# MATH 375 - Suggested Homework Problems

2.5: 5.1, 5.2, 5.3, 5.4, 5.8, 5.11, 5.14a, b, 5.15

2.6: 6.2, 6.3, 6.4, 6.5a, b, c, d, 6.6a, b, d, e

2.7: 7.1, 7.2, 7.4, 7.6, 7.10, 7.14, 7.15, 7.16

2.8: 8.1a, b, d, 8.2, 8.3, 8.4, 8.7, 8.8

3.10: 10.1, 10.3, 10.4, 10.8, 10.10

3.11: 11.1, 11.3, 11.4, 11.6, 11.7

3.12: 12.1a, b, c, d, e, f, g, 12.4, 12.6, 12.7, 12.8

4.16: 16.1, 16.2a, c, e, 16.3a, b, c, d, 16.5

4.17: 17.1a, 17.3a, d, f, g, 17.4, 17.5, 17.6, 17.7, 17.12, 17.13a

4.18: 18.1b, d, 18.2, 18.3, 18.4

5.20: 20.1a, b, c, e, f, 20.2a, 20.3c, 20.4, 20.5, 20.8

5.21: 21.1, 21.2, 21.3, 21.4, 21.8, 21.10

5.22: 22.4, 22.5, 22.7

5.23: 23.1c, e, 23.2a, b, 23.3, 23.4, 23.5

6.25: 25.1a, b, c, d, 25.3, 25.5a, 25.7

6.26: 26.1, 26.3a, b, c, e, 26.6, 26.8, 26.9

In addition, the following topics are covered from Riemann integration.

1. Definition of Riemann integral.
2. Proof of uniqueness.
3. Proofs of the linearity of the integral assuming appropriate hypotheses.
4. Proof of existence of the integral of f over a closed interval assuming f is continuous.
5. Proof of fundamental theorem of integral calculus.
6. Calculations of integrals from sums and from fundamental theorem.