MTH 265 Introduction to Series

Lecture Hours: 2
Credits: 2

Convergence and divergence of numerical series, including geometric series. Series of functions. Power series and their analytic properties. Taylor series expansions and Taylor polynomials.

Prerequisite: Placement into WR 115 or completion of WR 090 and MTH 252Z with a grade of C or better; or consent of instructor.
Student Learning Outcomes:

Recognize and apply the basic convergence tests for series, including the comparison test, integral test, alternating series test, ratio test and root test.
Determine the radius and interval of convergence for a power series.
Perform term-by-term differentiation and integration when valid.
Approximate functions using Taylor polynomials or partial sums of infinite series

Content Outline

Review of Complex Numbers
Series
- Sequences of Partial Sums
- Convergence and Divergence
- Geometric Series
Convergence Tests
- Divergence Test
- Integral Test
- Alternating Series Test
- Comparison and Limit Comparison Tests
- Absolute Convergence
- Root and Ratio Tests
- Error Bounds
Power Series
- Basic Properties
- Intervals of Convergence
- Power Series Representations of Functions
- Term-by-Term Differentiation and Integration
Taylor Series
- Compute Taylor Coefficients
- Approximate Functions with Taylor Polynomials
- Convergence of Taylor Series
- Taylor Series Expansions of Functions
- Maclaurin Series