SYLLABUS- COMPLEX ANALYSIS &amp; CALCULUS OF VARIATIONS, Section A Complex Analysis Analytic function. Cauchy-Riemann equations. Harmonic functions. Complex integration. Cauchy's theorem. Cauchy's integral formula. Derivatives. Taylor's series. Laurent's series. Liouville's theorem. Morera's theorem. Zeros and singularities. Poles and residues. Cauchy's residue theorem. Contour integration. Rouche's theorem. Hurwitz theorem. Jensen's theorem. Section B Expansion of simple functions in Fourier series. Fourier transform and its simple properties. Calculus of Variations Functionals. Variation of a functional. Euler's equation. Case of several variables. Natural boundary conditions. Variational derivative. Invariance of Eular's equation under transformation of coordinates. fixed end point problem for n unknown functions. Variational problem with subsidiary conditions. Isoperimetric problem. Finite subsidiary conditions.

Complex Analysis & Calculus of Variations PDF

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