Differential Equations & Vector Calculus

SYLLABUS- DIFFERENTIAL EQUATIONS & VECTOR CALCULUS,
Unit-1: Differential equation, formation of a differential equation, order and degree, methods of solution of a differential equation of first order and first degree, method of separation of variables, solution of homogeneous equation, linear equation and exact equations.
Unit-2: Linear differential equations with constant, coefficients, homogeneous linear differential equations. Differential equations of the first order but not of the first degree. Clairaut's equations and singular solutions, orthogonal trajec- tories.
Unit-3: Simultaneous linear differential equations with constant coefficients, general linear differential equations of the second order, method of solution in terms of one unknown integral belonging to the complementary function. Method of solution by transformation of the equation to the normal form, transformation of the equation by changing the independent variable. Method of operational factors, method of variation of parameters.
Unit-4: Vector differentiation and integration, gradient, divergence and curl, and their properties.
Unit-5: Line integrals, surface and volume integrals, Gauss, Green and Stokes theorems and problems based on these.