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Syllabus

Homework assignments:
Note that late HW is not accepted!

Practice Exam I.

Practice Exam II. (Now includes answers on popular demand!)

Practice Exam III.

Monthly HW assignments: HW1 (due 9/18), HW2 (due 10/30),
New problems added on Fr Nov 17 and Sat Nov 25 to HW3 below, plus re-writing of problem 1, this time not relying on matrices:
HW3 (NEW DUE DATE MON 12/4, this is the complete assignment!).

Solutions to HW1: p1, p2, p3.

Weekly HW assignments (not collected):

Wk 2 (ends Fr 9/1): 2.2 (12,24,34), 2.3 (14,20,30).

Wk 3 (ends Fr 9/8): 2.4 (7, 23), 2.6 (11, 14), 3.2 (3).

Wk 4 (ends Fr 9/15): 3.2 (11, 18: make an appropriate substitution!), 3.4 (5, 12).

Wk 5 (ends Fr 9/22): 3.4: 24. Determine the period of the orbit of Uranus, using Kepler's third law. (You can find all relevant quantities online via a google search; in fact the same search will help you in verifying your calculated answer).

Wk 6 (ends Fr 9/29): 3.5: 1, 3.

Wk 7 (ends Fr 10/6): 4.2: 13, 14, 27, 28.

Wk 8 (ends Fr 10/13): 4.3: 17, 18, 25, 26, 35. 4.4: 6, 15, 25, 29, 31, 32.

Wk 9 (ends Fr 10/20): 4.5: 19, 21, 27, 29, 36. 4.6: 13, 16. 5.2: Using the method discussed in class to solve systems, solve 4, 13, 29.

Answers 5.2: 4: m=(-3 +/- sqrt{21})/2; solutions (x(t) y(t))= exp[(-3+sqrt{21})t/2](1 (5-sqrt{21})/2) and exp[(-3-sqrt{21})t/2](1 (5+sqrt{21})/2). 13: m=1+/- 2i, solutions in back of text. 19: sum of roots of auxiliary eqn equals lambda+1 and should be negative or 0, while product of roots equals lambda+3 which should be positive of 0. This leads to the asnwer in the back of the text.

Wk 10 (ends Fr 10/27): 5.2: Solve following system using method from class: dx/dt=x-y, dy/dt=x+y, 5.4: calculate all critical points of dx/dt=x(y-1), dy/dt=y(1-x). Perform phase-plane analysis for dx/dt=-x ,dy/dt=ay, where a>0 is a parameter. What happens when a increases? Do you see the effect on the phase-portrait?

Wk 11 (ends Fr 11/3): No HW.

Wk 12 (ends Fr 11/10): (Note: These problems come from the booklet I distributed in class! ) 5.1:3, 7, 16, 26.

Wk 13 (ends Fr 11/17): 5.2: 8, 10, 18, 23, 5.3: 10, 16, 20, 21. Go to bottom of page and follow the link for evaluating the trial chapter.

Wk 14 (ends Fr 11/24): 5.4: 6, 7, 11, 15, 18.

Wk 15 (ends Fr 12/1): 5.5: 6, 12, 16, 5.7: 3, 9, 5.8: 6, 12, 25.

Announcements:

I'd like to fix a date for the first exam in the 6th week (which ends on Fr 9/29). We shall discuss this in class.
Clarification regarding the notation in problem 5 of HW1: The dot above a letter (like x-dot, y-dot and z-dot) is short for the derivative with respect to time. For instance x-dot means dx/dt, and similarly for y and z. Also, in the 2nd line from the bottom of p2, you should replace arctan x by arctan t.
As we decided in class, Exam I is on Fr 9/29 in class. It covers everything discussed in class on Chapters 1, 2 and 3 up to and including Section 3.4. Material in Chapter 3 following Section 3.4 is thus not included. Calculators are not allowed, nor are they needed. Please bring your own -blank- paper. Prior to Exam I, there will be a Review on Wed 9/27. Please consult the syllabus on the nature of this review session.
Problem 5, part 4 in HW1 is stated wrong. It should say that z_p(t)=tan(t) is a particular solution of the Riccati equation. You don't have to turn in this part of problem 5, only the first 3 parts of that problem.
We will decide in class on a date for Exam II which will cover the rest of chapter 3, chapter 4 and perhaps part of chapter 5. This exam will be in the week of October 30th and November 3rd. As usual a review session will precede the exam, see the syllabus on the format of review sessions.
As decided in class, Exam II is on Fr 11/3 in class, preceded by a Review on Wed 11/1. The topics you should know for this test are those covered in class, starting with Kepler's laws, 3.5, 4.2, 4.3, 4.4, 4.5, 4.6, and 5.2 (but using the method discussed in class).
Exam III will be in class on Wednesday December 6, preceded by a review session on Monday December 4. It will cover the rest of chapter 5, chapter 7 and perhaps parts of chapter 6.
On Monday October 23 I will hand out lecture notes on the Laplace transform.
Please provide feedback on the Brannan/Boyce chapter on Laplace transforms by following this link.