Calculus AB compatible with AP* Materials
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Calculus AB compatible with AP* Details
Thinkwell's Calculus AB includes all of these features to prepare you for the big exam:
 Equivalent to 11th or 12thgrade AP Calculus AB
 More than 180 video lessons ()
 1000+ interactive AP Calculus AB problems with immediate feedback allow you to track your progress (see sample)
 Calculus AB practice chapter tests for all 12 chapters, as well as a final exam to make sure you're ready for the AP Calculus AB exam (only available in the homeschool version).
 Printable illustrated notes for each topic
 Realworld 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:
 Understanding and evaluating limits and derivatives
 Computational techniques such as the power rule, product rule, quotient rule, and chain rule
 Trigonometric, exponential, and logarithmic functions
 Implicit differentiation
 Differentiation, optimization, and related rates
 Sketching curves
 Antiderivatives, integration, and the fundamental theorem of calculus
 Applications of integration such as motion, finding the area between two curves, and integrating with respect to y
Table of Contents
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1. The Basics
 1.1 Overview

1.1.1 An Introduction to Thinkwell Calculus

1.1.2 The Two Questions of Calculus

1.1.3 Average Rates of Change
 1.2 Precalculus Review

1.2.4 Some NonEuclidean Geometry
2. Limits
 2.1 The Concept of the Limit

2.1.1 Finding Rate of Change over an Interval

2.1.2 Finding Limits Graphically

2.1.3 The Formal Definition of a Limit

2.1.4 The Limit Laws, Part I

2.1.5 The Limit Laws, Part II

2.1.7 The Squeeze Theorem

2.1.8 Continuity and Discontinuity
 2.2 Evaluating Limits

2.2.2 Limits and Indeterminate Forms

2.2.3 Two Techniques for Evaluating Limits

2.2.4 An Overview of Limits
3. An Introduction to Derivatives
 3.1 Understanding the Derivative

3.1.1 Rates of Change, Secants, and Tangents

3.1.2 Finding Instantaneous Velocity
 3.2 Using the Derivative

3.2.1 The Slope of a Tangent Line

3.2.3 The Equation of a Tangent Line

3.2.4 More on Instantaneous Rate
 3.3 Some Special Derivatives

3.3.1 The Derivative of the Reciprocal Function

3.3.2 The Derivative of the Square Root Function
4. Computational Techniques
 4.1 The Power Rule

4.1.1 A Shortcut for Finding Derivatives

4.1.2 A Quick Proof of the Power Rule

4.1.3 Uses of the Power Rule
 4.2 The Product and Quotient Rules
 4.3 The Chain Rule

4.3.1 An Introduction to the Chain Rule

4.3.2 Using the Chain Rule

4.3.3 Combining Computational Techniques
5. Special Functions
 5.1 Trigonometric Functions

5.1.1 A Review of Trigonometry

5.1.2 Graphing Trigonometric Functions

5.1.3 The Derivatives of Trigonometric Functions
 5.2 Exponential Functions

5.2.1 Graphing Exponential Functions

5.2.2 Derivatives of Exponential Functions
 5.3 Logarithmic Functions

5.3.1 Evaluating Logarithmic Functions

5.3.2 The Derivative of the Natural Log Function

5.3.3 Using the Derivative Rules with Transcendental Functions
6. Implicit Differentiation and the Inverse Function
 6.1 Implicit Differentiation Basics

