PMAT 31033

>< Type/ Status : Elective
>< Title : Sequences and Series of Functions, and Theory of Integration
>< Pre- requisites : PMAT 22025
>< Objectives :
At the end of this course, students will understand under what conditions differentiation and integration can be performed on infinite series, and rudiments of Riemann integration and its applications.
>< Course Content :

Sequences and Series of Functions: Pointwise convergence of a sequence of functions, Uniform convergence of sequences and series of functions, Consequences of uniform convergence, Differentiation and integration of infinite series.

Theory of Integration: The Riemann integral, Properties of the Riemann integral, Fundamental theorem of calculus, Improper integrals, Leibnitz’s rule.

>< Methodology : A combination of lectures and tutorial discussions
>< Scheme of Evaluation : Based on tutorials, tests and end of course examination
>< Recommended Reading :
1. Munem M.A. & Foulis D.J. (1984). Calculus, Worth Publishers.
2. Somasundaran D. & Choudhary B. (1996). A first Course Mathematical Analysis, Narosha Publishing House, India.
3. Malik S.C. & Arora S. (1994). Mathematical Analysis, Wiley Eastern.

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