Estb. 1882

University of the Punjab

MATH-307 Real Analysis –II

The Riemann-Stieltjes Integrals  Definition and existence of integrals
 Properties of integrals
 Fundamental theorem of calculus and its applications
 Change of variable theorem
 Integration by parts Functions of Bounded Variation
 Definition and examples
 Properties of functions of bounded variation Improper Integrals
 Types of improper integrals
 Tests for convergence of improper integrals
 Beta and gamma functions
 Absolute and conditional convergence of improper integrals Sequences and Series of Functions
 Power series
 Definition of point-wise and uniform convergence
 Uniform convergence and continuity
 Uniform convergence and integration
 Uniform convergence and differentiation
 Examples of uniform convergence
Credit hours/ Marks:- 3

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