PMAT 21562: Infinite Series

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Course Code           : PMAT 21562

Title                         : Infinite Series

Pre-requisites         : PMAT 12543

 Learning Outcomes:

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

  • define the meaning of convergence of a real sequence of real numbers
  • use definition to discuss the behavior of a given sequence
  • describe the nature of the convergence of infinite series and conditions under what differentiation and integration can be performed.

 Course Contents:

Sequences: Limits and limit theorems for sequences, Monotone sequences.

Series: Convergence of Infinite Series, the Integral Test and Estimates of Sums, The Comparison Tests, Alternating Series, Absolute Convergence and the Ratio and Root Tests

Power Series: Representations of Functions as 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., (8th edition, 2015) Calculus Early Transcendentals, Cengage Learning.

 

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