Preface Acknowledgements and Apologies List of Symbols The Greek Alphabet Part 1: Introductory Calculus 1 Numbers - Revision 2 The Absolute Value, Inequalities and Intervals 3 Mathematical Induction 4 Functions and Mappings 5 Functions and Mappings Continued 6 Derivatives 7 Derivatives Continued 8 The Derivative as a Tool to Investigate Functions 9 The Exponential and Logarithmic Functions 10 Trigonometric Functions and Their Inverses 11 Investigating Functions 12 Integrating Functions 13 Rules for Integration Part 2: Analysis in One Dimension 14 Problems with the Real Line 15 Sequences and their Limits 16 A First Encounter with Series 17 The Completeness of the Real Numbers 18 Convergence Criteria for Series, b-adic Fractions 19 Point Sets in 20 Continuous Functions 21 Differentiation 22 Applications of the Derivative 23 Convex Functions and some Norms on Rn 24 Uniform Convergence and Interchanging Limits 25 The Riemann Integral 26 The Fundamental Theorem of Calculus 27 A First Encounter with Differential Equations 28 Improper Integrals and the F-Function 29 Power Series and Taylor Series 30 Infinite Products and the Gauss Integral 31 More on the F-Function 32 Selected Topics on Functions of a Real Variable Appendices Appendix I: Elementary Aspects of Mathematical Logic Appendix II: Sets and Mappings. A Collection of Formulae Appendix III: The Peano Axioms Appendix IV: Results from Elementary Geometry Appendix V: Trigonometric and Hyperbolic Functions Appendix VI: More on the Completeness of Appendix VII: Limes Superior and Limes Inferior Appendix VIII: Connected Sets in R Solutions to Problems of Part 1 Solutions to Problems of Part 2 References
Mathematicians Contributing to Analysis Subject Index 編輯手記
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