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• To describe the ideas of Fourier and Laplace Transforms and indicate their applications in the fields such as application of PDE, Digital Signal Processing, Image Processing, Theory of wave equations, Differential Equations and many others.
• To use Fourier series for solving boundary value problems appearing in scientific & engineering problems.
COs  Course outcomes  Mapping Cos with POs (High3, Medium2, Low1) 
CO1  · Evaluate the Fourier transform of a continuous function and be familiar with its basic properties.
· Solution of integral equation and their application.

PO1(3), PO2(2), PO9(3) 
CO2  · Solve differential & integral equations with initial conditions using Laplace transform.

PO1(3), PO2(2), 
CO5  · Learn application of MATLAB programming.

PO5(3), PO9(2) 
ModuleI(T4 h + Pr2 h+ Pj4 h)
Introduction to Integral Transforms, Laplace Transforms,Properties of Laplace transforms,unit step function,second shifting theorem.
Practice1
Laplace Transform and Inverse Laplace Transform Using Matlab.
Project1
Make a short draft of properties of Laplace transform from memory. Then compare your notes with the text and write a report of 23 pages on these operations and their significance in applications.
Project2
Find the Laplace transform of the following functions
ModuleII(T4 h + Pj4 h)
Unit impulse function,Laplace transforms of Derivatives and Integrals, Derivatives and Integrals of Transforms.
Project3
Find the inverse Laplace transform of Derivative and integral properties.
Project4
Find the Laplace transform of unit impulse function and unit step function.
ModuleIII(T4 h + Pr2 h+ Pj4 h)
Evaluation of integrals,convolution theorem,inverse Laplace transform
Practice2
To solve integral equations by using Matlab.
Project5
Evaluation of integrals by using Laplace transform.
Project6
Find the inverse Laplace transform by using convolution theorem.
ModuleIV(T4 h + Pr2 h+ Pj4 h)
Solution of differential equations,integral equations.
Practice3
Find the solution of differential equations by Laplace Transform Using Matlab.
Project7
Solve the differential equation by using Laplace transform.
Project8
Solve the integral equation by using Laplace transform.
ModuleV(T4 h + Pr2 h+ Pj4 h)
Periodic function,Fourier series,Fourier series expansion of an arbitrary period,even and odd functions,half Range Expansions of a Fourier series.
Practice4
Find the Fourier series expansion of a periodic function by using Matlab.
Project9
Find the Fourier series expansion of a 2pi periodic function.
Project10
Find the Half range expansion of Fourier cosine and sine series.
ModuleVI(T4 h + Pr2 h+ Pj2 h)
Complex form of Fourier series, Fourier Integrals, Different forms of Fourier Integral Theorem.
Practice5
Find the Fourier Series Coefficients by using Matlab.
Project11
Find the Fourier sine and cosine integral of the following functions.
ModuleVII(T4 h + Pr2 h+ Pj2 h)
Fourier Transforms, Infinite Fourier Transforms,Finite Fourier transform, Properties Fourier Transform.
Practice6
First Fourier transform by using Matlab.
Project12
Make a short draft of properties of Fourier transform from memory. Then compare your notes with the text and write a report of 23 pages on these operations and their significance in applications.
Text Book:
M.D. Raisinghania, H.C. Saxena and H.K. Dass: Integral Transforms, S. Chand & Company LTD.Chapters: 1(1.11.5,1.7 to 1.10,1.12) 2(2.2,2.4,2.5,2.6), 3(3.1 to 3.21), 4(4.1, 4.4, 4.5 to 4.13, 4.15 to 4.17), 5(5.1, 5.16), 6(6.1 to 6.3, 6.6 to 6.8, 6.11), 7(7.1 to 7.3).
Reference Text Book:
1.Higher Engineering Mathematics by B.V.Ramana
2.An introduction to non harmonic Fourier series,Author(s):Robert M. Young
3.Advanced Engineering Mathematics by E.Kreyszig (10th edition)
Properties of Laplace Transform
Practice1
Laplace Transform and Inverse Laplace Transform Using Matlab.
