Power Series

This course introduces an important class of series of functions, called power series. The introduction of radius of convergence is discussed. The determination of the radius of convergence of series of functions through Cauchy-Hadamard test, ratio test are illustrated through examples. The properties of power series are discussed through theorems. At the end of this course, the Uniqueness theorem and the Abel's theorem are described.

21 topics

74 lectures

Educators

Course Curriculum

Integration Review

5 videos

Differential Equations

2 videos

Area Between Curves

2 videos

Volume

4 videos

Arc Length and Surface Area

3 videos

Integration Techniques

3 videos

Trig Integrals

6 videos

Trig Substitution

3 videos

Integrating Rational Functions

3 videos

Improper Integrals

3 videos

Sequences

7 videos

Series

5 videos

Series Tests

5 videos

Comparison Tests

2 videos

Root and Ratio Tests

4 videos

Alternating Series Test

2 videos

Converge Or Diverge Review

1 videos

Power Series

2 videos

Taylor Series

4 videos

Parametric Equations

4 videos

Polar Coordinates

4 videos

Power Series Lectures

01:34

Power Series

Power Series - Intro

In mathematics, a power series is an infinite series of the form a_0+a_1x+a_2x^2+....a_nx^n. The coefficients a are real or complex numbers, and the exponent n is an integer. The power series converges (or diverges) for all values of x and any values of the coefficients a. This is a consequence of the Weierstrass factorization theorem. If the series converges for a specific value of x, it is said to be a power series in that value of x.

Jessica Wellington

52:21

Power Series

Power Series - Overview

Jessica Wellington