Instructor: Victor ROYTBURD (Amos Eaton 405, Ph.
276-6889, roytbv at rpi dot edu)
Tentative NEW Office hours: Mo 2-3, 5-6,
WE 4-5:30, FR 4-5 (or by appointment)
Teaching Assistant: Rajinder MAVI
Office hours: Tuesday, Thursday 6-7 pm, Union, McNeil Room
Class meets:
Lectures: Tu, Fr, 10-11:20,
Darrin 308
Recitations:
Section 9: Mo 2-2:50, Lally 102; Section 10: Mo 3-3:50, Sage 2704; Section 11: Th 3-3:50, Sage 2704; Section 12: Th 2-2:50, Lally 102
Web-page: http://www.rpi.edu/~roytbv/ode/f05.html (it will be linked to the math department COURSE MATERIALS page).
TEXT: W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, Eighth Edition, Wiley, 2005.
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, 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 |
|
3 days |
9.1-9.4, 9.5 |
|
2 days |
10.2, 10.3 |
|
2 days |
10.4, 10.1, (11.1), 10.5 |
|
3 days |
10.6 (December 9, last day of classes!) |
|
Friday December 16,
6:30-9:30 pm |
Final Exam: DCC 308 |
Homework problems: The principal measure of success in any course is whether you can apply the concepts learned in the course. In mathematics it is the ability to 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 from the text: Recommended Problems. Solutions to Recommended Problems are also available. This list of Recommended Problems is pretty long; a shorter sublist is included next to the assigned homework problems . Try to do the problems by yourself before looking up the solutions: you cannot learn much from reading solutions, you can learn from solving. Note that Solutions to the Recommended Problems are listed according to the 7th edition of the book; on the list of homework problems the corresponding problems from 7th edition are also given.
Homework assignments containing 4-6 problems similar to the Recommended Problems will be assigned weekly; they will be discussed in recitations. As a rule homework papers will not be collected, quizzes based on the homework problems will be given weekly instead.
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; the relevant Maple commands will be explained in class. 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 October 4, November 1, and December 2. For the tests you are allowed to use one sheet of hand-written notes.
Grading: Exams will each account for 20% of you grade; and the combined grade for the quizzes will account for 10%. The final exam will be 30% of the grade. In case if the final exam is better than the advance grade, the final will account for 50% of the course grade.
Other resources: In cooperation with other universities and departments, our department is developing interactive Web-based modules designed to give you a better understanding of differential equations and their use in science and engineering. Modules on mechanical and electromagnetic oscillations are especially instructive for our course. Here is a link: Project Links
Here is the list of homework problems and an annotated reading list for the semester. Here is the homework and reading assignment for the current week. Do problems on the list from the following sections:
Sec. 1.1-1.3 (8/29-9/2);
Sec. 2.1-2.2 (9/5-9/9); Start Sec. 2.3
Sec. 2.3, 2.5, Start Sec. 3.1 (9/12-9/17);
Sec. 3.1, 3.4-3.5 (9/19-9/26)
Sec. 3.6, 3.8. Read Sec. 7.2-7.3 (Due Friday 10/14)
HOMEWORK #6 (Due Tuesday 10/18). Sec. 3.7:
Probs. 3, 5; Sec. 7.1: Probs. 2, 5.
This homework will be collected and graded. To be graded the papers must be handed in by 3:30 on Tuesday (either in
class or in my mailbox, AE 301). Late papers will be
returned ungraded. Each homework grade will contribute to your course
grade, with the weight equal to the weight of a quiz.
Homework #7 (Due Tuesday 10/25). Do the following problem from the list: Sec. 7.2 #21(c,d), Sec. 7.3 #5, 17-18,
Sec. 7.5 #15, 26-27. This homework will be collected
and graded.
Homework #8 (Due Tuesday 11/01). Do the following problem from the list: Sec. 7.6 #10, 15. This
homework will be collected and graded.
Homework #9 (Due Tuesday 11/15) Do the following problem from the list: Sec. 9.3 #10 (do tasks (a)-(c),
listed above problem 5), Sec. 9.4 #2 (again do a-c
lasted above the problem). You are welcome to use Maple off the web-page to
compare your computations with the vector field. AGAIN this homework will be collected and
graded.
Homework #10 (Due Tuesday 11/29) Do the following problem from the list: Sec.10.5 #3, 10.1 #12,
10.2 #20 (a,b).
TEST
ANNOUNCEMENTS
Test 1 is scheduled for Tuesday October 4. It will contain the material covered in class up to and including September 27 (i.e., the first FOUR rows of the outline).
Test 2 is scheduled for Friday November 4. It will contain the material covered in class up to and including October 28 (i.e., Sections 3.6-3.8, 7.1-7.3, 7.5-7.6).
Test 3 is scheduled for Tuesday December 6. It
will contain the material from the following sections: Sections 9.1-9.4, and
10.1-10.5. Problems will be similar to homework problems. You will get a pretty
good idea of the test from the 2004 test. Here are
the notes on investigation of systems, which I
used in class. As a
bonus problem the test will contain a problem on finding steady-state
solutions, similar to 10.6.1―8. Test 3 solutions
A similar problem will be on
the final as well.
I will give a brief review
session on the material of the test on Monday 12/5, 8-10 pm, DCC330.
Final Exam Announcement:
I will
give a brief review session on Monday 12/12, 7―9 pm, Eaton 214
Office
hours:
Tuesday
12/13 10-11:30am, 4-5pm
Thursday
12/15 3-5pm
Friday
12/16 10-12 am
There are many old tests and solutions on the net; here are some representative tests I gave in the past:
Test #1 from 2001. (Answers to sample problems). Test #1 from 2004.
To prepare for Test #2
solve problems 1, 2, 5, 8 from the following list (here are the answers) and solve the following exam from 2001. Here are
notes on linear algebra.
Test #3 from 2004. Test solutions. Here are the notes on investigation of systems, which I showed
in class.
How to draw a direction field for a differential equation
Resonance for forced damped oscillators
Comparison of different types of Fourier series
How to solve systems and draw direction fields for them. A bit simpler Maple worksheet to do the same
Animation of phase dynamics
Some nonlinear systems
Some heat conduction illustrations
A BRIEF SUMMARY OF LINEAR ALGEBRA