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3ME6: ADVANCED ENGINEERING MATHEMATICS

 

  

2L+0T

MM:100

Ex Hrs:3
 

 

Unit-1

Fourier Series: Fourier series, Half-range series, Harmonic analysis.

integral Transform: Fourier integral theorem, Fourier transform, Convolution theorems, Inversion theorem for Fourier and Laplace transforms,  Simple applications of these transforms to one dimensional problems.

 

  
 

Unit-2

Method of separation of variables - applications to the solution of wave equation in one dimension, laplace's equation in two dimensions, Diffusion equation in one dimension.

Transform calculus : Laplace transform with its simple properties, applications to the solutions of ordinary and partial differential equations having constant co-efficient with special reference to wave and diffusion equation.

 

  
 

Unit-3

Complex Variable: Functions of a complex variable; Exponential, trigonometric, hyperbolic and logarithmic functions; Differentiation, Analytic functions, Cauchy-Riemann equations, conjugate functions; Application to two dimensional potential problems; Conformal transformations, Schwartz-Christoffel transformation; Cauchy's integral theorem. Taylor's and Laurent's expansions; Branch points, zeros, poles and residues; Simple problems on contour integration

 

  
 

Unit-4

Boundary value problems: Equations for vibrations of strings, heat flow and electrical transmission lines; Laplace's equation in Cartesian, cylindrical polar and spherical polar coordinates; Solution by separation of variables.

Solution in Series: Differentiation and integration of infinite series, Series solution of differential equations; Bessel and Legendre equations, their series solution, elementary properties of Bessel functions and Legendre polynomials

 

  
 

Unit-5

Numerical Methods: Difference operators: forward, backward, central shift and average operators and relations between them. Newton Backward and Interpolation; Lagrange's interpolation and the error formula for interpolation. Numerical differentiation and integration. Trapezoidal rule and Simpson's one-third rule including error formula.