Calculus of Functions of Several Variables: Limit, continuity and differentiability of functions of several variables, partial derivatives and their geometrical interpretation, Tangent plane and normal line. Euler’s theorem on homogeneous functions, Total differentiation, chain rules, Jacobian, Taylor’s formula, maxima and minima, Lagrange’s method of undetermined multipliers.
Multiple Integrals: Double and triple integrals, change of order of integration, change of variables, application to area, volumes, Mass, Centre of gravity.
Vector Calculus: Scalar and vector fields, gradient of scalar point function, directional derivatives, divergence and curl of vector point function, solenoidal and irrotational motion. Vector integration: line, surface and volume integrals, Green’s theorem, Stoke’s theorem and Gauss divergence theorem (without proof).
Ordinary Differential Equations: First order differential equations: Exact equation, Integrating factors, Reducible to exact differential equations, Linear and Bernoulli’s form, orthogonal trajectories, Existence and Uniqueness of solutions. Picard’s theorem, Picard’s iteration method of solution (Statements only). Solutions of second and higher order linear equation with constant coefficients, Linear independence and dependence, Method of variation of parameters, Solution of Cauchy’s equation, simultaneous linear equations.