Calculus of Several Real Variables

By Prof. Joydeep Dutta   |   IIT Kanpur
Learners enrolled: 1803
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

Course Status : Completed
Course Type : Core
Duration : 8 weeks
Category :
  • Mathematics
Credit Points : 2
Level : Undergraduate
Start Date : 23 Aug 2021
End Date : 15 Oct 2021
Enrollment Ends : 30 Aug 2021
Exam Date : 24 Oct 2021 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

Prof. Joydeep Dutta

IIT Kanpur
Prof.Joydeep Dutta is currently a Professor of Economics at the Department of Humanities and Social Sciences, IIT Kanpur. He was previously a Professor at the Department of Mathematics and Statistics at IIT Kanpur. His reseach interest primarily lies in optimization though he loves mathematics as a whole.

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: 24 October 2021 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.


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 will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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