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Integrated First Degree

B.E.(Biotechnology)
B.E.(Chemical)
B.E.(Civil)
B.E.(Computer Science)
B.E.(Electrical and Electronics)
B.E.(Electronics and Communication)
B.E.(Electronics and Instrumentation)
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Amiya Kumar Pani

goa Mathematics

Visiting Professor

Numerical Analysis and Scientific Computing, Partial Differential Equations and Control
Birla Institute of Technology & Science, Pilani KK Birla Goa Campus NH 17 B, Zuarinagar Goa-403 726 (India)
amiyap@goa.bits-pilani.ac.in
pani.amiya11@gmail.com
0832-2580485
9769697481
https://www.linkedin.com/in/amiya-pani-085872275/

Courses Taught

  • Course 01 (Elective) Mathematical Theory of Finite Element Methods:  Quick tour to the theory of Distributions and essential elements of Sobolev Spaces, Variational formulation of elliptic boundary value problems, Lax-Milgram theorem, Error estimates, Construction of FE spaces, Polynomial approximations, interpolation errors, Aubin-Nitsche duality argument, Parabolic initial and boundary value problems: Semi-discrete and fully discrete schemes, error estimates.
  • Course 02 (Ph.D. level) Advance Topics in Functional Analysis and Applications: Theory of Distributions (Test space, Distributions, Basic operations, classification, Distributional derivatives, supports); Convolution ( of functions and of Distribution); Fundamental Solutions; Fourier Transform with properties; Fourier Inversion and Plancherel identity; Schwartz space and Tempered Distributions  with applications; Sobolev spaces with properties (absolutely necessary ingredients); Fundamental Solution of Heat Equation.
References:
1. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer Verlag (2010).
2. S. Kesavan, Topics in Functional Analysis and Applications, New Age International (P) Ltd., New Delhi (2015).
3. W. Rudin, Functional Analysis, Tata McGraw-Hill,1974.
 

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