Homework Assignments for Math 307 F (Spring 2009)

• The section numbers for the homework problems refer to the Boyce & DiPrima textbook listed in the syllabus.
• Homework is (usually) due every Friday at the beginning of lecture. Late homework will not be accepted. If you are unable to attend class on a day homework is due, the assignment must be turned in to my mailbox in Padelford C-120/130 before class that day.
• Show all your work for full credit.
• Please staple your homework. The grader may dock points if you do not.
• Please arrange the problems in the order listed below, or clearly indicate any discrepency if your problems end up in a different order for some reason.

Homework 7 (due Friday 6/5/09)

I recommend that you make a copy of your homework before handing it in so that you can use it to study for the final.

• §6.2 #4, 9, 21, 28, 30, 31
• §6.3 #8, 9, 12, 13, 14, 15, 17 (For 8, 9, and 12, also draw a graph of the function f(t).)
• §6.4 #5, 9
• Hints

Homweork 6 (due Friday 5/29/09)

• §6.1 #1, 2, 5, 15, plus these additional problems
• §6.3 #1, 3, 19a (For problems 1 and 3, first write down the multipart rule for the function.)
• §6.2 #1, 2, 6, 7, 8, 13, 18, 24, 37
• Hints
  • §6.2 #7: Complete the square in the denominator. This is what you should do whenever you have an irreducible (i.e. non-factorable) quadratic in the denominator that's not already in the form s²+a².
  • §6.2 #37: Use Theorem 6.2.1 to compute the Laplace transform of g'(t). How are g'(t) and f(t) related?
  • Additional problem #1: If these look confusing, read this handout on operators and these examples showing how to decide whether an operator is linear.

Homework 5 (due Friday 5/15/09)

• §3.6 #9
• §3.8 #2, 3, 6, 8, 11, 12, 17
• §3.9 #1, 5, 6, 11, 12

Homework 4 (due Friday 5/8/09)

• §3.5 #38, 39
• §4.1 #7, 8, 11, 16
• §4.2 #12, 18, 20, 22
• §3.6 #1, 2, 3, 6, 15, 17, 19a, 20a, 21a, 27

Homework 3 (due Friday 5/1/09)

• §3.1 #1, 5, 7, 10, 15, 17, 19, 22
• Notes on Complex Numbers (Turn in all ten problems in excersise sets I and II.)
• §3.4 #4, 5, 8, 16, 18, 20, 31
• §3.5 #6, 8, 11

Homework 2 (due Friday 4/17/09)

• §2.4 #1, 9, 14, 23, 25 (For problem 9, also sketch the region in the ty-plane.)
• §2.5 #3, 5, 7, 12, 20, 22, 25
• §2.7 #1abd, 4a, 6

Homework 1 (due Friday 4/10/09)

• Review Problems (turn in all the problems on the first two pages, but only half of the integral problems on the last page – you get to choose which ones)
• §2.2 #2, 3, 14, 27, 30
• §2.1 #9, 16, 20, 32
• §2.3 #3, 5, 24
• Hints
  • §2.2 #27
    1. This differential equation is very similar to the logistic equation in §2.5. You will need to use integration by partial fractions in order to solve it. (See the basic formula sheet for a quick review of partial fractions.)
    2. For part (a), first determine the equilibrium solutions, then figure out a formula for the general solution that depends on y₀. What is the domain of y(t) when y₀ < 0?
  • §2.2 #30: You will also need partial fractions for this problem.
  • §2.3 #5: For part (c), you can estimate the amplitude graphically, or you can use the following formula:
    A cos(wt) + B sin(wt) = R cos(wt - u),
    where R² = A² + B² and tan(u) = B/A.