Fourier analysis is a fundamental component in the tool-kit of every pure and applied mathematician with numerous applications to signal processing, image processing, tomography and several other areas of engineering. In this course we shall look at the most basic theoretical foundations of this subject with several applications. Along the way we shall have to recapitulate some of the requisite results from functional analysis. We offer some Selected applications such as Hurwitz’s proof of the isoperimetric theorem and Weyl’s theorem on equidistribution modulo one. Some applications to differential equations will be indicated.

1) Fourier Analysis: E. M. Stein and R. Shakarchi, Princeton Univesity Press, Indian Reprint

2) R. Strichartz, Guide to distributions and Fourier transforms, CRC Press, Boca Raton.

2) R. Strichartz, Guide to distributions and Fourier transforms, CRC Press, Boca Raton.

Short Resume of Gopala Krishna Srinivasan (Professor)
Department of Mathematics
Indian Institute of Technology Bombay
Powai, Mumbai 400076
Personal Details:
• Gender: Male
• Age: 52
• Phone number: 9819807454 (Mobile), 022 256 7454 (Office)
Academic Qualifications:
• Bachelor of Science, University of Bombay, 1987.
• Master of Science, University of Bombay, 1989.
• Doctor of Philosophy, Mathematics, University of Minnesota, Minneapolis, in 1995.
Thesis: WTC Expansions and Painlevé Analysis.
Areas of Specialization/interest:
1. Partial Differential Equations, Shock waves in Hyperbolic Systems of Conservation Laws.
2. Dynamical systems.
3. Classical Analysis, Special Functions and History of Mathematics.
Publications:
1. S. Kichenassamy and G. K. Srinivasan, The Structure of WTC Expansions and Applications, Jour. Physics - A, 28 (2005) 1977-2004.
2. N. Joshi and G. K. Srinivasan,Well-Posedness of Painlevé Expansions, Nonlinearity, 10 (1997) 71-79.
3. G. K. Srinivasan and V. D. Sharma, Modulation Equations for Weakly nonlinear Geometrical Optics in
Media Exhibiting Mixed Nonlinearity, Studies in Applied Mathematics, 110 (2003) 103-122.
4. G. K. Srinivasan and V. D. Sharma, A Note on the Jump Conditions For Systems of Conservation Laws,
Studies in Applied Mathematics, 110 (2003) 391-396.
5. G. K. Srinivasan and V. D. Sharma, On Weakly Nonlinear Waves in Media Exhibiting Mixed Nonlinearity,
Journal of Mathematical Analysis and Applications, 285 (2003) 629-641.
6. G. K. Srinivasan and V. D. Sharma, Energy Dissipated Across Shocks in Weak Solutions of a Scalar
conservation Law, Studies in Applied Mathematics, 112 (2004) 281-291.
7. G. K. Srinivasan and V. D. Sharma, Implosion-Time for Converging Spherical and Cylindrical Shells,
Zeitschrift für Angewandte Mathematik und Physik, 55 (2004) 974-982.
8. V. D. Sharma and G. K. Srinivasan, Wave Interaction in a Non-equilibrium Flow, International Journal of
Non-Linear Mechanics, 40 (2005) 1031-1040.
9. G. K. Srinivasan, The gamma function - an eclectic tour, American Mathematical Monthly 114 (2007)
297-315.
10. G. K. Srinivasan, A Note on Lagrange’s Method of Variation of Parameters, Missouri Journal of
Mathematical Sciences, 19 (2007) 11-14.
11. G. K. Srinivasan, V. D. Sharma and B. S. Desale, An Integrable System of ODE Reductions of the
stratified Boussinesq Equations, Compt. Math. Appl, 53 No. 2, (2007) 296-304.
12. B. S. Desale and G. K. Srinivasan, Singular analysis of the system of ODE reductions of the stratified
Boussinesq equations, IAENG International journal of applied mathematics, 38 (2008) no. 4, 184-191.
13. G. K. Srinivasan and P. Zvengrowski, On the horizontal monotonicity of |Γ(s)|, Canadian Math. Bulletin,
54 (2011), no. 3, 538-543.
14. G. K. Srinivasan, Dedekind’s proof of Euler’s reflection formula via ODEs, Mathematics Newsletter
(published by Ramanujan Mathematical Socity) 21 (2011) no. 3, 82-83.
15. D. Chakrabarty and G. K. Srinivasan, On a remarkable formula of Ramanujan, Arch. Math. (Basel) 99
(2012), 125-135.
16. G. K. Srinivasan, A unified approach to the integrals of Mellin–Barnes–Hecke type, To appear in
Expositiones Mathematicae.
Ph.D student:
1. Title of Thesis: An Integrable System of ODE Reductions of the stratified Boussinesq Equations.
Defended in January 2007.
2> sunil Kumar Yadav.
Books I have completed a web-book on Algebraic Topology under the NPTEL Scheme. The link is
http://nptel.iitm.ac.in/courses/111101002/
Proficiency in foreign languages:
(i) Have completed four levels of basic German at the prestigious Göethe Institute (Max Muller Bhavan) upto
Mittelstuffe - I.
(ii) Completed the first two levels of French at Alliance Française de Mumbai.
Awards and Recognitions:
1. Award for Excellence in Teaching, Indian Institute of Technology, Bombay (Sept 5, 2011)
2. Award for Excellence in Teaching, Indian Institute of Technology, Bombay (Sept 5, 2007)
3. Award for Excellence in Teaching, Indian Institute of Technology, Bombay (Sept 5, 2002)
4. Citation For Excellence in Teaching, awarded by the Department of Mathematics at the University of
Minnesota, Minneapolis (1995).
5. Shri Pandharinath Moroba Mungre Prize, for the year 1989 for passing MSc examination with highest
number of marks on the aggregate.
6. The Late Shri Balkrishna Waman Deshpande Prize, for the year 1989 for passing MSc examination with
highest number of marks on the aggregate.
7. Principal V. K. Joag Memorial Prize, for the year 1989 for passing MSc examination with highest number
of marks on the aggregate.
8. Professor Laxman Vasudeo Gurjar Prize, for the year 1989 for passing MSc examination with highest
number of marks on the aggregate.
9. Certificate of Merit for Outstanding Performance and Being Among the Top 5% of Candidates Qualifying
in C.S.I.R - U.G.C Fellowship in Mathematics (1988)
2

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: **30 April 2023** 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.

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

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 Bombay .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

## DOWNLOAD APP

## FOLLOW US