**Course Code **** :** PMAT 21272

**Title **** :** Infinite Series

**Pre****-****requisites ****:** PMAT 12253

**Learning Outcomes****:**

At the end of this course, the student should be able to

1. define the meaning of convergence of a real sequence of real numbers

2. use definitions to discuss the behavior of a given sequence

3. describe the nature of the convergence of infinite series and conditions under what differentiation and

integration can be performed

4. demonstrate knowledge on power series representation of a series.

5. use applications of Taylor polynomial.

**Course Contents****:**

**Sequences****:** Limits and limit theorems for sequences, Monotone sequences and Cauchy sequences, Bounded

sequences, Monotone sequence theorem, Subsequences, Bolzano-Weierstrass theorem

**Series****:** Convergence of Infinite Series, Geometric series, Harmonic Series, the Integral Test and Estimates of Sums,

The Comparison Tests and Estimates of Sums, Alternating Series and estimates of Sums, Absolute and conditional

Convergence, Ratio Test and Root Test

**Power Series****:** Representation of Functions as Power Series, Differentiation and Integration of Power Series, Taylor

and Maclaurin Series, Binomial Series, Applications of Taylor Polynomials

** ****Method of Teaching and Learning****:** A combination of lectures and tutorial discussions.

**Assessment****:** Based on tutorials, tests and end of course examination.

** ****Recommended Reading****: **

1. Stewart. J. (2020) Calculus Early Transcendentals, Cengage Learning.

2. Knopp, K. (1956). Infinite sequences and series. Courier Corporation.

3. Knopp, K. (1990). Theory and application of infinite series. Courier Corporation.

4. Hirschman, I.I. (2014). Infinite series. Courier Corporation.

5. Bonar, D.D. & Khoury Jr., M.J. (2018). Real infinite series (Vol. 56). American Mathematical Soc.

6. Bromwich, T.J.I.A. (2005). An introduction to the theory of infinite series (Vol. 335). American

Mathematical Soc.