项目作者： luqmanmalik
项目描述 ：
Analysis on Manifolds: Corpus on Classical Theorems | Foundations in mathematical analysis | HRT Software Distributions® | MIT License | IMUPR 1A | UCB M 130
高级语言： HTML
项目地址: git://github.com/luqmanmalik/57-01_66-10910_9780805390216.git
Calculus on Manifolds
MSC2010_LCCCN_ISBN: 57-01_66-10910_9780805390216
Luqman MalikIMU P-RNK: 1A (adv. baccalaureate) Series: Foundations in Mathematical Analysis···························································· Distribution license: Hilix Research and Technologies, Inc.®
CONTENTS
Preface
| Part 1 |
Prologue |
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1. Basic Properties of Numbers 3 |
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2. Numbers of Various Sorts 21 |
| Part 2 |
Foundations |
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3. Functions 39| Appendix. Ordered Pairs 54 |
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4. Graphs 56| Appendix 1. Vectors 75 | | Appendix 2. The Conic Sections 80 | | Appendix 3. Polar Coordinates 84 |
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5. Limits 90 |
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6. Continuous Functions 113 |
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7. Three Hard Theorems 120 |
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8. Least Upper Bounds 131| Appendix. Uniform Continuity 142 |
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| Part 3 |
Derivatives and Integrals |
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9. Derivatives 147 |
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10. Differentiation 166 |
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11. Significance of the Derivative 185| Appendix. Convexity and Concavity 216 |
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12. Inverse Functions 227| Appendix. Parametric Representation of Curves 241 |
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13. Integrals 250| Appendix. Riemann Sums 279 |
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14. The Fundamental Theorem of Calculus 282 |
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15. The Trigonometric Functions 300 |
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16. π is Irrational 321 ⚐ |
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17. Planetary Motion 327 ⚐ |
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18. The Logarithm and Exponentail Functions 336 |
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19. Integration in Elementary Terms 359| Appendix. The Cosmopolitan Integral 397 |
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| Part 4 |
Infinite Sequences and Infinite Series |
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20. Approximation by Polynomial Functions 405 |
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21. e is Transcendental 435 ⚐ |
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22. Infinite Sequences 445 |
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23. Infinite Series 464 |
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24. Uniform Convergence and Power Series 491 |
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25. Complex Numbers 517 |
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26. Complex Functions 532 |
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27. Complex Power Series 546 |
| Part 5 |
Epilogue |
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28. Fields 571 |
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29. Construction of the Real Numbers 578 |
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30. Uniqueness of the Real Numbers 591| Suggested reading 599 | | Answers (to Selected Problems) 609 | | Glossery of Symbols 655 | | Index 659 |
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This is the second installment in Spivak’s analysis sequence. A strong footing in Calculus, A Hitchhiker’s Guide to Calculus, and the present text should prepare the serious student of mathematical analysis for Spivak’s five–volume Comprehensive introduction to Differential Geometry. Mathematicians use to polorize over the supremecy of pure versus applied mathematics; that paradigm has all but vanished. Today, it is a question of algebra versus analysis. If one finds themself pivoting between the two, I have no doubt that an honest attempt at Spivak will settle the matter for them.
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