11,19, 22,26.
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Oct. 25. Hour Exam I Solutions and Comments
Oct. 27. Section 3.8 Free Vibrations. Exercises: 7,13, 20,26.
Oct. 29. Section 3.9 Forced Vibrations. Exercises: 9,10, 12,/A>,13.
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Quiz 3 Tuesday Quiz ,Thursday Quiz
Nov. 1. Sums of Infinite Series. Exercises from Supplement "Problem Set 1": 2,4,6,8.
Nov. 3. An Axiom and Three Theorems. Exercises from Supplement "Problem Set 2": 1,3,4.
Nov. 5. Two Convergence Tests. Exercises from Supplement "Problem Set 2": 6,7,9,12,16.
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Quiz 4 Quiz A Solutions Quiz B Solutions
Nov. 8. Power Series I. Exercises from Supplement "Problem Set 3": 1,4,5,6,7.
Nov. 10. Section 5.1 Power Series II. Exercises: 12,16,21,24,26,28.
Nov. 12. Section 5.2 Series Solutions I. 2,5,7,8,9,21.
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Quiz 5 Tuesdy Quiz, Thursday Quiz (corrected)
Nov. 15. Section 5.3 Series Solutions II. 2,8,10,15.
Nov. 17. Review.
Nov. 19. Hour Exam II. Solutions and Comments
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Nov. 22. Section 7.1 Systems of Differential Equations. Exercises: 2,4,15,16.
Nov. 24. Section 7.3 Eigenvalues and Eigenvectors. Exercises: 14,15,18,21,24.
Nov. 26. Thanksgiving Holiday.
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Quiz 6 Tuesday Quiz ,Thursday Quiz
Nov. 29. Section 7.4 Existence, Uniqueness and the Wronskian. Exercises: 4,6,7.
Dec. 1. Section 7.5 Homogeneous Constant Coefficient Equations. Matrices with Distinct Eigenvalues Exercises: 1,7,10,11,17,31.
Dec. 3. Section 7.6 Complex Eigenvalues. Exercises: 5,6,7,18,19.
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Quiz 7 Tuesday Quiz, Thursday Quiz
Dec. 6. Section 7.7 Fundamental Matrices. Exercises: 1,5,6,12,15.
Dec. 8. Section 7.9 Inhomogeneous Systems. Exercises: 1,6,7,13.
Dec. 10. Review . Study Outline , revised 12/12/04, and some computational review problems
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Exam Week Schedule
Office Hours: MS5238 Mon. 2-3 (as usual), Thurs. 2-3.
Review Session: Haines 220 Wed. 2-4
FINAL EXAMINATION: Friday, Dec. 17, 11:30-2:30. People with last names beginning with A-K should take the final examination in Franz 1260; those with last names beginning with L-Z should take it in Boelter 3400. Please arrive a little early for the final. We will be checking your identification.