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# Engineering Mathematics II

## Overview

This course is about the basic mathematics that is fundamental and essential component in all streams of undergraduate studies in sciences and engineering. The course consists of topics in complex analysis,numerical analysis, vector calculus and transform techniques with applications to various engineering problems. This course will cover the following main topics.Function of complex variables. Analytic functions. Line integrals in complex plane. Cauchy’s integral theorem, Derivatives of analytic functions. Power series, radius of convergence. Taylor’s and Laurent’s series, zeros and singularities, residue theorem.Iterative method for solution of system of linear equations. Finite differences, interpolation. Numerical integration. Solution of algebraic and transcendental equations.Vector and scalar fields. Limit, continuity, differentiability of vector functions. Directional derivative, gradient, curl, divergence. Line and surface integrals, Green, Gauss and Stokes theorem.Laplace transform and its properties. Laplace Transform of specialfunction. Convolution theorem. Evaluation of integrals by LaplaceTransform. Solution of initial and boundary value problems.Fourier series representation of a function. Fourier sine and cosinetransforms. Fourier Transform. Properties of Fourier Transform.Applications to boundary value problems.

INTENDED AUDIENCE : all branches of science and engineeringPREREQUISITES : Engineering Mathematics - IINDUSTRY SUPPORT : Nil

## Syllabus

### COURSE LAYOUT

Week 1 :Vector and scalar fields. Limit, continuity, differentiability of vector functions. Directional derivative, gradient, curl, divergenceWeek 2 : Line and surface integrals, Green, Gauss and Stokes theorem.
Week 3 :Function of complex variables and their properties including continuity anddifferentiability. Analytic functions and CR equations. Line
integrals incomplex plane.Week 4 :Cauchy’s integral theorem, Power series, radius of convergence. Taylor’sand Laurent’s series, zeros and singularities, residue theorem.Week 5 :Iterative method for solution of system of linear equations. Finitedifferences, interpolation.Week 6 :Numerical integration. Solution of algebraic and transcendental equations.Week 7 :Laplace transform and its properties. Laplace Transform of special function.Week 8 :Convolution theorem. Evaluation of integrals by Laplace Transform.Solution of initial and boundary value problems.Week 9 :Fourier series & its convergenceWeek 10 :Fourier integral representationWeek 11 :Fourier sine and cosine transforms. Fourier Transform. Properties ofFourier Transform.Week 12 :Applications of Fourier series to boundary value problems.

### Taught by

Prof. Jitendra Kumar

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