Vector Calculus Independent Study

Unit 9: Infinite Series

In this section, you will learn:

• What an infinite sequence is, and how to take its limit.

• The definition of an infinite series, and what it means for it to converge or diverge.

• How to calculuate the value of a geometric series.

• The definition of a p-harmonic series.

• The limit test for the divergence of an infinite series.

• The comparison test.

• The integral test.

• The ratio test.

• The root test.

• The alternating series test.

• What a power series is, and how to find its radius and interval of convergence.

• How to add, subtract, differentiate, and integrate power series, and how to multiply one by a polynomial.

• How to find a power series approximation to a function near a point (Taylor series).

Suggested Procedure:

1. Read and do some problems from • Rogers Chapters 27 and 28, or • Simmons Chapters 13 and 14.

2. Take the sample test.

3. Take a unit test.