Start Date

01/07/2018

End Date

07/09/2018

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483 students

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**Created by**

IIT Madras

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Weekly Reading list

**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**

Academic institutes running undergraduate Programs in Science and Mathematics.

**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.

To access the content, please enroll in the course.

**Faculty**

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

**FAQs**

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