1. An Introduction to Calculus BC

• 1.1 Introduction
  • 1.1.1 Welcome to Calculus II
  • 1.1.2 Review: Calculus I in 20 Minutes

2. Techniques of Integration

• 2.1 Integration Using Tables
  • 2.1.1 An Introduction to the Integral Table
  • 2.1.2 Making u-Substitutions

• 2.2 Integrals Involving Powers of Sine and Cosine
  • 2.2.1 An Introduction to Integrals with Powers of Sine and Cosine
  • 2.2.2 Integrals with Powers of Sine and Cosine
  • 2.2.3 Integrals with Even and Odd Powers of Sine and Cosine

• 2.3 Integrals Involving Powers of Other Trigonometric Functions
  • 2.3.1 Integrals of Other Trigonometric Functions
  • 2.3.2 Integrals with Odd Powers of Tangent and Any Power of Secant
  • 2.3.3 Integrals with Even Powers of Secant and Any Power of Tangent

• 2.4 An Introduction to Integration by Partial Fractions
  • 2.4.1 Finding Partial Fraction Decompositions
  • 2.4.2 Partial Fractions
  • 2.4.3 Long Division

• 2.5 Integration by Partial Fractions with Repeated Factors
  • 2.5.1 Repeated Linear Factors: Part One
  • 2.5.2 Repeated Linear Factors: Part Two
  • 2.5.3 Distinct and Repeated Quadratic Factors
  • 2.5.4 Partial Fractions of Transcendental Functions

• 2.6 Integration by Parts
  • 2.6.1 An Introduction to Integration by Parts
  • 2.6.2 Applying Integration by Parts to the Natural Log Function
  • 2.6.3 Inspirational Examples of Integration by Parts
  • 2.6.4 Repeated Application of Integration by Parts
  • 2.6.5 Algebraic Manipulation and Integration by Parts

• 2.7 An Introduction to Trigonometric Substitution
  • 2.7.1 Converting Radicals into Trigonometric Expressions
  • 2.7.2 Using Trigonometric Substitution to Integrate Radicals
  • 2.7.3 Trigonometric Substitutions on Rational Powers

• 2.8 Trigonometric Substitution Strategy
  • 2.8.1 An Overview of Trigonometric Substitution Strategy
  • 2.8.2 Trigonometric Substitution Involving a Definite Integral: Part One
  • 2.8.3 Trigonometric Substitution Involving a Definite Integral: Part Two

• 2.9 The Calculus of Inverse Trigonometric Functions
  • 2.9.1 More Calculus of Inverse Trigonometric Functions

3. Parametric Equations and Polar Coordinates

• 3.1 Understanding Parametric Equations
  • 3.1.1 An Introduction to Parametric Equations
  • 3.1.2 The Cycloid
  • 3.1.3 Eliminating Parameters

• 3.2 Calculus and Parametric Equations
  • 3.2.1 Derivatives of Parametric Equations
  • 3.2.2 Graphing the Elliptic Curve
  • 3.2.3 The Arc Length of a Parameterized Curve
  • 3.2.4 Finding Arc Lengths of Curves Given by Parametric Equations

• 3.3 Understanding Polar Coordinates
  • 3.3.1 The Polar Coordinate System
  • 3.3.2 Converting between Polar and Cartesian Forms
  • 3.3.3 Spirals and Circles
  • 3.3.4 Graphing Some Special Polar Functions

• 3.4 Polar Functions and Slope
  • 3.4.1 Calculus and the Rose Curve
  • 3.4.2 Finding the Slopes of Tangent Lines in Polar Form

• 3.5 Polar Functions and Area
  • 3.5.1 Heading toward the Area of a Polar Region
  • 3.5.2 Finding the Area of a Polar Region: Part One
  • 3.5.3 Finding the Area of a Polar Region: Part Two
  • 3.5.4 The Area of a Region Bounded by Two Polar Curves: Part One
  • 3.5.5 The Area of a Region Bounded by Two Polar Curves: Part Two

4. Sequences and Series

• 4.1 Sequences
  • 4.1.1 The Limit of a Sequence
  • 4.1.2 Determining the Limit of a Sequence
  • 4.1.3 The Squeeze and Absolute Value Theorems

