Elementary Calculus

Preface
Contents
1 The Derivative
	1.1 Introduction
	1.2 The Derivative: Limit Approach
	1.3 The Derivative: Infinitesimal Approach
	1.4 Derivatives of Sums, Products and Quotients
	1.5 The Chain Rule
	1.6 Higher Order Derivatives
2 Derivatives of Common Functions
	2.1 Inverse Functions
	2.2 Trigonometric Functions and Their Inverses
	2.3 The Exponential and Natural Logarithm Functions
	2.4 General Exponential and Logarithmic Functions
3 Topics in Differential Calculus
	3.1 Tangent Lines
	3.2 Limits: Formal Definition
	3.3 Continuity
	3.4 Implicit Differentiation
	3.5 Related Rates
	3.6 Differentials
4 Applications of Derivatives
	4.1 Optimization
	4.2 Curve Sketching
	4.3 Numerical Approximation of Roots of Functions
	4.4 The Mean Value Theorem
5 The Integral
	5.1 The Indefinite Integral
	5.2 The Definite Integral
	5.3 The Fundamental Theorem of Calculus
	5.4 Integration by Substitution
	5.5 Improper Integrals
6 Methods of Integration
	6.1 Integration by Parts
	6.2 Trigonometric Integrals
	6.3 Trigonometric Substitutions
	6.4 Partial Fractions
	6.5 Miscellaneous Integration Methods
	6.6 Numerical Integration Methods
7 Analytic Geometry and Plane Curves
	7.1 Ellipses
	7.2 Parabolas
	7.3 Hyperbolas
	7.4 Translations and Rotations
	7.5 Hyperbolic Functions
	7.6 Parametric Equations
	7.7 Polar Coordinates
8 Applications of Integrals
	8.1 Area Between Curves
	8.2 Average Value of a Function
	8.3 Arc Length and Curvature
	8.4 Surfaces and Solids of Revolution
	8.5 Applications in Physics and Statistics
9 Infinite Sequences and Series
	9.1 Sequences and Series
	9.2 Tests for Convergence
	9.3 Alternating Series
	9.4 Power Series
	9.5 Taylor\'s Series
Appendix A Answers and Hints to Selected Exercises
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History
Index