Author(s): Michael Corral
Year: 2020
Language: English
Pages: 348
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
