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Guide to Analysis written by F. Mary Hart, Department of Pure Mathematics, University of Sheffield
. This is an other book of mathematics cover the following topics.

Editor's foreword
Preface
Glossary of symbols and notation

1. NUMBERS AND NUMBER SYSTEMS 1.1 Natural numbers
1.2 Integers
1.3 Rational numbers
1.4 The real number system
Appendix: Mathematical induction

2. SEQUENCES 2.1 Introduction
2.2 Sequences
2.3 Standard limits
2.4 Some general results for sequences
2.5 Subsequences
Appendix: Triangle inequal

3. INFINITE SERIES 3.1 Introduction
3.2 Series and notation
3.3 Tests for convergence
3.4 Absolute convergence, rearrangement of series, multiplication of series
Appendix
Tests for convergence-summary

4. FUNCTIONS Limits of functions, continuous functions 4.1 Limits offunctions
4.2 Continuity
4.3 Some properties of continuous functions on closed intervals

5. DIFFERENTIABLE FUNCTIONS Dilferentiable functions, Rolle's theorem, mean value theorem, Taylor's theorem, I'Hopital's rule, maxima and minima, Taylor series 5.1 Differentiation
5.2 Rolle's theorem and the mean value theorem
5.3 Taylor's theorem
5.4 L'Hopital's rule
5.5 Maxima and minima