05-01-2017, 03:31 PM
QUESTION PAPER:-
SYLLABUS:-
UNIT-I
Fourier series: Definition, Euler’s formula, conditions for Fourier expansion, functions having points of discontinuity, change of intervals, even and odd functions ,half range series, Harmonic analysis.
Fourier Transforms: Definition, Fourier integral, Fourier transform, inverse Fourier transform, Fourier sine and cosine transforms, properties of Fourier transforms (linearity, scaling, shifting, modulation), Application to partial differential equations.
UNIT-II
Difference equation: Definition, formation, solution of linear difference equation with constant coefficients ,simultaneous difference equations with constant coefficients, applications of difference equations .
Z- transform: Definition, Z- transform of basic functions, properties of Z-transform (linearity, damping, shifting, multiplication),initial value theorem, final value theorem, convolution theorem, convergence of Z- transform, inverse of Z- transform, Application to difference equations.
UNIT-III
Numerical Methods: Solution of algebraic and transcendental equations using bisection method, Regula-Falsi method and Newton – Raphson method. Solution of linear simultaneous equations using Gauss-Jacobi’s iteration method and Gauss-Seidal’s iteration methods.
Finite differences: Forward differences, backward differences and Central differences.
Interpolation: Newton’s interpolation for equi-spaced values. Stirling’s central difference interpolation formula, Divided differences and interpolation formula in terms of divided differences , Lagrange’s interpolation formula for unequi-spaced values.
UNIT-IV
Numerical Differentiation, maxima and minima of a tabulated function.
Numerical Integration: Newton-Cote’s quadrature formula, Trapezoidal rule, Simpson’s one-third rule and Simpson’s three-eighth rule .Numerical solution of ordinary differential equations: Picard’s method, Taylor’s method,Euler’s method, modified Euler’s method, Runge-Kutta method of fourth order.
SYLLABUS:-
UNIT-I
Fourier series: Definition, Euler’s formula, conditions for Fourier expansion, functions having points of discontinuity, change of intervals, even and odd functions ,half range series, Harmonic analysis.
Fourier Transforms: Definition, Fourier integral, Fourier transform, inverse Fourier transform, Fourier sine and cosine transforms, properties of Fourier transforms (linearity, scaling, shifting, modulation), Application to partial differential equations.
UNIT-II
Difference equation: Definition, formation, solution of linear difference equation with constant coefficients ,simultaneous difference equations with constant coefficients, applications of difference equations .
Z- transform: Definition, Z- transform of basic functions, properties of Z-transform (linearity, damping, shifting, multiplication),initial value theorem, final value theorem, convolution theorem, convergence of Z- transform, inverse of Z- transform, Application to difference equations.
UNIT-III
Numerical Methods: Solution of algebraic and transcendental equations using bisection method, Regula-Falsi method and Newton – Raphson method. Solution of linear simultaneous equations using Gauss-Jacobi’s iteration method and Gauss-Seidal’s iteration methods.
Finite differences: Forward differences, backward differences and Central differences.
Interpolation: Newton’s interpolation for equi-spaced values. Stirling’s central difference interpolation formula, Divided differences and interpolation formula in terms of divided differences , Lagrange’s interpolation formula for unequi-spaced values.
UNIT-IV
Numerical Differentiation, maxima and minima of a tabulated function.
Numerical Integration: Newton-Cote’s quadrature formula, Trapezoidal rule, Simpson’s one-third rule and Simpson’s three-eighth rule .Numerical solution of ordinary differential equations: Picard’s method, Taylor’s method,Euler’s method, modified Euler’s method, Runge-Kutta method of fourth order.