Engineering Mathematics II

By Prof. Jitendra Kumar | IIT Kharagpur

Learners enrolled: 1750 | Exam registration: 552

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 complex analysis,numerical analysis, vector calculus and transform techniques with applications to various engineering problems. This course will cover the following main topics.Function of complex variables. Analytic functions. Line integrals in complex plane. Cauchy’s integral theorem, Derivatives of analytic functions. Power series, radius of convergence. Taylor’s and Laurent’s series, zeros and singularities, residue theorem.Iterative method for solution of system of linear equations. Finite differences, interpolation. Numerical integration. Solution of algebraic and transcendental equations.Vector and scalar fields. Limit, continuity, differentiability of vector functions. Directional derivative, gradient, curl, divergence. Line and surface integrals, Green, Gauss and Stokes theorem.Laplace transform and its properties. Laplace Transform of specialfunction. Convolution theorem. Evaluation of integrals by LaplaceTransform. Solution of initial and boundary value problems.Fourier series representation of a function. Fourier sine and cosinetransforms. Fourier Transform. Properties of Fourier Transform.Applications to boundary value problems.

INTENDED AUDIENCE : all branches of science and engineering

PREREQUISITES : Engineering Mathematics - I - https://nptel.ac.in/courses/111105121

Summary

Course Status :	Ongoing
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Undergraduate
Start Date :	19 Jan 2026
End Date :	10 Apr 2026
Enrollment Ends :	02 Feb 2026
Exam Registration Ends :	20 Feb 2026
Exam Date :	25 Apr 2026 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 : Vector and scalar fields. Limit, continuity, differentiability of vector functions. Directional derivative, gradient, curl, divergence

Week 2 : Line and surface integrals, Green, Gauss and Stokes theorem.
Week 3 : Function of complex variables and their properties including continuity and differentiability. Analytic functions and CR equations. Line
integrals in complex plane.

Week 4 : Cauchy’s integral theorem, Power series, radius of convergence. Taylor’s and Laurent’s series, zeros and singularities, residue theorem.

Week 5 : Iterative method for solution of system of linear equations. Finite differences, interpolation.

Week 6 : Numerical integration. Solution of algebraic and transcendental equations.

Week 7 : Laplace transform and its properties. Laplace Transform of special function.

Week 8 : Convolution theorem. Evaluation of integrals by Laplace Transform. Solution of initial and boundary value problems.

Week 9 : Fourier series & its convergence

Week 10 : Fourier integral representation

Week 11 : Fourier sine and cosine transforms. Fourier Transform. Properties of Fourier Transform.

Week 12 : Applications of Fourier series to boundary value problems.

Books and references

1 Kreyszig, E. (2010). Advanced Engineering Mathematics, 10th edition. John Wiley & Sons.

2 O’Neil, Peter V. (2011). Advanced Engineering Mathematics, 7th edition. Cengage learning.

3 Colley, S.J. (2012). Vector Calculus, 4 th edition. Pearson Education, Inc.

4 Zill, D.G., Shanahan P.D. (2013). Complex Analysis: A First Course with Applications, 3rd Edition. Jones & Bartlett Learning.

5 Dyke, P.P.G. (2001). An Introduction to Laplace Transforms and Fourier Series. Springer-Verlag London Ltd.

6 Hanna, J.R. and Rowland, J.H. (1990). Fourier Series, Transforms and Boundary Value Problems. Second Edition. Dover Publications, Inc. New York.

7 Pinkus, A. and Zafrany, S. (1997). Fourier Series and Integral Transforms. Cambridge University Press. United Kingdom.

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: : April 25, 2026 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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