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