Integral Transformation
Teacher
Dr.Balaji Padhy
Category
Core Courses
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Course Name : Integral Transformation
Code(Credit) :CUTM1521(3-1-2)
Course Objectives
• 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.
Course Outcomes
| COs | Course outcomes | Mapping Cos with POs (High-3, Medium-2, Low-1) |
| 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) |
Course Syllabus
Module-I(T-4 h + Pr-2 h+ Pj-4 h)
Introduction to Integral Transforms, Laplace Transforms,Properties of Laplace transforms,unit step function,second shifting theorem.
Practice-1
Laplace Transform and Inverse Laplace Transform Using Matlab.
Project-1
Make a short draft of properties of Laplace transform from memory. Then compare your notes with the text and write a report of 2-3 pages on these operations and their significance in applications.
Project-2
Find the Laplace transform of the following functions
Module-II(T-4 h + Pj-4 h)
Unit impulse function,Laplace transforms of Derivatives and Integrals, Derivatives and Integrals of Transforms.
Project-3
Find the inverse Laplace transform of Derivative and integral properties.
Project-4
Find the Laplace transform of unit impulse function and unit step function.
Module-III(T-4 h + Pr-2 h+ Pj-4 h)
Evaluation of integrals,convolution theorem,inverse Laplace transform
Practice-2
To solve integral equations by using Matlab.
Project-5
Evaluation of integrals by using Laplace transform.
Project-6
Find the inverse Laplace transform by using convolution theorem.
Module-IV(T-4 h + Pr-2 h+ Pj-4 h)
Solution of differential equations,integral equations.
Practice-3
Find the solution of differential equations by Laplace Transform Using Matlab.
Project-7
Solve the differential equation by using Laplace transform.
Project-8
Solve the integral equation by using Laplace transform.
Module-V(T-4 h + Pr-2 h+ Pj-4 h)
Periodic function,Fourier series,Fourier series expansion of an arbitrary period,even and odd functions,half Range Expansions of a Fourier series.
Practice-4
Find the Fourier series expansion of a periodic function by using Matlab.
Project-9
Find the Fourier series expansion of a 2-pi periodic function.
Project-10
Find the Half range expansion of Fourier cosine and sine series.
Module-VI(T-4 h + Pr-2 h+ Pj-2 h)
Complex form of Fourier series, Fourier Integrals, Different forms of Fourier Integral Theorem.
Practice-5
Find the Fourier Series Coefficients by using Matlab.
Project-11
Find the Fourier sine and cosine integral of the following functions.
Module-VII(T-4 h + Pr-2 h+ Pj-2 h)
Fourier Transforms, Infinite Fourier Transforms,Finite Fourier transform, Properties Fourier Transform.
Practice-6
First Fourier transform by using Matlab.
Project-12
Make a short draft of properties of Fourier transform from memory. Then compare your notes with the text and write a report of 2-3 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(1.1-1.5,1.7 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)
Session Plan
Session 1
Session 2
Properties of Laplace Transform
Session 5 & 6
Practice-1
Laplace Transform and Inverse Laplace Transform Using Matlab.
https://www.youtube.com/watch?v=Epq128CiGrQ&feature=youtu.be
Session 7 & 8
Project-1
Make a short draft of properties of Laplace transform from memory. Then compare your notes with the text and write a report of 2-3 pages on these operations and their significance in applications.
Session 9 & 10
Project-2
Find the Laplace transform of the following functions
Session 15 & 16
Project-3
Find the inverse Laplace transform of Derivative and integral properties.
Session 17 & 18
Project-4
Find the Laplace transform of unit impulse function and unit step function.
Session 22 & 23
Practice-2
To solve integral Equation by using Matlab
https://www.youtube.com/watch?v=sZIzlRmyG00
Session 24 & 25
Project-5
Make a short draft of application of Laplace transform from memory. Then compare your notes with the text and write a report of 2-3 pages on these operations and their significance in applications.
Session 29 & 30
Practice-3
Solve the differential equations by Laplace Transform Using Matlab.
https://www.youtube.com/watch?v=igbwPMFC13w
Session 32 & 33
Project-7
Solve the differential equation by using Laplace transform.
Session 35 & 36
Project-8
Solve the integral equation by using Laplace transform
Session 38
Fourier series Expansion of a periodic functions
Lecture Note Link: http://courseware.cutm.ac.in/wp-content/uploads/2020/05/Session-1.3.pdf
video Lecture Link: https://www.youtube.com/watch?v=r6sGWTCMz2k
Session 39
Fourier expansion of a functions of any Periods 2L
Lecture Note Link: http://courseware.cutm.ac.in/wp-content/uploads/2020/05/Session-1.4.pdf
video Lecture Link: https://www.youtube.com/watch?v=Ud9Xtxsi2HI
Session 40 & 41
Practice-4
Find the Fourier series expansion of a periodic function by using Matlab.
https://www.youtube.com/watch?v=r6sGWTCMz2k
Session 42& 43
Project-9(Flip Class)
Find the Fourier series expansion of the following functions.
Session 44 & 45
Project-10(Flip Class)
Find the half range expansion of Fourier sine and cosine series
Session 46
Even and Odd Periodic extension of a Functions.
Lecture Note Link: http://courseware.cutm.ac.in/wp-content/uploads/2020/05/Session-1.5.pdf
video Lecture Link: https://www.youtube.com/watch?v=2XtL3H7gONk
Session 47
Half range Expansion of a Fourier series
Lecture Note Link:http://courseware.cutm.ac.in/wp-content/uploads/2020/05/Session-2.1.pdf
video Lecture Link: https://www.youtube.com/watch?v=Ry45T8VROCg
Session-48 &49
Practice-2
Find the Fourier Series Coefficients by using Matlab.
https://www.youtube.com/watch?v=o7O7vC0Bmms
Session 50
Session 51 & 52
Project-11(Flip Class)
Find the steady-state current I(t) m the RLC-circuit ,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.
Session 53
Fourier Integrals transform of a function f(t)
Lecture Note Link: http://courseware.cutm.ac.in/wp-content/uploads/2020/05/Session-2.3.pdf
video Lecture Link: https://www.youtube.com/watch?v=ZZfRuPpRX-o
Session 54
Different forms of Fourier Integral Theorems.
Lecture Note Link: http://courseware.cutm.ac.in/wp-content/uploads/2020/05/Session-2.4.pdf
video Lecture Link: https://www.youtube.com/watch?v=ZZfRuPpRX-o
Session 55
Fourier transform and Infinite Fourier Transforms
Lecture Note Link: http://courseware.cutm.ac.in/wp-content/uploads/2020/05/Session-6.0.pdf
video Lecture Link: https://www.youtube.com/watch?v=ykNtIbtCR-8
Session 56
Session 57
Fourier cosine Transforms and inverse fourier transform
Lecture Note Link: http://courseware.cutm.ac.in/wp-content/uploads/2020/05/Session-6.2.pdf
video Lecture Link: https://www.youtube.com/watch?v=ykNtIbtCR-8
Session 58 & 59
Practice-6
First Fourier transform by using Matlab.
Session 60 & 61
Project-12
A report of an Application of Convolution With FFTs .
Session 63
Session 64
Session 65 & 66
Project-12
Make a short draft of properties of Fourier transform from memory. Then compare your notes with the text and write a report of 2-3 pages on these operations and their significance in applications.
Our Main Teachers
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.