Page 184 - DMTH401_REAL ANALYSIS

Real Analysis

Notes 13.8 Review Questions

1. Define Discontinuous Functions.
2. Describe Classification of Discontinuities.

3. Explain Monotone Function.
4. Describe the Discontinuities of Monotone Functions.
5. Discuss the Discontinuities of Second Kind.

Answers: Self Assessment

1. Increasing and decreasing functions 2. Monotonic functions
3. Discontinuous 4. Absolutely monotonic

5. Monotonic transformation

13.9 Further Readings

Books Walter Rudin: Principles of Mathematical Analysis (3rd edition), Ch. 2, Ch. 3.
(3.1-3.12), Ch. 6 (6.1 - 6.22), Ch.7(7.1 - 7.27), Ch. 8 (8.1- 8.5, 8.17 - 8.22).
G.F. Simmons: Introduction to Topology and Modern Analysis, Ch. 2(9-13),
Appendix 1, p. 337-338.
Shanti Narayan: A Course of Mathematical Analysis, 4.81-4.86, 9.1-9.9, Ch.10,Ch.14,
Ch.15(15.2, 15.3, 15.4)
T.M. Apostol : Mathematical Analysis, (2nd Edition) 7.30 and 7.31.
S.C. Malik : Mathematical Analysis.
H.L. Royden : Real Analysis, Ch. 3, 4.

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