Differential Calculus in Several Variables

Start Date
01/07/2018

End Date
07/09/2018

Enrollment End Date
07/09/2018

No. of
Enrollments
683 students

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Created by

S Dutta
IIT Madras
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Course Language
English
Course Type
Scheduled
Video transcripts
Course Category
Mathematics
Learning Path
Undergraduate
Course Length
0 Hours
Weekly time commitments
0 Hours
Course Completion
Exam Date
To be announced
Credits
0

21

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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

S Dutta


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

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