Syllabus and Homework: Part II

(additional non-book problems below are also required)

March 13-17: §7.5, §7.6, §7.3, §8.2 in Anton

§7.6: 6, 10, 12, 36
§7.3: 2, 8, 10, 14, 16, 20, 28, 50
§8.2: 2, 4, 12, 15, 20, 35(a)(b), 45, 46
A: A particle moves on the x-axis with velocity $2\sin(3t)$ at time t and is at x = 1 when t = 0.
1. Find the position x(t) of the particle at time t. 2. Determine at which times in the interval $0 \le t \le 2\pi/3$ the particle is moving to the left. 3. Compute the total distance travelled from time t = 0 until time $t = 2\pi/3$ .

March 20-24: §8.4-8.7 in Anton

§8.4: 4, 8, 10, 19
§8.5: 2, 4, 8, 18
§8.6: 2, 4, 11, 12, 14, 17
§8.7: 4, 8, 12

Spring Break March 25-April 2

April 3-7: §9.2, §9.5 in Anton

§9.2: 2, 8, 10, 12, 28, 30, 32, 41
§9.5: 10, 12, 14, 16, 18, 20

April 10-14: §9.8 and review, in Anton

§9.8: 1, 4, 6, 10, 14, 16, 18, 26, 49, 52(a), 55
A: Sketch the graph of $y = \cos(x^2)$ for $x \ge 0$ , making sure to label when the graph crosses the x-axis. In terms of this picture, explain how the alternating series test can be used to show that the improper integral $\int_0^{\infty} \cos(x^2)\,{\rm {d}}x$ is convergent. Of course, you do not need to compute the value of this integral (the exact value is $(1/2)\sqrt{\pi/2}$ , but the usual proofs of this requires methods based on complex numbers)

Exam on Monday, April 17, 7:30-9:30pm, Science Center C

The remainder of the classes (April 17-May 5) will be covered by Part III of the Syllabus, which will be distributed later on during the course. This last segment of the course will deal with differential equations.

Thomas J. Brennan
2000-01-31