18MAT31 Transform Calculus, Fourier Series And Numerical Techniques syllabus for ME



A d v e r t i s e m e n t

Module-1 Laplace Transform 0 hours

Laplace Transform:

Definition and Laplace transforms of elementary functions (statements only). Laplace transforms of Periodic functions (statement only) and unit-step function – problems.

 

Inverse Laplace Transform:

Definition and problems, Convolution theorem to find the inverse Laplace transforms (without Proof) and problems. Solution of linear differential equations using Laplace transforms.

Module-2 Fourier Series 0 hours

Fourier Series:

Periodic functions, Dirichlet’s condition. Fourier series of periodic functions period 2π and arbitrary period. Half range Fourier series. Practical harmonic analysis.

Module-3 Fourier Transforms 0 hours

Fourier Transforms:

Infinite Fourier transforms, Fourier sine and cosine transforms. Inverse Fourier transforms. Problems.

 

Difference Equations and Z-Transforms:

Difference equations, basic definition, z-transform-definition, Standard z-transforms, Damping and shifting rules, initial value and final value theorems (without proof) and problems, Inverse z-transform and applications to solve difference equations.

Module-4 Numerical Solutions of Ordinary Differential Equations(ODE’s) 0 hours

Numerical Solutions of Ordinary Differential Equations(ODE’s):

Numerical solution of ODE’s of first order and first degree- Taylor’s series method, Modified Euler’s method. Runge -Kutta method of fourth order, Milne’s and Adam-Bash forth predictor and corrector method (No derivations of formulae)-Problems.

Module-5 Numerical Solution of Second Order ODE’s 0 hours

Numerical Solution of Second Order ODE’s:

Runge-Kutta method and Milne’s predictor and corrector method. (No derivations of formulae).

 

Calculus of Variations:

Variation of function and functional, variational problems, Euler’s equation, Geodesics, hanging chain, problems.

 

Course outcomes:

At the end of the course the student will be able to:

• CO1: Use Laplace transform and inverse Laplace transform in solving differential/ integral equation arising in network analysis, control systems and other fields of engineering.

• CO2: Demonstrate Fourier series to study the behaviour of periodic functions and their applications in system communications, digital signal processing and field theory.

• CO3: Make use of Fourier transform and Z-transform to illustrate discrete/continuous function arising in wave and heat propagation, signals and systems.

• CO4: Solve first and second order ordinary differential equations arising in engineering problems using single step and multistep numerical methods.

• CO5:Determine the externals of functionals using calculus of variations and solve problems arising in dynamics of rigid bodies and vibrational analysis.

 

Question paper pattern:

• The question paper will have ten full questions carrying equal marks.

• Each full question will be for 20 marks.

• There will be two full questions (with a maximum of four sub- questions) from each module.

• Each full question will have sub- question covering all the topics under a module.

• The students will have to answer five full questions, selecting one full question from each module.

 

Textbooks

1 Advanced Engineering Mathematics E. Kreyszig John Wiley & Sons 10th Edition, 2016

2 Higher Engineering Mathematics B. S. Grewal Khanna Publishers 44th Edition, 2017

3 Engineering Mathematics Srimanta Pal et al Oxford University Press 3 rd Edition, 2016

 

Reference Books

1 Advanced Engineering Mathematics C. Ray Wylie, Louis C. Barrett McGraw-Hill Book Co 6 th Edition, 1995

2 Introductory Methods of Numerical Analysis S.S.Sastry Prentice Hall of India 4 th Edition 2010

3 Higher Engineering Mathematics B.V. Ramana McGraw-Hill 11th Edition,2010

4 A Textbook of Engineering Mathematics N.P.Bali and Manish Goyal Laxmi Publications 6 th Edition, 2014

5 Advanced Engineering Mathematics Chandrika Prasad and Reena Garg Khanna Publishing, 2018

 

Web links and Video Lectures:

1. http://nptel.ac.in/courses.php?disciplineID=111

2. http://www.class-central.com/subject/math(MOOCs)

3. http://academicearth.org/

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Last Updated: Tuesday, January 24, 2023