Linear differential equations with constant coefficients:
Solutionsof second and higher order differential equations - inverse differentialoperator method, method of undetermined coefficients and method ofvariation of parameters.
Differential equations-2:
Linear differential equations with variable coefficients: Solution ofCauchy’s and Legendre’s linear differential equations.Nonlinear differential equations - Equations solvable for p,equations solvable for y, equations solvable for x, general and singularsolutions, Clairauit’s equations and equations reducible to Clairauit’sform.
Partial Differential equations:
Formulation of Partial differential equations by elimination ofarbitrary constants/functions, solution of non-homogeneous Partialdifferential equations by direct integration, solution of homogeneousPartial differential equations involving derivative with respect to oneindependent variable only.
Derivation of one dimensional heat and wave equations and theirsolutions by variable separable method.
Integral Calculus:
Double and triple integrals: Evaluation of double and tripleintegrals. Evaluation of double integrals by changing the order ofintegration and by changing into polar co-ordinates. Application ofdouble and triple integrals to find area and volume.
Beta and Gamma functions: definitions, Relation between beta and gammafunctions and simple problems.
Laplace Transform
Definition and Laplace transforms of elementary functions.Laplace transforms of (without proof) ,periodic functions and unit-step function- problemsInverse Laplace Transform
Inverse Laplace Transform - problems, Convolution theorem tofind the inverse Laplace transforms(without proof) and problems,solution of linear differential equations using Laplace Transforms.10