Instructor
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Dr. Salman Amin Malik
PhD
University of La Rochelle, France (2012)
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Course contents are:
The convergence of sequence of functions.
The pointwise convergence, uniform convergence, several tests for convergence.
Apply the interchange of limit and integration, derivative of sequence of functions.
The infinite series of functions, convergence, Weierstrass's test and some other results about the convergence.
Apply Dirichlet's test for uniform convergence, series of product of two functions, interchange of sum and intgeration.
Represention and study of the function which could be written as power series,term by term integral and derivative of a power series.
The concept of equicontinuous function, The Stone-Weierstrass Theorem.
The Fourier series, Fourier coefficients, convergence of Fourier series.
Apply the best approximation theorem and understand the Euler gamma function and the beta function and their properties.
The functions of several variables, Heine-Borel Theorem, limits and continuity of functions of several variables.
Vector valued functions and their calculus, Bounded functions and several results about vector valued functions.
Differentiablity in $\mathbb{R}^n$, Differentials, Directional derivatives, Partial derivatives, Maxima and minima.
Improper integrals, Multiple integrals, Functions of bounded variation.
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