MATH 375 - Intermediate Real Analysis

CATALOG DESCRIPTION: See catalog description here

Chapter 2

Chapter 3

Some necessary topology.

1. Every infinite bounded set on the line has a point of accumulation.
2. Every continuous function on a closed interval is uniformly continuous.

Chapter 5

Chapter 6

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

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.