Instructor: Victor Roytburd (Amos Eaton 405, Ph.
276-6889, roytbv at rpi.edu)
Office hours: Mo-Fr 10-10:45; Mo, We, 3-4, Fr 4-5, or by appointment
Teaching Assistant: Kaitlyn
Voccola (Amos Eaton 430)
Office hours: Monday-Thursday 12:30-1:30pm
Tuesday and Thursday (after recitations) 4:30-5:30pm
Class meets:
Lectures: Mo-Fr, 11-12:20, Jonssn 3207
Recitations: Tu, Th 3:00-4:20, Jonssn 3207
Web-page: http://www.rpi.edu/~roytbv/sum/sum07.html
TEXT: W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Eighth Edition, Wiley, 2005.
The class meets every day and moves extremely fast. You have to keep in mind that every two days of the summer class correspond to a whole week of the same class during regular semesters. Here is a rough outline of our pace through the book.
|
Number of days |
Sections |
|
2 days |
1.1-1.3, 2.1 |
|
2 days |
2.2, 2.3, 2.4 |
|
3 days |
2.5, 3.1, 3.5,
3.4 |
|
2 days |
3.4, 3.2 (summary), 3.3 |
|
2 days |
3.6-3.7,
outline of 3.8-3.9 |
|
3 days |
7.1, 7.2, 7.3,
7.5 |
|
2 days |
7.6, 7.4, 9.1 Summary of systems |
|
3 days |
9.1-9.4, 9.5 |
|
2 days |
10.2, 10.3 Fourier series summary |
|
2 days |
10.4, 10.1, (11.1), 10.5 |
|
3 days |
10.6, 10.7 |
|
June 29, 11:00 am – 2:00 pm |
Final Exam |
Homework problems: The principal measure of success in any course is whether you can apply the concepts learned in the course. In mathematics it means, whether you can solve problems; and the only way to learn how to solve problems is... to solve problems, the more the better.
Here is a link to a representative list of practice problems, including the homework problems to be handed in (given in bold). Solutions to the practice problems (plus solutions to some extra problems) are available. Try to do the practice problems on your own before looking up the solutions: you cannot learn much from reading solutions, you can learn from solving.
Homework assignments containing 4-6 problems similar to the Recommended Problems will be assigned roughly every other day and collected. You are welcome to work in groups and discuss the problems with your classmates; your papers however must be authored by you. In view of the fast pace of the course, late homework papers will not be accepted. There is an option that from time to time quizzes based on the homework problems will be given.
Maple and especially its graphing capabilities are extremely helpful for understanding parts of the material. Some shorter Maple problems might be included in homework assignments. Information about Maple for differential equations can be found on the Math Department web page under course materials. Links to some useful examples are given below.
Recitations are an integral part of the course. You are encouraged to attend all recitations with the expectation that you will raise questions about the new material and problems and engage into discussions with the Teaching Assistant and other students.
Tests: I plan to give 3 exams. They will cover all the major topics of the course: first order equations (1.1, 2.1--2.6); second order equations (3.1--3.7, 3.8--3.9); systems of first order equations (7.1--7.6); nonlinear equations and stability (9.1--9.5); Fourier series and partial differential equations (10.1--10.7). Some material on partial differential equations will be included into the (comprehensive) final exam. Exams are tentatively scheduled for Monday, June 4th, Thursday, June 14th, and Monday, June 25th.
Grading: Exams will each account for 20% of you grade; and the combined grade for the homework performance will account for 10%. The final exam will be 30% of the grade. In case if the final exam improves your standing, the final will account for 50% of the course grade.
Here is the list of homework problems and an annotated reading list for the semester. All the assignments below refer to the bold-faced problems from this list.
Homework 1: Sec. 1.1-2.1, due May 23.
Homework
2: Sec.2.2-2.4, due Friday May 25.
Homework 3: Sec. 2.5, 3.1, due May 30.
Homework 4: Sec. 3.4, 3.5, due June 1
Homework 1-4 Solutions
Homework 5: Sec. 3.6, 3.7, due June 6
Homework 6: Sec. 3.8, 3.9, 7.1, due June 8
Homework 7: Sec. 7.2-7.3, 7.5-7.6, due June 13
Homework 5-7 Solutions: Part 1, Part 2
Homework 8, due June 21: Sec. 9.3 Problem 7(a-c), extra credit for the part (d), which is Maple based; Sec. 9.4 Problem 2: do an analysis similar to the one required for the problem 9.3.7(a-c), again extra credit for the Maple based phase portrait; Sec. 10.2 Problem 20(a,b) , you don’t need any computer to work out this problem; Sec. 10.4 17,18, 22 For all these problems, don’t neglect to sketch the graphs.
Homework 9, due Monday, June 25. Sec. 10.1
Problems 2, 16; Sec. 10.5: #2, 3, 5, 11; Sec. 10.6: #1, 8.
Homework 8-9 Solutions
Test 1 will be given in class on Monday June 4th. It will cover the material of the first four homework assignments; see the section in blue in the outline above. You will be allowed one sheet of notes. Sample tests: Test 1 (2004), Test 1(2001) with answers.
Test 2 will be given in class on Friday, June 15. It will cover the material of the homework assignments #5-7; see the sections in green in the outline above. You will be allowed one sheet of notes. Sample test: Test 2 (2005) (with answers)
Test 3 will be given in class on Wednesday, June 27. It will cover the material of the homework assignments #8-9; see the sections in plum in the outline above. You will be allowed one sheet of notes. Sample test: Test 3 (2004) (with answers)
Final
Exam will be given on Friday 11-2. You will
be allowed ONE SHEET of notes. Sample final
How to draw a direction field for a differential equation
Resonance for forced damped oscillators
Sine and cosine Fourier series for the same function
How to solve systems and draw direction fields for them. A bit simpler Maple worksheet to do the same
A BRIEF SUMMARY OF LINEAR ALGEBRA
Last updated 6/26/07
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