# Power Series Defining Functions

## Lecture Notes

#### Power Series

PDF
Section 1, Page 1 to page 2

Definition, with examples of convergent and divergent power series. Radius of convergence is defined.

Instructor: Prof. Jason Starr
Prior Knowledge: Sequences and Series (lecture 30)
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#### Using Power Series to Solve Calculus Problems

PDF
Section 1, Page 1 to page 2

Describing functions that cannot be directly defined using power series, with example of finding the Taylor series for the integral of e(-t2).

Instructor: Prof. Jason Starr
Prior Knowledge: Power Series (section 1 of lecture 31)
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## Online Textbook Chapter

#### Expressions for Coefficients of a Power Series

Document

Finding the coefficients for a power series of a function expanded about a specific point.

Instructor: Prof. Daniel J. Kleitman
Prior Knowledge: Infinite Series (OT30.1)
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## Exam Questions

#### General Power Series

PDF - 2.2 MB
Problem 7D-1 (page 45) to problem 7D-3 (page 45)

Three multi-part questions which involve finding power series for various trigonometric, exponential, logarithmic, and rational functions, in addition to finding the radius of convergence and evaluating four limits using power series.

Instructor: Prof. David Jerison
Prior Knowledge: None
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