https://www.youtube.com/watch?v=Epq128CiGrQ&feature=youtu.be
Project1
Make a short draft of properties of Laplace transform from memory. Then compare your notes with the text and write a report of 23 pages on these operations and their significance in applications.
Project2
Find the Laplace transform of the following functions
Project3
Find the inverse Laplace transform of Derivative and integral properties.
Project4
Find the Laplace transform of unit impulse function and unit step function.
Practice2
To solve integral Equation by using Matlab
https://www.youtube.com/watch?v=sZIzlRmyG00
Project5
Make a short draft of application of Laplace transform from memory. Then compare your notes with the text and write a report of 23 pages on these operations and their significance in applications.
Practice3
Solve the differential equations by Laplace Transform Using Matlab.
https://www.youtube.com/watch?v=igbwPMFC13w
Project7
Solve the differential equation by using Laplace transform.
Project8
Solve the integral equation by using Laplace transform
Fourier series Expansion of a periodic functions
Lecture Note Link: http://courseware.cutm.ac.in/wpcontent/uploads/2020/05/Session1.3.pdf
video Lecture Link: https://www.youtube.com/watch?v=r6sGWTCMz2k
Fourier expansion of a functions of any Periods 2L
Lecture Note Link: http://courseware.cutm.ac.in/wpcontent/uploads/2020/05/Session1.4.pdf
video Lecture Link: https://www.youtube.com/watch?v=Ud9Xtxsi2HI
Practice4
Find the Fourier series expansion of a periodic function by using Matlab.
https://www.youtube.com/watch?v=r6sGWTCMz2k
Project9(Flip Class)
Find the Fourier series expansion of the following functions.
Project10(Flip Class)
Find the half range expansion of Fourier sine and cosine series
Even and Odd Periodic extension of a Functions.
Lecture Note Link: http://courseware.cutm.ac.in/wpcontent/uploads/2020/05/Session1.5.pdf
video Lecture Link: https://www.youtube.com/watch?v=2XtL3H7gONk
Half range Expansion of a Fourier series
Lecture Note Link:http://courseware.cutm.ac.in/wpcontent/uploads/2020/05/Session2.1.pdf
video Lecture Link: https://www.youtube.com/watch?v=Ry45T8VROCg
Practice2
Find the Fourier Series Coefficients by using Matlab.
https://www.youtube.com/watch?v=o7O7vC0Bmms
Project11(Flip Class)
Find the steadystate current I(t) m the RLCcircuit ,where R = 100 ohm, L = 10 H, C = 1/100 F and E(t) V as follows and periodic with period 2pi. Sketch or graph the first four partial sums.
Fourier Integrals transform of a function f(t)
Lecture Note Link: http://courseware.cutm.ac.in/wpcontent/uploads/2020/05/Session2.3.pdf
video Lecture Link: https://www.youtube.com/watch?v=ZZfRuPpRXo
Different forms of Fourier Integral Theorems.
Lecture Note Link: http://courseware.cutm.ac.in/wpcontent/uploads/2020/05/Session2.4.pdf
video Lecture Link: https://www.youtube.com/watch?v=ZZfRuPpRXo
Fourier transform and Infinite Fourier Transforms
Lecture Note Link: http://courseware.cutm.ac.in/wpcontent/uploads/2020/05/Session6.0.pdf
video Lecture Link: https://www.youtube.com/watch?v=ykNtIbtCR8
Fourier cosine Transforms and inverse fourier transform
Lecture Note Link: http://courseware.cutm.ac.in/wpcontent/uploads/2020/05/Session6.2.pdf
video Lecture Link: https://www.youtube.com/watch?v=ykNtIbtCR8
Practice6
First Fourier transform by using Matlab.
Project12
A report of an Application of Convolution With FFTs .
Project12
Make a short draft of properties of Fourier transform from memory. Then compare your notes with the text and write a report of 23 pages on these operations and their significance in applications.
Assistant Professor ,School of Applied Sciences, Centurion University of Technology and Management, Paralakhemundi, Odisha, India. He has over 11 years of teaching experiences. He has published 12 research articles in National and International refereed journals . He is continue their P.hD in the field of Fuzzy Inventory Control Models.