Multivariable calculus

By Prof. S. K. Gupta, Prof. Sanjeev Kumar   |   IIT Roorkee
Learners enrolled: 798
About the course:
This course is a basic course offered to UG and PG students of Engineering/Science background. It contains various topics related to the calculus of the functions of two or more variables. In particular, this course includes topics like differentiation and integration of the functions of two or more variables together with their various applications. This course also includes the calculus of vector functions with different applications. 
INTENDED AUDIENCE : UG students technical Universities/Colleges,It is a core course for UG. 

Course Status : Completed
Course Type : Core
Duration : 8 weeks
Category :
  • Mathematics
Credit Points : 2
Level : Undergraduate
Start Date : 23 Jan 2023
End Date : 17 Mar 2023
Enrollment Ends : 06 Feb 2023
Exam Registration Ends : 20 Feb 2023
Exam Date : 26 Mar 2023 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: Limits, continuity and partial derivatives of multivariable functions
Week 2: Differentiability and chain rule
Week 3: Change of variables, Euler’s theorem, tangent planes, normal lines and extreme values
Week 4: Taylor’s theorem, error approximation, polar curves and multiple integrals
Week 5: Change of order and change of variables in multiple integral 
Week 6: Beta and gamma functions
Week 7: Normal vector and potential field 
Week 8:
 vector identities and line integral

Books and references

1. E. Kreyszig, Advanced Engineering Mathematics, 9th edition, John Wiley and Sons, Inc., U.K. (2011) 
2. R.K. Jain and S.R.K. Iyenger, Advanced Engineering Mathematics, 2nd Edition, Narosa Publishing House (2005) 
3. M.D. Weir, J. Hass, F.R. Giordano, Thomas’ Calculus, 11th Edition, Pearson Education (2008)

Instructor bio

Prof. S. K. Gupta

Dr. S. K. Gupta is an Associate Professor in the Department of Mathematics, IIT Roorkee. His area of expertise includes nonlinear, non-convex and Fuzzy optimization. He has guided three PhD thesis and have published more than 40 papers in various international journals of repute.

Prof. Sanjeev Kumar

IIT Roorkee
Dr. Sanjeev Kumar is working as an associate professor with Department of Mathematics, IIT Roorkee. Earlier, he worked as a postdoctoral fellow with Department of Mathematics and Computer Science, University of Udine, Italy and assistant professor with IIT Roorkee. He is actively involved in teaching and research in the area of computational algorithms, inverse problems and image processing. He has published more than 55 papers in various international journals conferences of repute. He has completed a couple of sponsored research projects and written several chapters in reputed books published with Springer and CRC press.

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: 
26 March 2023 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 Roorkee.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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