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B.Tech. IT 3rd Sem Subject: Mathematics - III
UNIT – 1 Functions of Complex Variables Limit, Derivative, Analytic function, Cauchy-Riemann equations, Harmonic functions, Geometrical representation, Transformation, Bilinear transformation, Application to Flow point, Poles & residues, Residue theorem & its application to contour integration.
UNIT – 2 Fourier Series Periodic functions, Definition of Fourier series, Euler’s formulae, Dirichlet conditions, Change of interval, Even and odd functions, Half range Fourier Sine & Cosine series, Parseval’s identity, Practical harmonic analysis.
UNIT – 3 Laplace Transform Definition, Linearity, Shifting & scaling properties, Transform of elementary functions, Transform of Derivatives and integrals, Multiplication by t & division by t, Inverse Laplace transform, Convolution theorem, Transform of periodic functions, Unit step function & Dirac delta function, Initial value & final value theorems, Application to solution of ordinary differential equations.
UNIT – 4 Fourier Transform Definition of Fourier integrals – Fourier Sine & Cosine integrals, Complex form of Fourier integral, Fourier Sine & Cosine transforms, Complex form of Fourier transform, Linearity, Shifting & scaling properties, Modulation theorem, Inverse Fourier transform, Fourier transform of derivatives. Initial value & final value theorems,
UNIT – 5 Wavelet – Transform Introduction to wavelets, Basic functional Specification, Admissibility condition, Continuous wave transform definition, CWT as a correlation, Constant Q Factor, Filtering interpretation and time frequency resolution, Inverse CWT.
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