Calculus II, Spring 2013 (http://www.math.nthu.edu.tw/˜ wangwc/)

Homework Assignment for Week 05

1. Section 9.8: Problems 9, 13, 28, 29, 31, 32, 33, 34(a), 35, 43.

2. (s9.8-extra2) Solve the differential equation

dy/dx = 1 + y^{2}, y(0) = 0,

by power series expansion. That is, assume y(x) = a_{0} + a_{1}x + a_{2}x^{2} + ⋯, then compare the coefficients on both sides to solve for a_{0}, a_{1}, ⋯, successively. The differential equation can also be integrated directly. Verify your answer by comparing the first 2 nonzero coefficients of the Taylor series expansion of the exact solution.

3. Chap 9: Problems 27, 28, 29, 30, 32, 37, 47(a), 49-54(important), 71, 72.

4. Section 10.4: Problems 9, 13, 17, 23, 28, 29.

5. Section 10.6: Problems 15, 17, 31, 35.