3EX1-MATHEMATICS-III |
Units: I-LAPLACE TRANSFORM: |
Laplace transform with its simple properties, applications to the
Solution of ordinary and partial differential equations having constant coefficients with special
reference to wave and diffusion equations, digital transforms.
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Units: II-FOURIER TRANSFORM: |
Discrete Fourier transform, Fast Fourier transform, Complex
form of Fourier transform and its inverse applications, Fourier transform for the solution of
partial differential equations having constant coefficients with special reference to heat
equation and wave equation. |
Units: III-FOURIER SERIES: |
Expansion of simple functions in Fourier series, half range series,
changes of interval, harmonic analysis.
CALCULUS OF VARIATION:Functional, strong and weak variations, simple variation
problems, Euler’s equation
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Units: IV-COMPLEX VARIABLES: |
Analytic functions, Cauchy-Riemann equations, Elementary
conformal mapping with simple applications, Line integral in complex domain, Cauchy’s
theorem, Cauchy’s integral formula.
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Units: V-COMPLEX VARIABLES: |
Taylor’s series, Laurent’s series, poles, Residues. Evaluations of
simple definite real integrals using the theorem of residues. Simple contour integration.
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