E-Book, Englisch, 624 Seiten, Web PDF
Rankin An Introduction to Mathematical Analysis
1. Auflage 2014
ISBN: 978-1-4831-8503-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 624 Seiten, Web PDF
Reihe: International Series in Pure and Applied Mathematics
ISBN: 978-1-4831-8503-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
International Series of Monographs on Pure and Applied Mathematics, Volume 43: An Introduction to Mathematical Analysis discusses the various topics involved in the analysis of functions of a single real variable. The title first covers the fundamental idea and assumptions in analysis, and then proceeds to tackling the various areas in analysis, such as limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. The book will be most useful to undergraduate students of mathematical analysis.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;An Introduction to Mathematical Analysis;4
3;Copyright Page;5
4;Table of Contents;8
5;Dediction;6
6;PREFACE;10
7;LIST OF SYMBOLS AND NOTATIONS;14
8;CHAPTER 1.
FUNDAMENTAL IDEAS AND ASSUMPTIONS;18
8.1;1. INTRODUCTION;18
8.2;2. ASSUMPTIONS RELATING TO THE FIELD OPERATIONS;19
8.3;3. ASSUMPTIONS RELATING TO THE ORDERING OF THE REAL NUMBERS;21
8.4;4. MATHEMATICAL INDUCTION;24
8.5;5. UPPER AND LOWER BOUNDS OF SETS OF REAL NUMBERS;30
8.6;6. FUNCTIONS;37
9;CHAPTER 2.
LIMITS AND CONTINUITY;52
9.1;7. LIMITS OF REAL FUNCTIONS DEFINED ON THE POSITIVE INTEGERS;52
9.2;8. LIMITS OF REAL FUNCTIONS OF A REAL VARIABLE x AS x TENDS TO INFINITY;75
9.3;9. ELEMENTARY TOPOLOGICAL IDEAS;79
9.4;10. LIMITS OF REAL FUNCTIONS AT FINITE POINTS;83
9.5;11. CONTINUITY;91
9.6;12. INVERSE FUNCTIONS AND FRACTIONAL INDICES;109
10;CHAPTER 3.
DIFFERENTIABILITY;126
10.1;13. DERIVATIVES;126
10.2;14. GENERAL THEOREMS CONCERNING REAL FUNCTIONS;137
10.3;15. MAXIMA, MINIMA AND CONVEXITY;152
10.4;16. COMPLEX NUMBERS AND FUNCTIONS;157
11;CHAPTER 4.
INFINITE SERIES;167
12;17. ELEMENTARY PROPERTIES OF INFINITE SERIES;167
12.1;18. SERIES WITH NON-NEGATIVE TERMS;174
12.2;19. ABSOLUTE AND CONDITIONAL CONVERGENCE;183
12.3;20. THE DECIMAL NOTATION FOR REAL NUMBERS;201
13;CHAPTER 5. FUNCTIONS DEFINED BY POWER SERIES;208
13.1;21. GENERAL THEORY OF POWER SERIES;208
13.2;22. REAL POWER SERIES;221
13.3;23. THE EXPONENTIAL AND LOGARITHMIC FUNCTIONS;226
13.4;24. THE TRIGONOMETRIC FUNCTIONS;247
13.5;25. THE HYPERBOLIC FUNCTIONS;258
13.6;26. COMPLEX INDICES;263
14;CHAPTER 6.
INTEGRATION;277
14.1;27. THE INDEFINITE INTEGRAL;277
14.2;28. INTERVAL FUNCTIONS AND FUNCTIONS OF BOUNDED VARIATION;304
14.3;29. THERIE MANN-STIELTJES INTEGRAL;333
14.4;30. THE RIEMANN INTEGRAL;368
14.5;31. CURVES;408
14.6;32. AREA;443
15;CHAPTER 7.
CONVERGENCE AND UNIFORMITY;454
15.1;33. UPPER AND LOWER LIMITS AND THEIR APPLICATIONS;454
15.2;34. FURTHER CONVERGENCE TESTS FOR INFINITE SERIES;469
15.3;35. UNIFORM CONVERGENCE;484
15.4;36. IMPROPER INTEGRALS;513
15.5;37. DOUBLE SERIES;558
15.6;38. INFINITE PRODUCTS;580
16;HINTS FOR SOLUTIONS OF EXERCISES;600
17;INDEX;618
