MA 425-003
Mathematical Analysis I
Mathematics
Homework
Assigned Jan. 13
Sec. 1.1, problems 6, 14, 15, 20. Turn in Friday, Jan. 17.
Assigned Jan. 17
Sec. 2.1, problems 4, 5, 11b, 18, 20a. (On 4 and 5, justify each step from the axioms; on the others you can use other things we have proved.) Sec. 2.2, problems 5, 15. Turn in Friday, Jan. 24.
Assigned Jan. 27
Sec. 2.3, problems 5, 6, 9, 10; sec. 2.4, problems 6 (sup only), 7 (sup only). Turn in Friday, Jan. 31.
Assigned Jan. 31
Sec. 2.5, problem 2. Turn in Monday, Feb. 10.
Assigned Feb. 3
Sec. 3.1, problems 5b, 6c, 8, 10, 17. Turn in Monday, Feb. 10.
Assigned Feb. 7
1. Suppose lim(x_n)=x and c is fixed real number. Use the definition of limit (not theorems about limits) to show that lim(cx_n)=cx.
2. Sec. 3.2, problem 7.
3. Sec. 3.2, problem 21. Do the following: Let x = lim(x_n). Prove that y_n -> x.
Turn in Monday, Feb. 17.
Assigned Feb. 11
Sec. 3.3, problem 2. Suggested steps:
1. Show 1 < x_2 < 2.
2. Show by induction that for all n > 1, 1 < x_n < 2.
3. Show by induction that the sequence (x_n) is decreasing.
4. Find lim (x_n) by solving an appropriate equation.
Turn in Monday, Feb. 17.
Assigned Feb. 24
Click here. Turn in Monday, Mar. 3.
Assigned Mar. 3
Click here. Turn in Monday, Mar. 17.
Assigned Mar. 17
Click here. Turn in Monday, Mar. 24.
Assigned Mar. 21
Sec. 5.4, problems 2, 6, 9. Sec. 6.1, problems 1b, 1c, 2, 4. Turn in Monday, Mar. 31.
Assigned Mar. 31
Sec. 6.2, problems 6, 8, 13 (see definition on p. 171), 15. Sec. 6.4, problems 11, 15, 17. Turn in Monday, Apr. 7.
Assigned Apr. 14
Sec. 7.1, problems 1a, 2b, 6a, 9, 11. Sec. 7.2, problems 4, 8, 16. A sheet of instructions and suggestions for these problems was passed out in class. If you missed class, please pick up the sheet outside my office.
Turn in Monday, Apr. 28.
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Last modified Mon Apr 14 2003
Send questions or comments to schecter@math.ncsu.edu