7.1 Polynomial Approximation of Functions

In this lesson, you will learn about polynomial approximation of functions.

Lesson Objectives

  • Extend linear polynomial approximation of a function (the tangent line in Calculus I) to higher degrees.
  • Find Taylor Polynomials for a given differentiable function.
  • Identify and estimate the remainder for a Taylor Polynomial approximation of a function.
  • Recognize that a power series can be thought of as an infinite-degree polynomial.

Lesson Content

View all of the following instructional videos. These will help you master the objectives for this module.

  1. YouTube videos: Polynomial Approximation of Functions
    Part 1:

    Part 2:

    Part 3:

    Part 4:

    Part 5:

    Part 6:

    Part 7:

  2. YouTube video: Taylor Polynomials
  3. YouTube video: Error or Remainder of a Taylor Polynomial Approximation
  4. YouTube video: Proof: Bounding the Error or Remainder of a Taylor Polynomial Approximation

Lesson Readings

The following required readings cover the content for this module. As you go through each reading, pay close attention to the content that will help you learn the objectives for this module.

  1. Taylor Polynomials
  2. Chapter 4: Approximating Functions by Taylor Polynomials

Lesson Practice Exercises/Activities

Make your way through each of the practice exercises. This is where you will take what you have learned from the lesson content and lesson readings and apply it by solving practice problems.

  1. The Taylor Polynomial
  2. Taylor Polynomials

Additional Resources

Below are additional resources that help reinforce the content for this module.

YouTube videos: Finding a Taylor Polynomial to Approximate a function

Example 1:

Example 2:

Example 3:

Example 4: