PMAT 32612: Theory of Riemann Integration

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Course Code            : PMAT 32612

Title                          : Theory of Riemann Integration

Pre-requisites          : PMAT 12543

 Learning Outcomes:

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

  • demonstrate knowledge of the basic concepts of Riemann Integration improper integrals
  • apply knowledge in solving problems

 Course Contents:

Riemann Integration: The Riemann integral, Properties of the Riemann integral, Intermediate Value Theorem for Integrals, Dominated Convergence Theorem, Monotone Convergence Theorem, Fundamental theorem of calculus.

Improper integrals: Properties of Improper Integrals, Leibnitz’s rule.

 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. Ross, K.A., (2nd edition, 2015) Elementary Analysis. The Theory of Calculus, Springer.
  2. Widder, D.V. (2nd edition, 2012) Advanced Calculus. Courier Corporation.

 

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