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SASTRA Deemed to be University                          B. Tech. in Computer Science and Engineering



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               Course Code: MAT201
               Semester: III
                                          ENGINEERING MATHEMATICS – III
                                               (Common to all Branches)

               Course Objectives
               To  help  the  learners  in  understanding  Laplace  transforms  techniques  used  in  engineering
               disciplines.  Also  it  provides  an  insight  into  Fourier  series  techniques  and  its  applications
               Further the  course  provides  a  knowledge  on  complex  differentiation  and  integration  which
               helps in solving some special type of integrations known as contour integrations which come
               in many engineering fields.

               UNIT - I                                                                                15 Periods
               Laplace Transforms
               Properties of the Laplace transform - Transforms of derivatives and Derivatives of transforms
               -  Shifting  theorems  -  Initial  and  Final  value  Theorems  -  Change  of  scale  property  -
               Convolution  theorem  -  Periodic  function  theorem  -  Inversion  Laplace  transforms.  Solving
               First order and Second order Ordinary Differential equations and simultaneous Differential
               equations using Laplace Transforms

               L-C-R Circuit problems, Mechanical vibrating string problems (with damped, without damped
               models), simple problems of stability theory in Control systems

               UNIT - II                                                                         15 Periods
               Fourier Series
               Introduction to Fourier series-Dirichlet’s conditions, Fourier series of odd and even functions,
               Half-Range Fourier Series and Parseval’s theorem, Root-mean square value of a function,
               Complex form of Fourier series

               Harmonic analysis, Fourier series solution to Transverse vibrations of a stretched vibrating
               strings - Problems.

               UNIT - III                                                                         15 Periods
               Complex Differentiation
               Analytic functions - Cauchy Riemann Equations and other properties-Harmonic functions -
               Milne’s -Thomson Circle theorem (Statement Only) - Standard transformations - Conformal
                                                     z
               mapping( sin z, cos z, sinh z, cosh z, e  , z + (1/z) - Mobius transformation

               Construction of an Analytic function by Milne’s  - Thomson method - Simple problems related
               to Steady State Heat Flow and Electrostatic Potential

               UNIT - IV                                                                               15 Periods
               Complex Integration
               Cauchy’s  Integral  theorem  and  Integral  Formula  -  Taylor  and  Laurent’s  series  -  Types  of
               Singularities - Calculus of residues - Cauchy's residue theorem

               Evaluation of Contour integrals, Evaluation of Real definite integrals, Application of Blasius
               theorem to find the Net Force and momentum exerted by the boundary on the fluid when two
               line sources are located at a given distance from a rigid boundary
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