6.1.1 An Introduction to Implicit Differentiation

6.1.2 Finding the Derivative Implicitly
 6.2 Applying Implicit Differentiation

6.2.1 Using Implicit Differentiation

6.2.2 Applying Implicit Differentiation
 6.3 Inverse Functions

6.3.1 The Exponential and Natural Log Functions

6.3.2 Differentiating Logarithmic Functions

6.3.3 Logarithmic Differentiation

6.3.4 The Basics of Inverse Functions

6.3.5 Finding the Inverse of a Function
 6.4 The Calculus of Inverse Functions

6.4.1 Derivatives of Inverse Functions
 6.5 Inverse Trigonometric Functions

6.5.1 The Inverse Sine, Cosine, and Tangent Functions

6.5.2 The Inverse Secant, Cosecant, and Cotangent Functions

6.5.3 Evaluating Inverse Trigonometric Functions
 6.6 The Calculus of Inverse Trigonometric Functions

6.6.1 Derivatives of Inverse Trigonometric Functions
 6.7 The Hyperbolic Functions

6.7.1 Defining the Hyperbolic Functions

6.7.2 Hyperbolic Identities

6.7.3 Derivatives of Hyperbolic Functions
7. Applications of Differentiation
 7.1 Position and Velocity

7.1.1 Acceleration and the Derivative

7.1.2 Solving Word Problems Involving Distance and Velocity
 7.2 Linear Approximation

7.2.1 HigherOrder Derivatives and Linear Approximation

7.2.2 Using the Tangent Line Approximation Formula
 7.3 Optimization

7.3.1 The Connection Between Slope and Optimization

7.3.5 The WireCutting Problem
 7.4 Related Rates

7.4.3 The Baseball Problem
8. Curve Sketching
 8.1 Introduction

8.1.1 An Introduction to Curve Sketching
 8.2 Critical Points

8.2.2 Maximum and Minimum

8.2.3 Regions Where a Function Increases or Decreases

8.2.4 The First Derivative Test
 8.3 Concavity

8.3.1 Concavity and Inflection Points

8.3.2 Using the Second Derivative to Examine Concavity
 8.4 Graphing Using the Derivative

8.4.1 Graphs of Polynomial Functions

8.4.2 Cusp Points and the Derivative

8.4.3 DomainRestricted Functions and the Derivative

8.4.4 The Second Derivative Test
 8.5 Asymptotes

8.5.1 Vertical Asymptotes

8.5.2 Horizontal Asymptotes and Infinite Limits

8.5.3 Graphing Functions with Asymptotes

8.5.4 Functions with Asymptotes and Holes

8.5.5 Functions with Asymptotes and Critical Points
9. The Basics of Integration
 9.1 Antiderivatives

9.1.1 Antidifferentiation

9.1.2 Antiderivatives of Powers of x

9.1.3 Antiderivatives of Trigonometric and Exponential Functions
 9.2 Integration by Substitution

9.2.1 Undoing the Chain Rule

9.2.2 Integrating Polynomials by Substitution
 9.3 Illustrating Integration by Substitution

9.3.1 Integrating Composite Trigonometric Functions by Substitution

9.3.2 Integrating Composite Exponential and Rational Functions by Substitution

9.3.3 More Integrating Trigonometric Functions by Substitution

9.3.4 Choosing Effective Function Decompositions
 9.4 The Fundamental Theorem of Calculus

9.4.1 Approximating Areas of Plane Regions

9.4.2 Areas, Riemann Sums, and Definite Integrals

9.4.3 The Fundamental Theorem of Calculus, Part I

9.4.4 The Fundamental Theorem of Calculus, Part II

9.4.5 Illustrating the Fundamental Theorem of Calculus

9.4.6 Evaluating Definite Integrals
 9.5 Trigonometric Substitution Strategy

9.5.1 An Overview of Trigonometric Substitution Strategy

9.5.2 Trigonometric Substitution Involving a Definite Integral: Part One

9.5.3 Trigonometric Substitution Involving a Definite Integral: Part Two
 9.6 Numerical Integration

9.6.1 Deriving the Trapezoidal Rule

9.6.2 An Example of the Trapezoidal Rule
10. Applications of Integration
 10.1 Motion

10.1.1 Antiderivatives and Motion

10.1.2 Gravity and Vertical Motion

10.1.3 Solving Vertical Motion Problems
 10.2 Finding the Area between Two Curves

10.2.1 The Area between Two Curves

10.2.2 Limits of Integration and Area

10.2.3 Common Mistakes to Avoid When Finding Areas

10.2.4 Regions Bound by Several Curves
 10.3 Integrating with Respect to y

10.3.1 Finding Areas by Integrating with Respect to y: Part One

10.3.2 Finding Areas by Integrating with Respect to y: Part Two

10.3.3 Area, Integration by Substitution, and Trigonometry
 10.4 The Average Value of a Function

10.4.1 Finding the Average Value of a Function
 10.5 Finding Volumes Using CrossSections

10.5.1 Finding Volumes Using CrossSectional Slices

10.5.2 An Example of Finding CrossSectional Volumes
 10.6 Disks and Washers

10.6.1 Solids of Revolution

10.6.2 The Disk Method along the yAxis

10.6.3 A Transcendental Example of the Disk Method

10.6.4 The Washer Method across the xAxis

10.6.5 The Washer Method across the yAxis
 10.7 Shells

10.7.1 Introducing the Shell Method

10.7.2 Why Shells Can Be Better Than Washers

10.7.3 The Shell Method: Integrating with Respect to y
 10.8 Work

10.8.1 An Introduction to Work
 10.9 Moments and Centers of Mass

10.9.2 The Center of Mass of a Thin Plate
 10.10 Arc Lengths and Functions

10.10.1 An Introduction to Arc Length

10.10.2 Finding Arc Lengths of Curves Given by Functions
11. Differential Equations
 11.1 Separable Differential Equations

11.1.1 An Introduction to Differential Equations

11.1.2 Solving Separable Differential Equations

11.1.3 Finding a Particular Solution

11.1.5 Euler's Method for Solving Differential Equations Numerically
 11.2 Growth and Decay Problems

11.2.1 Exponential Growth
12. L'Hôpital's Rule and Improper Integrals
 12.1 Indeterminate Quotients

12.1.1 Indeterminate Forms

12.1.2 An Introduction to L'Hôpital's Rule

12.1.3 Basic Uses of L'Hôpital's Rule

12.1.4 More Exotic Examples of Indeterminate Forms
 12.2 Other Indeterminate Forms

12.2.1 L'Hôpital's Rule and Indeterminate Products

12.2.2 L'Hôpital's Rule and Indeterminate Differences

12.2.3 L'Hôpital's Rule and One to the Infinite Power

12.2.4 Another Example of One to the Infinite Power
 12.3 Improper Integrals

12.3.1 The First Type of Improper Integral

12.3.2 The Second Type of Improper Integral

12.3.3 Infinite Limits of Integration, Convergence, and Divergence
13. Math Fun
 13.1 Paradoxes

13.1.1 An Introduction to Paradoxes

13.1.2 Paradoxes and Air Safety
 13.3 The Close of Calculus AB

13.3.1 A Glimpse Into Calculus II
About the Author
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 UTAustin 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.
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 of 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, padic 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.