MSc (Mathematics and Computing) Programme:Mathematical MethodsThapar University
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Real Analysis – I
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Based Management Systems
Computer Based Optimization Techniques
Laplace Transform: Review of Laplace transform, Applications of Laplace transform in initial and boundary value problems: Heat equation, wave equation, Laplace equation.
Fourier Series and Transforms: Definition, properties, Fourier integral theorem, Convolution theorem and Inversion theorem. Discrete Fourier Transforms (DFT), relationship of FT and Fast Fourier Transforms (FFT), linearity, symmetry, time and frequency shifting. Convolution and Correlation of DFT. Applications of FT to heat conduction, vibrations and potential problems, Z-Transform.
Hankel Transform: Hankel transforms, inversion formula for the Hankel transform, infinite Hankel transform, Hankel transform of the derivative of a function, Parseval's theorem, The finite Hankel transforms, Application of Hankel transform in boundary value problems.
Integral Equations: Linear integral equations of the first and second kind of Fredholm and Volterra type, Conversion of linear ordinary differential equations into integral equations, Solutions by successive substitution and successive approximation, Neumann series and Resolvent kernel methods.
Calculus of Variations: The extrema of functionals: The variation of a functional and its properties, Euler equations in one and several independent variables, Field of extremals, sufficient conditions for the extremum of a functional conditional extremum, moving boundary value problems, Initial value problems, Ritz method.