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Calculus AB compatible with AP*
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Learn from the best! Award-winning Professor Edward Burger teaches you the fundamentals of Calculus AB in a dynamic, enriching, multimedia format. You'll learn and remember exactly what you need to know to score a perfect 5 on the Calculus AB Exam. Thinkwell's online Calculus AB subscription gives you access to a complete web-based solution that includes all of the content and tools you'll need to succeed in AP Calculus.
- Thinkwell's video lectures cover the comprehensive scope and sequence of topics covered on the Calculus AB exam.
- Our interactive exercises with immediate feedback allow you to quickly determine which areas you'll need to spend extra time studying.
- Concise, illustrated review notes help you distill the fundamental ideas, concepts, and formulas from Calculus you'll need to know in order to succeed on the AP Calculus exam.
- Chapter practice tests ensure that you’re up to speed, prepped, and ready to go.
Preparing for the Calculus AB exam has never been easier. Sign up now and get started down your path to success with AP Calculus!
*AP is a registered trademark of the College Board, which was not involved in the production of, and does not endorse, this product.
Thinkwell's Calculus AB Compatible with AP* Calculus lays the foundation for success because, unlike a traditional textbook, students actually like using it. Thinkwell works with the learning styles of students who have found that traditional textbooks are not effective. Watch one Thinkwell video lecture and you'll understand why Thinkwell works better.
Comprehensive Video Tutorials
We've built Calculus AB around more than 175 multimedia tutorials that provide dozens of hours of instructional material. Thinkwell offers a more engaging, more effective way for you to learn.
Instead of reading dense chunks of text from a printed book, you can watch video lectures filled with illustrations, examples, and even humor. Students report learning more easily with Thinkwell than with traditional textbooks.
Interactive Exercises with Feedback
There are hundreds of exercise items with fully worked-out solutions and explanations. Each video topic has corresponding exercises to test your understanding.
Test your understanding with hundreds of exercises that are automatically graded. Your results are available immediately, including fully worked-out solutions and explanations for each exercise. You can work on the exercises at the computer or print them out to work on later. Access your cumulative results anytime.
Review Notes and More
While the video lectures are the heart of Thinkwell products, we also offer concise, illustrated review notes, a glossary, transcripts of the video lectures, and links to relevant websites. All of these materials may be viewed online, and the notes and transcripts may be printed and kept for reference.
1.1 Overview
1.1.1 An Introduction to Thinkwell's Calculus
1.1.2 The Two Questions of Calculus
1.1.3 Average Rates of Change
1.1.4 How to Do Math
1.2 Precalculus Review
1.2.1 Functions
1.2.2 Graphing Lines
1.2.3 Parabolas
1.2.4 Some Non-Euclidean Geometry
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
2.1.6 One-Sided Limits
2.1.7 The Squeeze Theorem
2.1.8 Continuity and Discontinuity
2.2 Evaluating Limits
2.2.1 Evaluating Limits
2.2.2 Limits and Indeterminate Forms
2.2.3 Two Techniques for Evaluating Limits
2.2.4 An Overview of Limits
3.1 Understanding the Derivative
3.1.1 Rates of Change, Secants, and Tangents
3.1.2 Finding Instantaneous Velocity
3.1.3 The Derivative
3.1.4 Differentiability
3.2 Using the Derivative
3.2.1 The Slope of a Tangent Line
3.2.2 Instantaneous Rate
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
4.1 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
4.2.1 The Product Rule
4.2.2 The Quotient Rule
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
5.1 Trigonometric Functions
5.1.1 A Review of Trigonometry
5.1.2 Graphing Trigonometric Functions
5.1.3 The Derivatives of Trigonometric Functions
5.1.4 The Number Pi
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
6.1 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
7.1 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 Higher-Order Derivatives and Linear Approximation
7.2.2 Using the Tangent Line Approximation Formula
7.2.3 Newton's Method
7.3 Optimization
7.3.1 The Connection Between Slope and Optimization
7.3.2 The Fence Problem
7.3.3 The Box Problem
7.3.4 The Can Problem
7.3.5 The Wire-Cutting Problem
7.4 Related Rates
7.4.1 The Pebble Problem
7.4.2 The Ladder Problem
7.4.3 The Baseball Problem
7.4.4 The Blimp Problem
7.4.5 Math Anxiety
8.1 Introduction
8.1.1 An Introduction to Curve Sketching
8.1.2 Three Big Theorems
8.1.3 Morale Moment
8.2 Critical Points
8.2.1 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
8.2.5 Math Magic
8.3 Concavity
8.3.1 Concavity and Inflection Points
8.3.2 Using the Second Derivative to Examine Concavity
8.3.3 The Möbius Band
8.4 Graphing Using the Derivative
8.4.1 Graphs of Polynomial Functions
8.4.2 Cusp Points and the Derivative
8.4.3 Domain-Restricted 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
9.1 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
10.1 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 Cross-Sections
10.5.1 Finding Volumes Using Cross-Sectional Slices
10.5.2 An Example of Finding Cross-Sectional Volumes
10.6 Disks and Washers
10.6.1 Solids of Revolution
10.6.2 The Disk Method along the y-Axis
10.6.3 A Transcendental Example of the Disk Method
10.6.4 The Washer Method across the x-Axis
10.6.5 The Washer Method across the y-Axis
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
10.8.2 Calculating Work
10.8.3 Hooke's Law
10.9 Moments and Centers of Mass
10.9.1 Center 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
11.1 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
11.1.4 Direction Fields
11.1.5 Euler's Method for Solving Differential Equations Numerically
11.2 Growth and Decay Problems
11.2.1 Exponential Growth
11.2.2 Logistic Growth
11.2.3 Radioactive Decay
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
13.1 Paradoxes
13.1.1 An Introduction to Paradoxes
13.1.2 Paradoxes and Air Safety
13.1.3 Newcomb's Paradox
13.1.4 Zeno's Paradox
13.2 Sequences
13.2.1 Fibonacci Numbers
13.2.2 The Golden Ratio
13.3 The Close of Calculus AB
13.3.1 A Glimpse Into Calculus II
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 named him in the "100 Best of America".
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, 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.
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