Electronics & Communications (EC)
Numerical Methods: Solution of nonlinear equations, single and multi-step methods for differential equations, convergence criteria.
Differential Equations: First order equations (linear and nonlinear), higher order linear differential equations,
Cauchy's and Euler's equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems.
Complex Analysis: Analytic functions, Cauchy's integral theorem, Cauchy's integral formula; Taylor's and
Laurent's series, residue theorem.
Electrical Engineering (EE)
Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multiâ€step methods for differential equations.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchyâ€™s equation, Eulerâ€™s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables.
Complex variables: Analytic functions, Cauchyâ€™s integral theorem, Cauchyâ€™s integral formula, Taylor series,
Laurent series, Residue theorem, Solution integrals.
Instrumentation Engineering (IN)
Numerical Methods: Matrix inversion, solutions of non-linear algebraic equations, iterative methods for solving differential equations, numerical integration, regression and correlation analysis.
Differential equations: First order equation (linear and nonlinear), higher order linear differential equations with constant coefficients, method of variation of parameters, Cauchyâ€™s and Eulerâ€™s equations, initial and boundary value problems, solution of partial differential equations: variable separable method.
Analysis of complex variables: Analytic functions, Cauchyâ€™s integral theorem and integral formula, Taylorâ€™s and Laurentâ€™s series, residue theorem, solution of integrals.
Mechanical Engineering (ME)
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpsonâ€™s rules; single and multi-step methods for differential equations.
Differential equations: First order equations (linear and nonlinear); higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave and Laplace's equations.
Complex variables: Analytic functions; Cauchy-Riemann equations; Cauchyâ€™s integral theorem and integral formula; Taylor and Laurent series.
Civil Engineering (CE)
Numerical Methods: Accuracy and precision; error analysis. Numerical solutions of linear and non-linear algebraic equations; Least square approximation, Newtonâ€™s and Lagrange polynomials, numerical differentiation, Integration by trapezoidal and Simpsonâ€™s rule, single and multi-step methods for first order differential equations.
Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher order linear equations with constant coefficients; Euler-Cauchy equations; Laplace transform and its application in solving linear ODEs; initial and boundary value problems.
Partial Differential Equation (PDE): Fourier series; separation of variables; solutions of one-dimensional diffusion equation; first and second order one-dimensional wave equation and two-dimensional Laplace equation.