# MA211

## Unit I

Laplace Transforms of standard functions. Unit Step functions. Dirac delta functions, derivatives and integrals. Inverse Laplace Transforms. Convolution theorem. Periodic functions. Application to ordinary differential equations and simultaneous equations with constant coefficients and integral equations.

## Unit II

Gamma and Beta functions. Frobenius method of finding series solution of ordinary differential equations.

## Unit III

Bessel's equation. Bessel functions. Recurrence formulae. Orthogonality property. Generating function. Legendre's equation. Legendre polynomials. Rodrigue's formula. Orthogonality property. Generating function. Recurrence relations.

## Unit IV

Laplace Transforms of standard functions. Unit Step functions. Dirac delta functions, derivatives and integrals. Inverse Laplace Transforms. Convolution theorem. Periodic functions. Application to ordinary differential equations and simultaneous equations with constant coefficients and integral equations.

## Unit V

Moment generating function. Characteristic function. Chebyshev's inequality. Law of large numbers. Central Limit Theorem.

## References** **

1. GREWAL, B.S.,

* Higher Engineering Mathematics*, Khanna Publishers.

2. GUPTA, S.C., and KAPOOR, V.K.,

* Fundamentals of Mathematical Statistics*, Sultan Chand and Sons.

3. VENKATARAMAN, M. K.,

* Higher Mathematics for Engineering and Science*, National Publishing Company.