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SASTRA Deemed to be University B. Tech. in Computer Science and Engineering
L T P C
3 1 0 4
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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