3EE6.1-MATHEMATICS |
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, change 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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