Engineering Mathematics - I

By Prof. Jitendra Kumar | IIT Kharagpur

Learners enrolled: 486 | Exam registration: 2

ABOUT THE COURSE:

This course is about the basic mathematics that is fundamental and essential component in all streams of undergraduate studies in sciences and engineering. The course consists of topics in differential calculus,integral calculus, linear algebra and differential equations with applications to various engineering problems. This course will cover the following main topics: Mean Value Theorems; Indeterminate Forms; Taylor's and Maclaurin's Theorems. Partial Derivatives; Differentiability; Taylor's Expansion of Functions of Several Variables. Maxima and Minima. Improper Integrals. Differentiation under Integral Sign (Leibnitz rule).Multiple Integrals and their Properties. Applications of Multiple Integrals. System of Linear Equations. Vector Spaces; Basis and Dimension of a Vector Space. Rank of a Matrix and its Properties. Linear Transformation. Eigenvalues and Eigen vectors. Diagonalization . First Order Differential Equations. Higher Order Differential Equations with Constant Coefficients. Cauchy-Euler Equations.

INTENDED AUDIENCE : All branches of science and engineering

Summary

Course Status :	Upcoming
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Undergraduate
Start Date :	21 Jul 2025
End Date :	10 Oct 2025
Enrollment Ends :	28 Jul 2025
Exam Registration Ends :	15 Aug 2025
Exam Date :	25 Oct 2025 IST
NCrF Level	4.5 — 8.0

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

Page Visits

Course layout

Week 1 : Differential Calculus - Functions of One Variable

Week 2 : Partial Derivatives

Week 3 : Total Differential and Differentiability

Week 4 : Taylor's Expansion of Functions. Maxima and Minima

Week 5 : Improper Integrals

Week 6 : Double Integrals

Week 7 : Multiple Integrals & their Applications

Week 8 : System of Linear Equations - Gauss Elimination. Vector Spaces

Week 9 : Linear Transformations

Week 10 : Eigenvalues and Eigenvectors, Diagonalization

Week 11 : First Order Differential Equations

Week 12 : Higher Order Differential Equations with Constant Coefficientss

Books and references

Piskunov, N., Differential and Integral Calculus, Vol 1 & 2, 2nd edition.Mir Publishers, 1974.
Kreyszig, E., Advanced Engineering Mathematics, 10th edition. John Wiley & Sons, 2010.
Thomas Jr, George B., Weir, Maurice D. and Hass, Joel R., Thomas’ Calculus, 12th edition. Pearson 2014.
O’Neil, Peter V., Advanced Engineering Mathematics, 7th edition. Cengage learning, 2011.
Strang, G., Linear Algebra and its Applications, Fourth Edition, 2009.
Thomas, G.B. and Finney, R.L., Calculus and Analytic Geometry, 9th Edition, Pearson, Reprint, 2002.

Instructor bio

Prof. Jitendra Kumar

IIT Kharagpur

Dr. Jitendra Kumar is currently serving as a Professor and Head of the Department of Mathematics at IIT Ropar, Punjab, India. Prior to joining IIT Ropar, he was associated with IIT Kharagpur, where he served as an Assistant Professor from 2009 to 2014, Associate Professor from 2014 to 2019, and Professor from 2020 to 2022. He obtained his M.Sc. in Industrial Mathematics from IIT Roorkee, followed by a second M.Sc. from the Technical University of Kaiserslautern, Germany. He was awarded a doctorate in 2006 by Otto-von-Guericke University Magdeburg, Germany. Following his Ph.D., he held a lectureship at the Institute for Analysis and Numerical Mathematics at the same university from 2006 to 2008.

Dr. Kumar is the recipient of several prestigious awards and fellowships, including the Alexander von Humboldt Fellowship, and DAAD and DFG scholarships. He has published more than 100 research articles in reputed international journals and has supervised 15 Ph.D. students. His research interests include numerical solutions of integro-differential equations, numerical analysis, and the modelling and simulation of problems in particulate systems.

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: October 25, 2025 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 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Please note that assignments encompass all types (including quizzes, programming tasks, and essay submissions) available in the specific week.

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 Kharagpur .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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