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Course Co-ordinated by IIT Kanpur
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Prof. Sudipta Dutta
IIT Kanpur

 

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This is part of a standard course contents in Several Variable Calculus. The idea of the course is to provide students with different backgrounds a common platform to take up further topics in Mathematics, Physics and Engineering. 

Week. No.

Topics

1

Functions of several variables and examples; continuity; concept of distances in higher dimension; examples; how to define differentiable functions.

2

Directional derivatives as direct generalization from one variable; drawbacks; definition of differentiable functions of several variable; examples; matrix of a linear transformation; Jacobian matrix; recovering directional derivative from derivative; chain rule.

3

Comparison with one variable calculus: version of MVT, higher derivatives and Taylor’s formula; Sufficient condition for equality of mixed derivatives; extremas for real valued function and special case for  functions with two variables.

4

Statement of Implicit Function Theorem and Inverse Function Theorem.; deriving Inverse Function Theorem form Implicit Function Theorem; Illustration of Implicit Function Theorem for function of two variables; examples from solutions of ordinary differential equations; proof of Implicit Function Theorem; Lagrange’s Multipliers.

 

 

 

 

 

 

A course in one variable calculus


  1. Principles of Mathematical Analysis, W. Rudin
  2. Calculus ? T. Apostol
  3. Mathematical Analysis, T. Apostol


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