Series: Calculus
- Author: Thinkwell
- Bio: Founded in 1997, Thinkwell has succeeded in creating... more
- Joined: Nov 13, 2008
- Teaches: 122 Lessons
Taught by Professor Edward Burger, these lessons were selected from a broader, comprehensive course, College Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/calculus. The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'H⌠pital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.
Lessons
Calculus: The Limit Laws, Part I
In this lesson, you will learn about the limits of functions. Since limits are real numbers, you can apply many of the...
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Calculus: The Limit Laws, Part II
In this lesson you will look at a number of limit laws and their applications. These will include rules that govern the...
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Calculus: Evaluating Limits
The limit is the range value that a function is tending towards as you get closer to a domain value. In this lesson you...
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Calculus: Limits and Indeterminate Forms
The limit is the range value that a function is tending towards as you get closer to a domain value. In this lesson,...
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Calculus: Two Techniques for Evaluating Limits
The limit is the range value that a function is tending towards as you get closer to a domain value. This lesson will...
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Calculus: Finding Instantaneous Velocity
This lesson will start with a recap of average and instantaneous rates as well as their relationships with secants, and...
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Calculus: The Derivative
This lesson is a review of how we arrive at the derivative. We start with secants and tangents and then move to average...
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Calculus: The Slope of a Tangent Line
In this lesson, we will review tangent lines, learn how to find the derivative, and learn how to use the derivative once...
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Calculus: Instantaneous Rate
In this lesson, you will practice using position functions and determining the instantaneous rate at a given point in...
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Calculus: The Equation of a Tangent Line
In this lesson, you will cover how to find the equation of a line tangent to a curve, equations of tangent lines, how to...
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Calculus: Derivative of the Reciprocal Function
In this lesson, we will calculate the derivative of 1/x (the reciprocal function) using the definition of derivative. ...
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Calculus: Derivative of the Square Root Function
In this lesson, we will calculate the derivative of the square root of x using the definition of the derivative. As...
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Calculus: Uses of the Power Rule
This lesson covers the power rule, the sum rule, and the constant multiple rule (all related to differentiation). ...
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Calculus: The Product Rule
In this lesson, we learn about taking the derivatives of products and applying the product rule of differentiation. The...
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Calculus: The Quotient Rule
In this lesson, we learn about taking the derivatives of quotients and applying the quotient rule of differentiation. ...
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Calculus: Using the Chain Rule
The chain rule is a technique used for differentiating composite functions. In this lesson, you will learn the chain...
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Calculus: Derivatives of Trigonometric Functions
In this lesson you will learn how to calculate the derivative of different trigonometric functions. Professor Burger...
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Calculus: Derivatives of Exponential Functions
The power rule for differentiation does not apply to exponential functions (e.g. the derivative of 2^x does NOT equal...
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Calculus: Derivative of the Natural Log Function
In this lesson, you will learn how to find the derivative of the natural log function. To start with, we will review...
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Calculus: Using Implicit Differentiation
Here, we will use implicit differentiation (in which you find the dy/dx of things that aren't simple functions). This...
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Calculus: Higher-Order Derivatives, Linear Approx
In this lesson, we learn about multiple derivatives and tangent line approximations for these. Higher-order derivatives...
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Calculus: The First Derivative Test
To find the maxima and minima of a graph, you first have to find all of the critical points. Thus, you will always find...
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Calculus: The Second Derivative Test
Where the first derivative test is a method used to determine whether critical points are maxima or minima, the second...
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Calculus: Antidifferentiation
This lesson is an introduction to integration and antiderivatives. Where calculus begins with differential calculus...
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Calculus: Antiderivatives of Powers of x
This lesson is a more advanced view of antidifferentiation and integration. In it, you will be introduced to the proper...
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Calculus: Integrals of Trig and Exponent Functions
This lesson will teach you how to approach and solve problems involving antiderivatives and integration for...
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Calculus: Undoing the Chain Rule
In this video, you will learn to do integration by substitution, which is a fancy way of saying that we'll learn to...
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Calculus: Integrating Polynomials by Substitution
This lesson will teach you how to do integration of polynomials using substitution. Before digging in on substitution...
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Calculus: Substitution to Integrate Trig Functions
In this lesson, we will work on solving antidifferentiation problems involving composite trigonometric functions using...
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Calculus: Fundamental Theorem of Calculus, Part I
In this lesson, you will learn how the derivative and the integral are related. This is the first part of the...
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Calculus: Fundamental Theorem of Calculus, Part II
The Second part of the Fundamental Theorem of Calculus provides the link between velocity and area. It states that the...
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Calculus: Regions Bound by Several Curves
In this lesson, you will learn how to find the area of a region bounded by 3 or more curves. This is basically a...
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Calculus: Integrating with Respect to y: Part I
To find the area between two curves (or relations), you take the antiderivative across a range of values. This is, in...
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Calculus: Integrating with Respect to y: Part II
To find the area bounded by two curves (or relations), it is sometimes simpler to add up the areas of the horizontal...
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Calculus: Basic Uses of L'Hôpital's Rule
In this lesson, we will look at applications of L'Hopital's rule, when to use it, what to watch out for, etc. When...
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Calculus: L'Hôpital's Rule, Indeterminate...
Some indeterminate forms, including indeterminate products, must be manipulated before L'Hôpital's Rule can be applied....
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Calculus: L'Hôpital's Rule, Indeterminate Diffs
This lesson will show you how to recognize indeterminate forms that are camouflaged as indeterminate differences rather...
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Calculus: L'Hôpital's Rule, One to Infinite Power
The limit of a function is called an indeterminate form when it produces a mathematically meaningless result. Some...
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Calculus: Differentiating Logarithmic Functions
In this lesson, you will learn how to take the derivative of logarithmic functions. While the derivative of ln x is...
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Calculus: Logarithmic Differentiation
In this, we will start by learning how to use logarithmic differentiation to find the derivative of equations like y =...
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Calculus: Derivatives of Inverse Functions
In this lesson, we will review the properties of inverse functions and learn about finding the derivative of an inverse...
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Calculus: Inverse Sine, Cosine, and Tangent
In this lesson, you will learn about the existence of trigonometric inverse functions when the domain is restricted. ...
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Calculus: Inverse Secant, Cosecant, and Cotangent
In this lesson, you will learn about the existence of trigonometric inverse functions when the domain is restricted. ...
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Calculus: Evaluating Inverse Trig Functions
In this lesson, you will learn how to evaluate inverse trig functions by hand or with a graphing calculator such that...
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Calculus: Derivatives of Hyperbolic Functions
In this lesson, you will learn how to find the derivatives of hyperbolic functions, like hyperbolic sine. In explaining...
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Calculus: Making u-Substitutions
In this lesson, you will learn about the u-substitution expression, how to use it, and how to use it under a radical...
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Calculus: Integrals with Powers of Sine and Cosine
In this lesson, you will review the integration of sin^3(x) and sin^3(x)*cos^3(x). By substituting for equivalent...
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Calculus: Integrals of Other Trig Functions
In this lesson, you will learn how to integrate tangent, cotangent and secant. You will see how solving tangent and...
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Bio
About Thinkwell
Founded in 1997, Thinkwell has succeeded in creating a "next-generation" textbook, one that helps students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com.
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.