• 4.2 Monotonic and Bounded Sequences
  • 4.2.1 Monotonic and Bounded Sequences

• 4.3 Infinite Series
  • 4.3.1 An Introduction to Infinite Series
  • 4.3.2 The Summation of Infinite Series
  • 4.3.3 Geometric Series
  • 4.3.4 Telescoping Series
  • 4.3.5 Applications of Series

• 4.4 Convergence and Divergence
  • 4.4.1 Properties of Convergent Series
  • 4.4.2 The nth-Term Test for Divergence

• 4.5 The Integral Test
  • 4.5.1 An Introduction to the Integral Test
  • 4.5.2 Examples of the Integral Test
  • 4.5.3 Using the Integral Test
  • 4.5.4 Defining p-Series

• 4.6 The Direct Comparison Test
  • 4.6.1 An Introduction to the Direct Comparison Test
  • 4.6.2 Using the Direct Comparison Test

• 4.7 The Limit Comparison Test
  • 4.7.1 An Introduction to the Limit Comparison Test
  • 4.7.2 Using the Limit Comparison Test
  • 4.7.3 Inverting the Series in the Limit Comparison Test

• 4.8 The Alternating Series
  • 4.8.1 Alternating Series
  • 4.8.2 The Alternating Series Test
  • 4.8.3 Estimating the Sum of an Alternating Series

• 4.9 Absolute and Conditional Convergences
  • 4.9.1 Absolute and Conditional Convergence

• 4.10 The Ratio and Root Tests
  • 4.10.1 The Ratio Test
  • 4.10.2 Examples of the Ratio Test
  • 4.10.3 The Root Test

• 4.11 Polynomial Approximations of Elementary Functions
  • 4.11.1 Polynomial Approximation of Elementary Functions
  • 4.11.2 Higher-Degree Approximations

• 4.12 Taylor and Maclaurin Polynomials
  • 4.12.1 Taylor Polynomials
  • 4.12.2 Maclaurin Polynomials
  • 4.12.3 The Remainder of a Taylor Polynomial
  • 4.12.4 Approximating the Value of a Function

• 4.13 Taylor and Maclaurin Series
  • 4.13.1 Taylor Series
  • 4.13.2 Examples of the Taylor and Maclaurin Series
  • 4.13.3 New Taylor Series
  • 4.13.4 The Convergence of Taylor Series

• 4.14 Power Series
  • 4.14.1 The Definition of Power Series
  • 4.14.2 The Interval and Radius of Convergence
  • 4.14.3 Finding the Interval and Radius of Convergence: Part One
  • 4.14.4 Finding the Interval and Radius of Convergence: Part Two
  • 4.14.5 Finding the Interval and Radius of Convergence: Part Three

• 4.15 Power Series Representations of Functions
  • 4.15.1 Differentiation and Integration of Power Series
  • 4.15.2 Finding Power Series Representations by Differentiation
  • 4.15.3 Finding Power Series Representations by Integration
  • 4.15.4 Integrating Functions Using Power Series

5. Differential Equations

• 5.1 Solving a Homogeneous Differential Equation
  • 5.1.1 Separating Homogeneous Differential Equations
  • 5.1.2 Change of Variables

• 5.2 Solving First-Order Linear Differential Equations
  • 5.2.1 First-Order Linear Differential Equations
  • 5.2.2 Using Integrating Factors

6. Vector Calculus and the Geometry of R² and R³

• 6.1 Vectors and the Geometry of R² and R³
  • 6.1.1 Coordinate Geometry in Three-Dimensional Space
  • 6.1.2 Introduction to Vectors
  • 6.1.3 Vectors in R² and R³
  • 6.1.4 An Introduction to the Dot Product
  • 6.1.5 Orthogonal Projections
  • 6.1.6 An Introduction to the Cross Product
  • 6.1.7 Geometry of the Cross Product
  • 6.1.8 Equations of Lines and Planes in R³

• 6.2 Vector Functions
  • 6.2.1 Introduction to Vector Functions
  • 6.2.2 Derivatives of Vector Functions
  • 6.2.3 Vector Functions: Smooth Curves
  • 6.2.4 Vector Functions: Velocity and Acceleration