Total Marks – 200
Marks – 100
Candidates will be asked to attempt any two questions from Section A, one question from Section B and two questions from Section C.
Differential Equations: Linear differential equations with constant and variable coefficients, Non-linear equations, Systems of equations, Variations of parameters and the power series method. Formation of partial differential equations, Types of integrals of partial differential equations, Partial differential equations of first order, Partial differential equations with constant coefficients, Monge’s method, Classification of partial differential equations of second order, Laplace’s equation and its
boundary value problems, standard solution of wave equation and equation of heat induction.
Tensor: Definition of tensors as invariant quantities. Coordinate transformations, Contravariant and covariant laws of transformation of the components of tensors, addition and multiplication of tensors, contracts and inner product of tensors, The Kronecker delta and Levi-Civita symbol, the metric tensor in Cartesian, polar and other coordinates, covariant derivatives and the Christoffel symbols., The gradient, divergence and curl operators in tensor notation.
Elements of Numerical Analysis: Solution of nonlinear equations, use of x = g (x) form, Newton Raphson method, Solution of system of linear equations, Jacobi and Gauss-Seidel method, Numerical Integration, Trapezoidal and Simpson’s re?? Regula Falsi and iterative method for solving nonlinear equation with convergence, Linear and Lagrange interpolation, graphical solution of linear programming problems.