COMPLEX VARIABLES AND PARTIAL DIFFERENTIAL EQUATIONS ( 3130005 )

Polar Form of Complex Numbers,  Powers and Roots (3 Question),  Differentiation,  Cauchy-Riemann equations,  Analytic functions (2 Question),  Harmonic functions (1 Question),  Finding harmonic conjugate (1 Question),  Elementary analytic functions (Exponential, Trigonometric, Logarithm) and their properties (2 Question),  Conformal mappings (3 Question),  Mobius transformations and their properties (2 Question), 

Contour integrals,  Cauchy-Goursat theorem (3 Question),  Cauchy Integral formula (2 Question),  Liouville’s theorem,  Maximum-Modulus theorem,  Sequences,  Series,  Convergence Tests,  Power Series (1 Question),  Functions Given by Power Series,  Taylor Series,  Maclaurin Series,  Uniform Convergence, 

Laurent’s series (2 Question),  Zeros of analytic functions,  Singularities (1 Question),  Residues (1 Question),  Cauchy Residue theorem (2 Question),  Residue Integration Method,  Residue Integration of Real Integrals (1 Question), 

First order partial differential equations,  Solutions of first order linear PDEs (1 Question),  Solutions of first order nonlinear PDEs (5 Question),  Charpit’s Method (1 Question), 

Solution to homogeneous linear partial differential equations,  Solution to nonhomogeneous linear partial differential equations (1 Question),  second and higher order by complementary function and particular integral method (4 Question),  Separation of variables method to simple problems in Cartesian coordinates (4 Question),  Second order linear equations and their classification,,  Initial and boundary conditions,  Modeling and solution of the Heat equations (3 Question),  Modeling and solution of the Wave equations (3 Question),  Modeling and solution of the Laplace equations,