Problem sets will appear here as they are assigned.
| Problem Set #1 | due Wed. Aug. 30 | 1.4, 1.7, 1.8a, 1.9, 1.11, 2.3, 2.6, 3.1, 3.4 |
| Problem Set #2 | due Wed. Sept. 6 | 3.5a, 3.6b, 4.1a-j, 4.2a-j, 4.3a-j, 4.4a-j, 4.6, 4.14a, Prove that the set of algebraic numbers is countable. |
| Problem Set #3 | due Wed. Sept. 13 | 4.15, 7.2, 8.2d, 8.2e, 8.4, 8.6, 9.1c, 9.10c, 9.17 |
| Problem Set #4 | due Wed. Sept. 20 | 10.2, 10.6, 11.4, 11.10, 9.9c, 12.3, 12.4 |
| Problem Set #5 | due Fri. Sept. 29 | 13.2, 13.4, 13.6, 13.8 |
| Problem Set #6 | due Wed. Oct. 4 | 13.9, 13.10, 13.11, 13.12, 13.13 |
| Problem Set #7 | due Wed. Oct. 11 | 14.4, 14.5, 14.6, 14.12, 17.5, 17.6, 17.9(a,c), 17.10(a,b) (14.1, 14.2, 14.3 are highly recommended, but don't turn them in.) |
| Problem Set #8 | due Wed. Oct. 18 | 18.2, 18.4, 18.6 (you may assume that the cosine function is continuous), 18.12, 19.1, 19.4, 20.1, 20.5 |
| Problem Set #9 | due Mon. Oct. 30 | 21.3, 21.4, 21.6, 21.8, 21.10, 21.11, use the criterion (1) in Corollary 20.7 to prove that the limit of x sin(1/x) is 0 as x approaches 0. |
| Problem Set #10 | due Wed. Nov. 8 | 22.1, 22.5, 23.1, 23.7, 23.8, 23.9, 24.1, 24.2 |
| Problem Set #11 | due Wed. Nov. 15 | 24.6, 24.10, 24.11, 24.13, 25.6, 25.8, 25.9, 25.12 |
| Problem Set #12 | due Wed. Nov. 29 | 26.6, 26.7, 28.2a, 28.3bc, 28.6, 28.8, 28.11, 29.1, 29.5, 29.13, Prove that f^(n)(0)=0 for all natural numbers for the function f(x)= e^(-1/x^2) for x not equal to 0 and defined as f(0)=0 (That is, prove that first derivative, second derivative, etc. evaluated at 0 is 0. Use the definition of derivative and induction on n. It can be done without finding an exact formula for all f^(n)(x).) |
| Problem Set #13 | due Wed. Dec.6 | 32.3, 32.7, 33.3a, 33.4 |
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