MTH-221 Mathematics V (Complex Variables, Laplace Transforms)
Complex Variables, Complex numbers, Properties, Modulus & amplitudes of complex numbers. Analytic functions, Cauchy - Riemann equations, Polar form of C-R equation, Line integral of complex function, Complex integration, Cauchy Theorem, Cauchy’s Residue theorem, Cauchy’s integral formula, Higher order derivatives, Liouville’s Theorem, Taylors and Laurent’s theorems, singularities, Zero and poles of an analytic function, Residue, Fundamental theorem of algebra, Evaluation & calculation of residues of real definite integral by contour integrations, Bilinear mappings, mappings by elementary functions, Conformal mapping.
Vector Analysis, Limit, continuity and differentiability of scalar and vector point functions, Vector integration, line, surface and volume integrals, Gradient, Divergeance and Curl of point function, Gauss’s Theorem, Stocks Theorem and Green’s Theorem.
Beta and Gamma Functions, The factorial function, Different forms of Beta function, Reduction formula, Transformation of Gamma function, Relation between Beta and Gamma function. Fourier Series, Periodic functions and Trigonometric series, Fourier series, Fourier series, Process of determining the co-efficient, Fourier cosine and sine series.