TEW Multivariable Calculus (2013)

Proposed Scientific plan: In the proposed TEW, our theme would be Multivariable calculus with applications. We propose to have six mini-courses in this program each consisting of between two and four lectures. The rest of the time will be devoted to group discussions and tutorials.

Objectives : The objective is same as that of the proposed RMS-TEW. That is (i) to promote student-initiative activities at the UG-PG levels. (ii) to increase the knowledge of the fundamentals among college teachers. Emphasis will be given on basic examples and problem-solving..

Syllabus of the Workshop: The syllabus of the workshop has been designed in a way so that the major part of the workshop will be devoted to foundational aspects of the topic. The details of the courses are given below :

• Course Title: Linear algebra 
  Speaker:  Nitin Nitsure
  Topics : Vector spaces and inner product spaces. Linear maps. Rank, determinant and volume. Vector calculus and its applications. (4 lectures).
• Course Title: Differential calculus in one variable     
  Speaker:  Anand Sawant
  Topics : Continuous functions and differentiable functions. Computation of the derivative. Mean Value Theorem. Tests for local extremum. Applications. (3 lectures)
• Course Title: Integration
  Speaker: Siddhartha Bhattacharya
  Topics: Riemann integrations. Integrability of continuous functions. Fundamental theorems of calculus. Applications.  (2 lectures).
• Course Title:  Multivariate calculus
  Speaker:  Amitava Bhattacharya
  Topics : Partial derivatives. Total derivative of a function. Computation of the total derivative. Chain rule. (2 lectures)..
•  Course Title : Multiple integrals
  Speaker :  Sandeep Varma
  Topics : Definition of multiple integration. Basic examples. Fubini's theorem. Change of variable formula. (3 lectures).
• Course Title : Inverse function theorem
  Speaker :   Arvind Nair
  Topics : Contraction mapping principle. Inverse function theorem. Implicit function theorem. (2 lectures).

 Professor MS Raghunathan will also be giving two talks in the workshop, giving an overview of the subject.

Participants : Participants would mostly be under-graduate college teachers. Preferences will be given to teachers from the region. We are expecting around  50 college teachers to participate.