Top GRE Preparation

http://www.mindbites.com/lesson/836

Where the first derivative test is a method used to determine whether critical points are maxima or minima, the second derivative test is used to test concavity for a critical point. If the derivative of a function at a critical point equals zero and the second derivative of that function at that point is positive, you have a minimum (min) and a concave up curve. If the derivative of a function at a critical point equals zero and the second derivative at that same point is negative, you have a maximum (or max) in a curve that is concave down. If the first derivative is zero and the second derivative is zero, the second derivative test is inconclusive – it doesn’t mean that the point isn’t a max or a min. It just means you need to go back to the first derivative test.

Taught by Professor Edward Burger, this lesson was 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’Hôpital’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.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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.

Duration : 0:2:28

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Technorati Tags: calculus, concave, derivative, how to, math, min, mindbites, positive, second, tutorial, video

http://www.mindbites.com/lesson/848-calculus-basic-uses-of-lhopitals-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 essing limits, start by plugging in using substitution to evaluate them. If this gives you an indeterminate form, apply L’Hôpital’s rule. The L’Hôpital rule is applicable to f(x) and g(x) if they are differentiable functions across an interval containing c, except possibly at c. If the limit as x approaches c of f(x)/g(x) produces the indeterminant form of 0/0 or (+-infinity)/(+-infinity), then the limit as x approaches c or f(x)/g(x) is equal to the limit as x approaches c of [the derivative of f(x)] / [the derivative of g(x)] provided the limit on the right exists or is infinite. L’Hôpital’s rule can also be applied to one-sided limits and, as long as the limit is indeterminate, you can take the limit again if L’Hôpital’s rule doesn’t give you an answer the first time around (and you are again left with an indeterminate form as the limit). Note that the rule may mislead you if you misapply it to a limit that doesn’t produce an indeterminate form.

Taught by Professor Edward Burger, this lesson was 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’Hôpital’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.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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 ociation 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.

Duration : 0:2:42

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Technorati Tags: calculus, college, GRE, math, mindbites, prep, SAT, simplify, Test, trig, Tutor

http://www.mindbites.com/lesson/1237-pre-calculus-graph-sine-cosine-with-phase-shifts
Now that you have learned how to graph the sine and cosine functions, Professor Burger asks the question “”How does changing the x-value affect the graph?”" He shows you how adding or subtracting to the x-value can actually change graphs of the sine and cosine functions, a process called translation. Professor Burger also warns you about classic mistake #8, reminding you that adding and subtracting to the x-value actually creates the opposite effect when graphed (adding to X moves the graph in the negative direction). Finally, Professor Burger shows you how to simplify the equation y = 3sin(x + Pi/2) using translation. The key lies in the fact that adding or subtracting pi/2 or 2*pi to a sine or cosine function means there are some shortcuts that you can take to determine what the graph of the function looks like (e.g. the graph of sine of (x+pi/2) is the same as the graph of cosine and the same as the graph of sine of (x+2*pi)).

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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 ociation 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.

Duration : 0:3:8

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Technorati Tags: calculator, calculus, college, graphing, GRE, math, mindbites, prep, SAT, simplify, Test, ti, trig, Tutor

http://www.mindbites.com/lesson/949-int-algebra-the-pythagorean-theorem
The Pythagorean Theorem describes the relationship between the sides of a right triangle. It erts that if the hypotenuse is length c and the other two legs are a and b, then a^2+b^2=c^2. This formula has a number of applications, and you will go through many of them in this lesson. Professor Burger will show you how to find one leg of a right triangle if you know the other two or if you know the length of one side and have two polynomials to express the lengths of the other two sides (e.g. if you know the three sides are c=x+2 and a=x and b=x+2).

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Intermediate Algebra. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/intermediatealgebra. The full course covers real numbers, equations and inequalities, exponents and polynomials, rational expressions, roots and radicals, relations and functions, the straight line, systems of equations, quadratic equations and quadratic inequalities, conic sections, inverse and exponential and logarithmic functions, and a variety of other AP algebra and advanced algebra.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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 ociation 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.

Duration : 0:2:17

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Technorati Tags: calculus, college, GRE, math, mindbites, prep, SAT, simplify, Test, trig, Tutor

http://www.mindbites.com/lesson/821-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 we find it. We begin by finding the slope the tangent line f(x) = 2x^2 at x=3. We find the slope by taking the derivative of f(x). We compute this derivative by evaluating the limit as delta x approaches 0 of [f(x + delta x) - f(x)]/delta x or, in this case, the limit as delta x approaches zero of [2(x+ delta x)^2 - 2x^2]/delta x.

Taught by Professor Edward Burger, this lesson was 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’Hôpital’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.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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 ociation 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.

