3EC1-Mathematics-III |
Units: I-LAPLACE TRANSFORM |
Laplace transform with its simple properties, applications to the
solution of ordinary and partial differential equations having constant co-efficients with special reference
to the wave and diffusion equations.
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Units: II-FOURIER SERIES & Z TRANSFORM |
Expansion of simple functions in fourier series. Half
range series, Change of intervals, Harmonic analysis. Z TRANSFORM - Introduction, Properties, Inverse
Z Transform . |
Units: III-FOURIER TRANSFORM |
Complex form of Fourier Transform and its inverse, Fourier sine and
cosine transform and their inversion. Applications of Fourier Transform to solution of partial differential
equations having constant co-efficient with special reference to heat equation and wave 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, Evaluation of simple
definite real integrals using the theorem of residues. Simple contour integration.
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