Table of Contents
 1 • Foundation for Calculus: Functions and Limits
 2 • Key Concept: The Derivative

3 • ShortCuts to Differentiation
 Power Rule of Derivatives
 Differentiation of Exponential Functions
 The Product Rule
 The Quotient Rule
 The Chain Rule
 Differentiation of Trigonometric Functions
 Differentiation of Reciprocal Trigonometric Functions
 Differentiation of Inverse Functions
 Differentiation of Logarithmic Functions
 Derivatives of Inverse Trigonometric Functions
 Implicit Differentiation
 Linear Approximation
 The Mean Value Theorem

4 • Using the Derivative
 Increasing and Decreasing Intervals of a Function Using Derivatives
 Critical Points and Local Extrema of a Function
 Second Derivative Test for Local Extrema
 Absolute Extrema
 Optimization Using Derivatives
 Related Rates
 L’Hôpital’s Rule
 Indeterminate Forms and L’Hôpital’s Rule
 Conversion between Parametric and Rectangular Equations
 Derivatives of Parametric Equations
 5 • Key Concept: The Definite Integral
 6 • Constructing Antiderivatives

7 • Integration
 Integration by Substitution: Indefinite Integrals
 Integration by Parts
 Integration by Partial Fractions with Linear Factors
 Integration by Partial Fractions with Quadratic Factors
 Integration by Partial Fractions of Improper Fractions
 Integration by Trigonometric Substitutions
 Numerical Integration: Riemann Sums
 Numerical Integration: The Trapezoidal Rule
 Numerical Integration: Simpson’s Rule
 Improper Integrals: Infinite Limits of Integration
 Comparison Test for Improper Integrals

8 • Using the Definite Integral
 Volumes by Slicing
 Volumes of Solids of Revolution Using the Disk and Washer Methods
 Arc Length by Integration
 Arc Length of Parametric Curves
 Polar Coordinates
 Graphing Polar Curves
 Conversion between Rectangular and Polar Equations
 Area Bounded by Polar Curves
 Arc Length of a Polar Curve
 Center of Mass of Laminas
 Center of Mass of Solids
 Histograms
 Continuous Random Variables
 Normal Distribution

9 • Sequences and Series
 Representing Sequences
 Using Arithmetic Sequence Formulas
 Finding the Arithmetic Sequence
 Recursive Formula of a Sequence
 Convergent and Divergent Sequences
 Monotone Convergence Theorem
 Infinite Geometric Series
 Sum of a Finite Geometric Sequence
 Sum of an Infinite Geometric Sequence
 Integral Test for Series
 Harmonic and pSeries
 Comparison Test for Series
 Limit Comparison Test
 Ratio Test
 Conditional and Absolute Convergence
 10 • Approximating Functions Using Series
 11 • Differential Equations
 12 • Functions of Several Variables
 13 • A Fundamental Tool: Vectors
 14 • Differentiating Functions of Several Variables
 15 • Optimization: Local and Global Extrema
 16 • Integrating Functions of Several Variables
 17 • Parameterization and Vector Fields
 18 • Line Integrals
 19 • Flux Integrals and Divergence
 20 • The Curl and Stokes’ Theorem
 21 • Parameters, Coordinates, and Integrals