Duration : 0:3:11

(more…)

Technorati Tags: calculator, calculus, college, graphing, GRE, math, mindbites, prep, SAT, simplify, Test, ti, trig, Tutor

http://www.mindbites.com/lesson/856
In this lesson, you will learn about the existence of trigonometric inverse functions when the domain is restricted. Though trig functions are not one-to-one, they do have defined inverses. Professor Burger will walk you through an explanation of how you arrive at the inverse secant, inverse cosecante, and inverse cotangent functions. Inverse trig functions can be denoted by inverse notation or with arc-notation, and his lesson will cover both of these methods of notation. This video should serve as in introduction to arcsec, arccsc, and arccot functions and the asymptotes that are created when you graphically depict these inverses.

Taught by Professor Edward Burger, this lesson was 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’Hôpital’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.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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 ociation 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.

Duration : 0:3:6

(more…)

Technorati Tags: cal, calculus, cotangent, GRE, inverse, math, mindbites, SAT

http://www.mindbites.com/lesson/839-calculus-integrals-of-trig-and-exponent-functions

This lesson will teach you how to approach and solve problems involving antiderivatives and integration for trigonometric functions and exponential functions. To do this, we will review the power rule, the trig derivatives and some exponential derivatives. Professor Burger will go through integration problems involving functions such as sin, cos, tan, sec, cot, csc, e^x, a^x, ln a, etc. To attack these problems, you will break down the integration/antidifferentiation problems into component parts and apply the laws of integration to arrive at the correct solution.

Taught by Professor Edward Burger, this lesson was 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’Hôpital’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.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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 ociation 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.

Duration : 0:3:11

(more…)

Technorati Tags: calculus, derivative, GRE, math, mindbites, prep, SAT, tan, Test

http://www.mindbites.com/lesson/789-college-algebra-finding-the-inverse-of-a-function
This lesson will teach you how to find the inverse of a function [f-1(x)] when you are given the function [f(x)] as a formula algebraically. Some functions, however, have no mathematically defined inverse. Professor Burger will show you how to recognize when a provided function has no inverse. For example, a parabola function cannot be inverted.

This lesson is perfect for review for a CLEP test, mid-term, final, summer school, or personal growth!

Taught by Professor Edward Burger, this lesson was 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/collegealgebra. The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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 ociation 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.

Duration : 0:2:47

(more…)

Technorati Tags: calculus, derivative, GRE, math, mindbites, prep, SAT, tan, Test

http://www.mindbites.com/lesson/786-college-algebra-piecewise-defined-functions
In this lesson, we will learn to define, recognize, write, graph and evaluate piecewise math functions. Piecewise-defined functions are unique in that they are defined to be equal to different things for different ranges of variable values.

This lesson is perfect for review for a CLEP test, mid-term, final, summer school, or personal growth!

Taught by Professor Edward Burger, this lesson was 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/collegealgebra. The full course covers equations and inequalities, relations and functions, polynomial and rational functions, exponential and logarithmic functions, systems of equations, conic sections and a variety of other AP algebra, advanced algebra and Algebra II topics.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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 ociation 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.

Duration : 0:2:27

(more…)

Technorati Tags: calculator, calculus, college, graphing, GRE, math, mindbites, prep, SAT, simplify, Test, ti, trig, Tutor

http://www.mindbites.com/lesson/1235-pre-calculus-using-double-angle-identities
Double-angle identities allow you to simplify trigonometric equations with a 2 as the coefficient. (similar formulae exist for trig functions with 1/2 or 3 as the coefficient). In this lesson, Professor Burger uses the equation cos2x = sinx as an example. If this equation were simply cos x = sinx, we could divide to re-write the formula as sinx/cosx = tan x = 0, but in this case, we have a coefficient in advance of one of the arguments, which is why we need to use the double-angle formulas. After using the double-angle formulas in the provided example to simplify, you can further simplify these equations using trig identities (like the Pythagorean identity) and factoring. These tools will help you to solve many trig equations. The duble angle identities for sine, cosine, tangent and cotangent are: sin2x = 2sinxcosx, cos2x = cos^2x-sin^2x, tan 2x = 2tanx/(1-tan^2x), and cot2x = (cot^2x-1)/2cotx.

Taught by Professor Edward Burger, this lesson was selected from a broader, comprehensive course, Precalculus. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/precalculus. The full course covers angles in degrees and radians, trigonometric functions, trigonometric expressions, trigonometric equations, vectors, complex numbers, and more.

Edward Burger, Professor of Mathematics at Williams College, earned his Ph.D. at the University of Texas at Austin, having graduated summa 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 ociation 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.

Duration : 0:2:49

(more…)

Technorati Tags: calculus, college, GRE, math, mindbites, prep, SAT, simplify, Test, trig, Tutor