Linear differential equations with constant coefficients : Solutions ofsecond and higher order differential equations - inverse differential operatormethod, method of undetermined coefficients and method of variation ofparameters
Solutions of simultaneous differential equations of first order.Linear differential equations with variable coefficients : Solution ofCauchy’s and Legendre’s linear differential equations.Nonlinear differential equations : Equations solvable for p, equationssolvable for y, equations solvable for x, general and singular solutions,Clairauit’s equations and equations reducible to Clairauit’s form.
Formulation of PDE by elimination of arbitrary constants/functions, solutionof non-homogeneous PDE by direct integration, solution of homogeneousPDE involving derivative with respect to one independent variable only.Derivation of one dimensional heat and wave equations and their solutionsby variable separable method.Double and triple integrals :Evaluation of double integrals. Evaluation by changing the order ofintegration and changing into polar coordinates. Evaluation of tripleintegrals.
Integral Calculus :Application of double and triple integrals to find area and volume. Betaand Gamma functions, definitions, Relation between beta and gammafunctions and simple problems.Curvilinear coordinates :Orthogonal curvilinear coordinates - Definition, unit vectors and scalefactors. Expressions for gradient, divergence and curl. Cylindrical andspherical coordinate systems.
Laplace Transform :Definition and Laplace transforms of elementary functions. Laplacetransforms of (without proof), periodic functions, unitstepfunction and Impulse function - problemsInverse Laplace Transform :Inverse Laplace Transform - problems, Convolution theorem and problems,solution of linear differential equations using Laplace Transforms.