Taylor series is a very important concept that is used in numerical methods. From the concept of truncation error to finding the true error in Trapezoidal rule, having a clear understanding of Taylor series is extremely important. Other places in numerical methods where Taylor series concept is used include: the derivation of finite difference formulas for derivatives, finite difference method of solving differential equations, error in Newton Raphson method of solving nonlinear equations, Newton divided difference polynomial for interpolation, etc.
I have written a short chapter on Taylor series. After reading the chapter, you should be able to:
1. understand the basics of Taylor’s theorem,
2. see how transcendental and trigonometric functions can be written as Taylor’s polynomial,
3. use Taylor’s theorem to find the values of a function at any point, given the values of the function and all its derivatives at a particular point,
4. errors and error bounds of approximating a function by Taylor series,
5. revisit the chapter whenever Taylor’s theorem is used to derive or explain numerical methods for various mathematical procedures.
This post is brought to you by Holistic Numerical Methods: Numerical Methods for the STEM undergraduate at http://numericalmethods.eng.usf.edu.