Calculus

Description

Bookmarks added to digitized version from the Internet Archive. Cover Title Copyright Preface Contents Part I Prologue 1 Basic Properties of Numbers 2 Numbers of Various Sorts Part II Foundations 3 Functions Appendix. Ordered Pairs 4 Graphs Appendix 1. Vectors Appendix 2. The Conic Sections Appendix 3. Polar Coordinates 5 Limits 6 Continuous Functions 7 Three Hard Theorems 8 Least Upper Bounds Appendix. Uniform Continuity Part III Derivatives and integrals 9 Derivatives 10 Differentiation 11 Significance of the Derivative Appendix. Convexity and Concavity 12 Inverse Functions Appendix. Parametric Representation of Curves 13 Integrals Appendix. Riemann Sums 14 The Fundamental Theorem of Calculus 15 The Trigonometric Functions *16 pi is Irrational *17 Planetary Motion 18 The Logarithm and Exponential Functions 19 Integration in Elementary Terms Appendix. The Cosmopolitan Integral Part IV Infinite Sequences and Infinite Series 20 Approximation by Polynomial Functions *21 e is Transcendental 22 Infinite Sequences 23 Infinite Series 24 Uniform Convergence and Power Series 25 Complex Numbers 26 Complex Functions 27 Complex Power Series Part V Epilogue 28 Fields 29 Construction of the Real Numbers 30 Uniqueness of the Real Numbers Suggested Reading Answers (to selected problems) Glossary of Symbols Index