# Manipulating Taylor Series

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## Lecture Notes

#### Algorithm for Computing Taylor Series

PDF
Section 3, Page 4 to page 5

Step-by-step method for computing a Taylor series, with example of finding the Taylor series expansion of f(x) = (1-x)-1 about x = 0.

Instructor: Prof. Jason Starr
Prior Knowledge: Power Series and Taylor Series (sections 1 and 2 of this lecture)

#### More Examples of Taylor Series

PDF
Section 4, Page 5 to page 9

Taylor series expansions of (1-x)-1, ex, sin(x), and cos(x) about any point x = a.

Instructor: Prof. Jason Starr
Prior Knowledge: Power Series and Taylor Series (sections 1 to 3 of this lecture)

## Exam Questions

#### Taylor Series

PDF
Problem 9.1 (page 6) to problem 9.6 (page 6)

Six questions which involve computing Taylor Series expansions of logarithmic and trigonometric functions.

Instructor: Prof. Jason Starr
Prior Knowledge: None

#### Taylor Series

PDF
Problem 18 (page 2) to problem 19 (page 2)

Two questions that involve finding the Taylor series for √(1+x) and the inverse tangent function.

Instructor: Prof. David Jerison
Prior Knowledge: None