3 Hours/Week, 3 Credits

Numerical methods: interpolation and extrapolation; shifting operators; difference operators and their relationships; Newton’s interpolation formulae; Lagrange’s formula; Newton’s divided difference formula; central difference formulae (Stirling and Bessel’s); relationship between divided difference and simple difference.; inverse interpolation formula; numerical differentiation; numerical integration by different formulas; numerical solution of equations by various methods; convergence of these methods and their inherent errors; numerical solution of simultaneous linear equation; solution by determinants, by inverse matrices, by iteration and by successive elimination of the unknowns. Complex functions; elementary single and many valued functions of complex variables; differentiable functions; analytic functions; Cauchy’s theorem for simple contours; Taylor’s theorem; Laurent’s theorem; Liouville’s theorem; different types of singularity; Cauchy’s residue theorem; evaluation of integral by contour integration.