Calculus

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