AP Calculus BC
- 12-month Online Subscription to our complete AP Calculus BC course with video lessons, day-by-day lesson plans, automatically graded exercises, and much more.
- Printed Notes (optional, AB + BC) are the AP Calculus course notes from the Online Subscription printed in a black & white, on-the-go format. These are available for purchase from the AP Calculus BC Course Site.
AP Calculus BC details
Did you know that fewer than 50% of students taking the AP Calculus exam make a 3 or above? The AP Calculus BC exam is one of the toughest around, so use the best teacher possible; learn the fundamentals of calculus from award-winning teacher Edward Burger. Your student will learn and remember everything they need to ace the AP Calculus BC exam by using calculus on the web instead of an old-fashioned textbook.
The AP Calculus BC exam requires mastery of the AB topics; AP Calculus AB is sold separately.
Thinkwell's Calculus BC includes all of these features to prepare you for the big exam:
- Equivalent to 11th- or 12th-grade AP Calculus BC
- More than 100 video lessons
- 144 available contact hours (What is this?)
The number of contact hours in a course reflects the amount of time a student will typically spend completing the assignments in each course (i.e. watching videos, doing exercises, taking exams, etc...). Many people think about contact hours as the "seat time" for a course. Thinkwell provides this information so you can ensure that the amount of instruction in a Thinkwell course meets the standards and requirements for your state or region.
- 1000+ interactive AP Calculus BC problems with immediate feedback allow you to track your progress (See sample)
- Calculus BC practice chapter tests for all 5 chapters, as well as a final exam to make sure you're ready for the AP Calculus BC exam.
- Printable illustrated notes for each topic
- Real-world application examples in both lectures and exercises
- Closed captioning for all videos
- Glossary of more than 200 mathematical terms
- Engaging content to help students advance their mathematical knowledge:
- Indeterminate forms and L'Hopital's rule
- Elementary functions and their inverses
- Techniques of integration, including integration by partial fractions and trigonometric substitution
- Improper integrals
- Disks, washers, shells, and other applications of integral calculus
- Sequences and series
- Differential equations
- Parametric equations and polar coordinates
- Vector calculus
About the Author
Table of Contents
(Expand All - Close All)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 R^{2} and R^{3}
- 6.1 Vectors and the Geometry of R^{2} and R^{3}
- 6.1.1 Coordinate Geometry in Three Dimensional Space
- 6.1.2 Introduction to Vectors
- 6.1.3 Vectors in R^{2} and R^{3}
- 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 R^{3}
- 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