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MTH621 : Real Analysis I

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Course Info

Course Category

Mathematics

Course Level

Undergraduate

Credit Hours

3

Pre-requisites

N/A

Instructor

Dr. Salman Amin Malik
PhD
University of La Rochelle, France

Course Contents

The Real Number System: Set theoretic statements, the real and complex number systems,  principle of mathematical induction, ordered sets.
Sequences and Series: convergent or divergent sequences and series, Some Special Sequences, Subsequence, Tests for convergent or divergent sequences and series.
Limits, Continuity and Differentiability: Limit of a function, prove various theorems about limits, sequences and functions. Continuity of real valued  functions, prove various theorems about continuous functions with emphasize on the proofs. Derivative of a function, proof of various theorems about dif-
ferentiability of the function. Bolzano-Weierstrass theorem, Mean value theorem.
Riemann Integration:   Riemann sums,  Riemann integral, proof of various results about the Riemann integrals.