Calculus for Cranks

Cover
Half Title
Title
Copyright
Contents
Preface
1: Induction and the Real Numbers
	1.1 Induction
	1.2 Induction for derivatives of polynomials
	1.3 The real numbers
	1.4 Limits
2: Sequences and Series
	2.1 Cauchy sequences and the Bolzano-Weierstrass and Squeeze theorems
	2.2 Infinite series
	2.3 Power series
3: Functions and Derivatives
	3.1 Continuity and limits
	3.2 Derivatives
	3.3 Mean Value Theorem
	3.4 Applications of the Mean Value Theorem
	3.5 Exponentiation
	3.6 Smoothness and series
	3.7 Inverse function theorem
4: Integration
	4.1 Definition of the Riemann integral
	4.2 Integration and uniform continuity
	4.3 The fundamental theorem
	4.4 Taylor's theorem with remainder
	4.5 Numerical integration
5: Convexity
	5.1 Convexity and optimization
	5.2 Inequalities
	5.3 Economics
6: Trigonometry, Complex Numbers, and Power Series
	6.1 Trigonometric functions by arclength
	6.2 Complex numbers
	6.3 Power series as functions
7: Complex Analysis
	7.1 Roots of polynomials
	7.2 Analytic functions
	7.3 Cauchy's theorem
	7.4 Taylor series of analytic functions
A: Appendix
	A.1 How to Use This Book
	A.2 Logic, Axioms, and Problem Solving
	A.3 Further Reading
Index
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	U
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