Table of Contents

1 • Precalculus Review
 Real Numbers
 Intervals
 Distance on the Coordinate Plane: Pythagorean Formula
 Even and Odd Functions
 Equation of a Straight Line: Standard and Point–Slope Forms
 Equation of a Straight Line: General Form
 Equation of a Straight Line: Slope–Intercept Form
 Completing the Square
 Solving Quadratics: Completing the Square
 Composite Functions
 Absolute Value Functions
 Conversion between Radians and Degrees
 Simple Trigonometric Equations
 Evaluating Trigonometric Functions Using Pythagorean Identities
 Inverse Trigonometric Functions
 Solving Exponential Equations Using Exponent Properties
 Laws of Logarithms
 Solving Exponential Equations Using Logarithms

2 • Limits
 Average and Instantaneous Rates of Change
 Limits from Tables and Graphs
 Limits by Direct Substitution
 Continuity at a Point
 Classifying Discontinuities
 Continuity of Functions
 Evaluating Limits Using Algebraic Techniques
 Limits of Trigonometric Functions
 Limits at Infinity and Unbounded Limits
 Horizontal and Vertical Asymptotes of a Function
 Intermediate Value Theorem
 Formal Definition of a Limit

3 • Differentiation
 Definition of the Derivative
 Interpreting Graphs of Derivatives
 The Differentiability of a Function
 Power Rule of Derivatives
 The Product Rule
 The Quotient Rule
 Differentiation of Trigonometric Functions
 Differentiation of Reciprocal Trigonometric Functions
 Derivatives of Inverse Trigonometric Functions
 The Chain Rule
 Implicit Differentiation
 Differentiation of Exponential Functions
 Differentiation of Logarithmic Functions
 Logarithmic Differentiation
 Related Rates
 4 • Applications of the Derivative

5 • The Integral
 Riemann Sums
 Definite Integrals as Limits of Riemann Sums
 The Fundamental Theorem of Calculus: Evaluating Definite Integrals
 Antiderivatives
 Indefinite Integrals: The Power Rule
 The Fundamental Theorem of Calculus: Functions Defined by Integrals
 The Net Change Theorem
 Integration by Substitution: Indefinite Integrals
 Exponential Growth and Decay Models
 Exponential Growth and Decay
 6 • Applications of the Integral

7 • Techniques of Integration
 Integration by Parts
 Indefinite Integrals: Trigonometric Functions
 Trigonometric Integrals
 Integration by Trigonometric Substitutions
 Reduction Formulae for Integration
 Integration by Partial Fractions with Linear Factors
 Integration by Partial Fractions with Quadratic Factors
 Integration by Partial Fractions of Improper Fractions
 Improper Integrals: Infinite Limits of Integration
 Improper Integrals: Discontinuous Integrands
 Numerical Integration: Riemann Sums
 Numerical Integration: The Trapezoidal Rule
 Numerical Integration: Simpson’s Rule
 8 • Further Applications of the Integral and Taylor Polynomials
 Appendices