Calculus of Several Real Variables

By Prof. Joydeep Dutta | IIT Kanpur

Learners enrolled: 3579

This course introduces the very important subject called the calculus of several real variables, which has important applications in science and engineering. The modern world would have been impossible without it. We introduce and discuss the subject in a non-traditional way taking the vector approach in most places. We start with the basics of Vectors, study continuity and partial derivatives, study multiple integrals and their applications and end with the stokes Theorem and Gauss divergence theorem.

INTENDED AUDIENCE: Any Interested Learners

PREREQUISITES: Calculus of One Real Variable

Summary

Course Status :	Completed
Course Type :	Core
Duration :	8 weeks
Category :	Mathematics
Credit Points :	2
Level :	Undergraduate
Start Date :	26 Aug 2019
End Date :	18 Oct 2019
Exam Date :	17 Nov 2019 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Vectors and Matrices

Week 2: Functions of several variables and partial derivatives

Week 3: IFT, Taylor’s Theorem, Maxima and Minima

Week 4: Lagrange Multiplier Rule

Week 5: Multiple Integrals

Week 6: Line Integrals

Week 7: Surface Integrals

Week 8: Green’s Theorem Strokes Theorem and Gauss Divergence Theorem

Books and references

Basic Multivariable Calculus by J. E. Marsden, A. J. Tromba, A. Weinstein

Instructor bio

Joydeep Dutta, is a Professor in the Department of Economic Sciences at IIT Kanpur. His research interest lies in convex analysis and optimization. He had given several MOOC courses including a course of “Calculus of one real variable”. Calculus continues to fascinate him and intrigue him.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 17 November 2019 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100
Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75.

If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Kanpur. It will be e-verifiable at nptel.ac.in/noc.
Only the e-certificate will be made available. Hard copies are being discontinued from July 2019 semester and will not be dispatched

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