July 13, 2011
School of Arts & Sciences, Amritapuri
 

Mathematical Analysis aka Advanced Calculus is a branch of pure mathematics wherein students learn theories of differentiation, integration, limits, infinite series and analytic functions. Students don’t always find these concepts easy to understand.
 

In order to help budding research scholars benefit from advances in this area, the Department of Mathematics at the Amritapuri campus recently organized a three-day lecture workshop.
 

Several postgraduate and PhD students, post doctoral researchers and faculty members from both Amrita as well as other colleges attended.
 

The workshop was jointly sponsored by the Science Academies viz., the Indian Academy of Sciences (Bangalore); The National Academy of Sciences (Allahabad) and Indian National Science Academy (New Delhi).
 

“The main objective of the workshop was to lead participants from a strong understanding of the fundamentals in this area to the frontiers of research,” stated Dr. P. V. Usha Kumari, Associate Professor, who coordinated the program.
 

Dr. A. K. Nandakumaran from the Indian Institute of Sciences began the series of lectures with an exposition on the analysis and limitations of Riemann integration. Providing an introduction to measure theory, he introduced the concepts of Lp –spaces and duals.
 

“The study of partial differential equations that originated in the 18th century was used to model mathematically, problems in continuum mechanics such as the vibration of a string, vibration of a thin membrane and acoustics,” he explained, during a subsequent lecture.
 

Dr. K.S.S. Moosath from Indian Institute of Space Science and Technology (Trivandrum), Drs. K. Sandeep and Mythily Ramaswamy from Center for Applicable Mathematics (CAM, Bangalore), Tata Institute of Fundamental Research were other distinguished professors who delivered lectures.
 

While Dr. Moosath taught Lebesgue measure, Lebesgue integral-definition and their basic properties, insightful sessions by CAM faculty elaborated on the fundamentals of distribution theory, the need to define distribution derivatives and Sobolov spaces and distributions, with suitable examples.
 

Dr. V. Krishnakumar of Amritapuri Campus taught the Convergence Theorem and the Dirac delta function.
 

“All experts were available for formal and informal discussions at all times,” stated Dr. Usha Kumari. “They stayed on campus and participated fully in all the discussions. Their continued presence was a source of inspiration to all participants.”
 

“We are happy and proud to report that the lecture workshop was successful and met all its objectives,” she proudly concluded.