APPLIED MATHEMATICS-III
Paper Code: ETMA-201
Paper: Applied Mathematics-III
INSTRUCTIONS TO PAPER SETTERS: Maximum Marks: 75 Question No. 1 should be compulsory and cover the entire syllabus. This question should have objective or short answer type questions. It should be of 25 marks. 2. Apart from Question No. 1, rest of the paper shall consist of four units as per the syllabus. Every unit should have two questions. However, student may be asked to attempt only 1 question from each unit. Each question should be 12.5 marks.
Objectives: The objective of this course is to teach the students the applications of fourier series, fourier transform, difference equation and numerical methods to solve various engineering problems.
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.
Paper Code: ETMA-201
Paper: Applied Mathematics-III
INSTRUCTIONS TO PAPER SETTERS: Maximum Marks: 75 Question No. 1 should be compulsory and cover the entire syllabus. This question should have objective or short answer type questions. It should be of 25 marks. 2. Apart from Question No. 1, rest of the paper shall consist of four units as per the syllabus. Every unit should have two questions. However, student may be asked to attempt only 1 question from each unit. Each question should be 12.5 marks.
Objectives: The objective of this course is to teach the students the applications of fourier series, fourier transform, difference equation and numerical methods to solve various engineering problems.
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.
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