Complex Variables & Partial Differential Equations for GTU 18 Course (III - MECH. - 3130005) (Decode)

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1. Polar Form of Complex Numbers, Powers and Roots, Complex Variable - Differentiation : Differentiation, Cauchy- Riemann equations, analytic functions, harmonic functions, finding harmonic conjugate; elementary analytic functions (exponential, trigonometric, logarithm) and their properties; Conformal mappings, Mobius transformations and their properties. (Chapter - 1) 2. Complex Variable - Integration : Contour integrals, Cauchy-Goursat theorem (without proof), Cauchy Integral formula (without proof), Liouville’s theorem and Maximum-Modulus theorem (without proof); Sequences, Series, Convergence Tests, Power Series, Functions given by Power Series, Taylor and Maclaurin Series, Uniform Convergence. (Chapter - 2) 3. Laurent’s series; Zeros of analytic functions, singularities, Residues, Cauchy Residue theorem (without proof), Residue Integration Method, Residue Integration of Real Integrals. (Chapter - 3) 4. First order partial differential equations, solutions of first order linear and nonlinear PDEs, Charpit’s Method. (Chapter - 4) 5. Solution to homogeneous and nonhomogeneous linear partial differential equations second and higher order by complementary function and particular integral method. Separation of variables method to simple problems in Cartesian coordinates, second-order linear equations and their classification, Initial and boundary conditions, Modeling and solution of the Heat, Wave and Laplace equations. (Chapter - 5)

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Pages: 309 Edition: 2022 Vendors: Technical Publications