# Differential Calculus in Several Variables

Start Date
01/07/2018

End Date
07/09/2018

Enrollment End Date
07/09/2018

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682 students

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S Dutta
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Course Language
English
Course Type
Scheduled
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Course Category
Mathematics
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Course Length
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0 Hours
Course Completion
Exam Date
To be announced
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Overview

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.

INTENDED AUDIENCE

First/second year undergraduates with a course in one variable calculus.

PRE-REQUISITES

A course in one variable calculus

INDUSTRIES THAT WILL RECOGNIZE THIS COURSE

COURSE LAYOUT

Week 1: Functions of several variables and examples; continuity; concept of distances in higher dimension; examples; how to define differentiable functions.

Week 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.

Week 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.

Week 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.

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Faculty

### S Dutta

Prof. S. Dutta  is currently a Professor at the Department of Mathematics and Statistics, IIT Kanpur.

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