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Thinkwell Home-school Curriculum

AP Calculus BC

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AP Calculus BC Online Course 12-month access $125.00
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Our complete AP Calculus BC package includes:
  • 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?)
  • 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

Professor Edward Burger

Edward Burger
Williams College

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa cum laude with distinction in mathematics from Connecticut College.

He has also taught at UT-Austin and the University of Colorado at Boulder, and he served as a fellow at the University of Waterloo in Canada and at Macquarie University in Australia. Prof. Burger has won many awards, including the 2001 Haimo Award for Distinguished Teaching of Mathematics, the 2004 Chauvenet Prize, and the 2006 Lester R. Ford Award, all from the Mathematical Association of America. In 2006, Reader's Digest listed him in the "100 Best of America". After completing his tenure as Gaudino Scholar at Williams, he was named Lissack Professor for Social Responsibility and Personal Ethics. In 2010, he won the prestigious Robert Foster Cherry Award for Great Teaching.

Prof. Burger is the author of over 50 articles, videos, and books, including the trade book Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas and the textbook The Heart of Mathematics: An Invitation to Effective Thinking. He also speaks frequently to professional and public audiences, referees professional journals, and publishes articles in leading math journals, including The Journal of Number Theory and American Mathematical Monthly. His areas of specialty include number theory, Diophantine approximation, p-adic analysis, the geometry of numbers, and the theory of continued fractions.

Prof. Burger's unique sense of humor and his teaching expertise combine to make him the ideal presenter of Thinkwell's entertaining and informative video lectures.

Table of Contents

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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
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When I use Thinkwell, the retention rate of what I've learned is significantly increased. I would say that Thinkwell not only makes the material easier to digest but creates a fun way to actually learn math.
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Thinkwell contains all the necessary components for you to gain a thorough understanding of the course. The lectures are there, the notes are there, and the quizzes are there. It's a complete package.
Throughout the Thinkwell lectures, I never got lost. I never got confused. I was able to understand... The lecture section is outstanding.
Thinkwell is a program that allows students like me to learn these subjects while still keeping us entertained. Good job, Thinkwell.
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Professor Burger is passionate about Math and he is able to transmit his passion and clear thinking through his lectures. I could understand not only the concepts and HOW to solve the problems, but WHY we solve them in a certain way... You meet just a few of those instructors in a lifetime.
I have recommended them to many friends, all of whom have used them with great success. Dr. Burger's sense of humor really adds to the class and makes it particularly engaging for my son.
Our family has enjoyed the format and scope of the Thinkwell course we've used in our homeschool program. It is well organized, easy to use and has been an asset to our homeschool curriculum.
Thinkwell is a great resource, with videos, notes, sample problems, and animations to help students understand the material and solve problems.
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