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?2 I
CURRIGULUM - BACHELOR'S DEGREE IN COMPUTER ENGINEERING
APPTIED MATHEMATICSsH 551
LectureTutorialPractical
Year : llPart : ll
Coutse ObjectiveThis course focuses on several branches of applied mathematics. The students areexposed to complex variable theory and a study of the Fourier and Z-Transforms,topics of current importance in signal processing. The course concludes withstudies of the wave and heat equations in Cartesian and polar coordinates.1. Complex Analysis (18 hours)1.1 Complex Analytic Functions1.1.1 Functions and sets in the complex plane1.1.2 Limits and Derivatives of complex functions1.1.3 Analytic functions. The Cauchy -Riemann equations1.1 .4 Harmonic functions and it's conjugate1.2 Conformal Mapping1.2.1 Mapping1.2.2 Some familiar functions as mappinp1.2.3 Conformal mappings and special linear functionaltransformations1.2.4 Constructing conformal mappings between given domains1.3 lntegral in the Complex Plane1.3.1 Line integrals in the complex plane1.3.2 Basic Problems of the complex line integrals1.3.3 Cauchy's integral theorem,l.3.4 Cauchy's integral formula1.3.5 Supplementaryproblems1.4 Complex Power Series, Complex Taylor series and Lauren series1.4.1 Complex power series1.4.2 Functions represented by power series1.4.3 Taylor series, Taylor series of elementary functions1.4.4 Practical methods for obtaining power series, Laurent series1.4.5 Analyticity at infinity, zeros, singularities, residues, Cauchy'sresidue theorem1.4.6 Evaluation of real integrals2. The Z-Transform (9 hours)2.1 lntroduction2.2 Properties of Z-Transform2.3 Z- transform of elementary functions2.4 Linearityproperties2.5 First shifting theorem, second shifting theorem, lnitial value theorem,
310
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