Hi! We show you're using Internet Explorer 6. Unfortunately, IE6 is an older browser and everything at MindBites may not work for you. We recommend upgrading (for free) to the latest version of Internet Explorer from Microsoft or Firefox from Mozilla.
Click here to read more about IE6 and why it makes sense to upgrade.

Series: Calculus: Taylor and Maclaurin Polynomials

Preview

Buy the Series and be able to watch all of the lessons.

About this Series

  • Lessons: 4
  • Total Time: 0h 35m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 07/30/2009
  • Last Updated At: 07/20/2010

In this four-lesson series, we'll define, derive and evaluate Taylor Polynomials and Maclaurin polynomials. We'll also learn about the remainder of a Taylor polynomial and calculate the degree of error in your approximation.

Higher-degree polynomial approximations can be represented using sigma notation. There is a mathematical convention that zero factorial equals one. These polynomial approximations are called Taylor polynomials. To find a Taylor polynomial, find all the necessary derivatives and evaluate them at x = c, then insert the values into the Taylor polynomial function. If you center the Taylor polynomial approximation of a function about the point x = 0, you get the Maclaurin polynomial approximation of the function.

Since the Taylor approximation is not exactly equal to the original function, there is an error term, called the remainder. If you add the remainder to the Taylor approximation, then the result does equal the original function. You can use the remainder expression to determine what the largest possible error is for your approximation.

Taught by Professor Edward Burger, this series comes from a comprehensive Calculus course. 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'Hopital'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.

About this Author

Thinkwell
Thinkwell
2174 lessons
Joined:
11/14/2008

Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help 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 or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

None of the lesson in this series have been reviewed.

Below are the descriptions for each of the lessons included in the series:

Supplementary Files: