IST - Real Analysis (2022)

Speakers and Syllabus

Speakers:

1. Biswaranjan Behera, Stat-Math Unit, ISI Kolkata

2. Anjan Kumar Chakrabarty, Department of Mathematics, IIT Guwahati

3. Sudhir R. Ghorpade, Department of Mathematics, IIT Bombay

4. P. Shunmugaraj, Department of Mathematics and Statistics, IIT Kanpur

Tutors:

1. Sumit Kumar Rano, Post-doctoral fellow, Stat-Math Unit, ISI Kolkata

2. Kuldeep Sarma, Completed Ph.D. (Mathematics) in 2022 from Tezpur University

Speakers and Syllabus:

• Sudhir R. Ghorpade (6 lectures of 1.5 hours each)

  • Sequence and series of real numbers, Limit and continuity of functions, Pointwise and uniform convergence of sequence and series of functions, Power series

• Biswaranjan Behera (6 lectures of 1.5 hours each)

  • Derivative, Taylor's theorem, Riemann integral, Fundamental theorem of calculus, Improper integral

• Anjan Kumar Chakrabarty (6 lectures of 1.5 hours each)

  • Functions of several variables, Differentiability and related results, Chain rule, Mean value theorem

• P. Shunmugaraj (6 lectures of 1.5 hours each)

  • Double integral and triple integral, Change of variables, Line integral and surface integral, Green's theorem

References:

1. S. R. Ghorpade and B. V. Limaye : A Course in Calculus and Real Analysis, 2nd edition (Springer)

2. K. A. Ross : Elementary Analysis - The Theory of Calculus, 2nd edition (Springer)

3. S. R. Ghorpade and B. V. Limaye : A Course in Multivariable Calculus and Analysis (Springer)

4. W. Fleming : Functions of Several Variables (Springer) 5 T. M. Apostol : Calculus, Vol.II (Wiley)

Time Table

 Schedule