18HS0834

**UNIT- I**

Numerical Method-I: Solution of polynomial and transcendental equations: Bisection method, Newton-Raphson method and Regula-Falsi method, Finite differences, Interpolation using Newton’s forward and backward difference formulae. Numerical integration: Trapezoidal rule and Simpson’s 1/3rd and 3/8rules.**UNIT- II**

Numerical Method-II:Ordinary differential equations: Taylor’s series, Euler and Runge- Kutta method of fourth order for solving first and second order equations. Partial differential equations: Finite difference solution two dimensional Laplace equation.**UNIT- III**Transforms Calculus-I:Laplace Transform, Properties of Laplace Transform, Laplace transform of periodic functions. Finding inverse Laplace transform by different methods, Convolution theorem. Evaluation of integrals by Laplace transform,Solving ODEs by Laplace Transform method.

Transforms Calculus-II: Fourier transforms: Fourier sine and cosine transform, properties, inverse Fourier transforms, finite Fourier transforms.UNIT-V Partial Differential Equations: First order partial differential equations, solutions of first order linear and non-linear PDEs, Solution to homogenous and non-homogenous linear partial differential equations second and higher order by complimentary function and particular integral method, Solution of one dimensional equation, Heat equation.

1. Higher Engineering Mathematics, B.S.Grewal, Khanna publishers.

2. Engineering Mathematics I&II by T.K.V. Iyengar, S.Chand publications.

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