Unit-1 Functions of Complex Variable:
Limit continuity & differentiability, Analytic function & Cauchy-Riemann equations (Cartesian form), Harmonic function, Conjugate function, Milne Thomson method.
Unit-2 Vector Calculus:
Differentiation of vectors, Scalar & vector point functions, vector differential operator Del, Gradient of a scalar function & their geometrical meaning, Normal & Directional derivative, Divergence of a vector function and their physical interpretation, Curl of a vector function & their physical meaning, Line integral, Surface integral, Volume integral- illustrative examples, Green’s theorem (for a plane), Stoke’s theorem- illustrative examples*, Gauss’s theorem- illustrative examples* (Note: In case of illustrative examples*, question are not to be set).
Unit-3 Ordinary Differential Equations of First Order and First Degree:
Exact differential equations, Equations reducible to exact form by integrating factors, Bernoulli’s differential equations. Linear differential equations of higher orders with constant coefficients, Complementary functions, Particular integrals, Method of variation of parameters (second order only) Simultaneous linear differential equations with constant coefficients.
Unit-4 8 Fourier Series & Partial Differential Equation:
Periodic functions, Fourier series & Dirichlet’s conditions, Fourier series of period 2π and Euler’s formulae, Even function & odd function, Half range series (Period π), Fourier series of functions having arbitrary period (Period 2c), Half range, series (arbitrary period), Introduction & formation of partial differentiate equation, Linear partial differentiate equation with constant coefficient, Non- homogeneous linear equations.
Unit-5 Application of Partial Differential Equation:
Introduction & Method of separation of variables, One dimensional wave equation (without proof) and problems, One dimensional heat equation (without proof) and problems, Two dimensional steady state heat flow equation (without proof) & problems.
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