Introduction to Fourier Analysis

By Prof. Parasar Mohanty | IIT Kanpur

Learners enrolled: 416 | Exam registration: 12

ABOUT THE COURSE:
This course will cover the fundamental theory of Fourier series and Fourier integrals, as well as Fourier series for finite abelian groups. Some applications of Fourier series in differential equations, the isoperimetric problem, and number theory will be explored. Basic calculus and Riemann integrals will be required as prerequisites. The book “Introduction to Fourier Analysis” by E. Stein and R. Shakarchi will serve as the basis for this course.

INTENDED AUDIENCE: Undergraduate

PREREQUISITES: Basic Calculus, Riemann Integration

INDUSTRY SUPPORT: This topic holds significant importance in mathematics and is considered a central theme that every mathematics student should be familiar with.

Summary

Course Status :	Completed
Course Type :	Elective
Language for course content :	English
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Undergraduate
Start Date :	22 Jul 2024
End Date :	11 Oct 2024
Enrollment Ends :	05 Aug 2024
Exam Registration Ends :	16 Aug 2024
Exam Date :	03 Nov 2024 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1 : Introduction and Overview, Derivation of heat equation periodic function and Review of Riemann Integration, Definition of Fourier Coefficients

Week 2 : Computation of Fourier series for some functions, Partial sum as convolution with Dirichlet Kernel Properties of Convolution

Week 3 : Riemann Lebesgue Lemma Decay for differentiable functions Fej´er’s Theory and applications

Week 4 : Abel Summability Pointwise convergence localization Gibb’s Phenomena

Week 5 : Basic Inner product spaces Convergence in 2-mean Trigonometric series which are not Fourier series

Week 6 : Applications Isoperimetric Problem Weyl Equidistributions

Week 7 : Improper Integral Fourier Transform on R Computations of Fourier transform

Week 8 : Schwartz Space Approximate Identity Fourier Inversion

Week 9 : Plancherel Formula Applications Poisson summation formula

Week 10 : Heisenberg Uncertainity Principle Heat Equation

Week 11 : Fourier Analysis on Z(N) Fast Fourier Transform

Week 12 : Fourier Analysis on Finite Abelian Groups Applcations

Books and references

Introduction To Fourier Analysis- E. Stein, R.Shakarchi

Instructor bio

Prof. Parasar Mohanty

IIT Kanpur

Prof. Parasar Mohanty is a professor in Department of Mathematics and Statistics at IIT Kanpur. He did his PhD in Mathematics from IIT Kanpur in 2001. He has a proven track record in both teaching and research. His areas of research include Mathematical, Functional Analysis and Harmonic analysis. He was honored with the Gopal Das Bhandari Memorial Distinguished Teacher Award 2017. He was also awarded the prestigious INSA Teacher Award 2021 for his contributions in inspiring and mentoring students.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 03 November 2024 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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