Elementary Calculus

Description

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 GNU Free Documentation License History Index