Advanced Engineering Mathematics

By Prof. Hari Shankar Mahato   |   IIT Kharagpur
Learners enrolled: 567
This course will provide an essential introduction to Engineering mathematics which is required for allUG (BTech and BSc) level courses. I will try to keep the course self-explanatory by providing examples and explain the theories as well wherever necessary. I believe on NPTEL this course hasn’t been offered specially for engineering students yet and, for the students looking to attend online courses on engineering mathematics this course will give them a nice opportunity to do so.

INTENDED AUDIENCE: BTech. 1st year of all branches, BSc. 1st year students in Mathematics

PREREQUISITES: Differential calculus of one variables, Integral calculus
Course Status : Upcoming
Course Type : Core
Duration : 12 weeks
Start Date : 23 Jan 2023
End Date : 14 Apr 2023
Exam Date : 30 Apr 2023 IST
Enrollment Ends : 30 Jan 2023
Category :
  • Mathematics
Credit Points : 3
Level : Undergraduate

Page Visits

Course layout

Week 1: Differentiability, Lagrange’s mean value theorem, Cauchy’s mean value theorem, Taylor’s and Maclaurin’s theorem. Functions of several variables: Limit, continuity, partial derivatives and their geometrical interpretation, total differential and differentiability, Derivatives of composite and implicit functions, implicit function theorem, derivatives of higher order and their commutativity, Euler’s theorem on homogeneous functions, Taylor’s expansion of functions, maxima and minima, constrained maxima/minima problems using Lagrange’s method of multipliers
Week 2: Convergence of improper integral, test of convergence, Gamma and Beta functions, their properties, differentiation under the integral sign, Leibnitz rule of differentiation Double and triple integral, change of order of integration, change of variables, Jacobian transformation, Fubini theorem, surface, area and volume integrals, integral dependent on parameters applications, Surface and Volume of revolution. Calculation of center of gravity and center of mass.
Week 3: Differential Equations – first order, solution of first order ODEs, Integrating factor, exact forms, second order ODEs, auxiliary solutions
Week 4: Numerical analysis: Iterative method for solution of system of linear equations, Jacobi and Gauss-Seidal method, solution of transcendental equations: Bisection, Fixed point iteration, Newton-Raphson method.
Week 5: Finite differences, interpolation, error in interpolation polynomials, Newton’s forward and backward interpolation formulae, Lagrange’s interpolation, Numerical integration: Trapezoidal and Simpson’s 1/3rd and 3/8th rule.
Week 6: Vector spaces, basis and dimension, Linear transformation, linear dependence and independence of vectors, Gauss elimination method for system of linear equations for homogeneous and nonhomogeneous equations
Week 7: Rank of a matrix, its properties, solution of system of equations using rank concepts, Row and Column reduced matrices, Echelon Matrix, properties,
Week 8: Hermitian, Skew Hermitian and Unitary matrices, eigenvalues, eigenvectors, its properties, Similarity of matrices, Diagonalization of matrices,
Week 9: Scalar and vector fields, level surface, limit, continuity and differentiability of vector functions, Curve and arc length, unit vectors, directional derivatives,
Week 10: Divergence, Gradient and Curl, Some application to Mechanics, tangent, normal, binormal, Serret-Frenet Formulae, Application to mechanics
Week 11: Line integral, parametric representations, surface integral, volume integral, Gauss divergence theorem, Stokes theorem, Green’s theorem.
Week 12: Limit, continuity, differentiability and analyticity of functions, Cauchy-Riemann equations, line integrals in complex plane Cauchy’s integral formula, derivatives of analytic functions, Cauchy’s integral theorem, Taylor’s series, Laurent series, zeros and singularities, residue theorem, evaluation of real integrals

Books and references

1. Advanced Engineering Mathematics by E. Kreyszig, Wiley Publication, 10th edition, 2010
2. Differential and Integral Calculus by N. Piskunov, Volume I & II, 1999.
3. Integral Calculus by S. Narayan & R. K. Mittal, S. Chand, 2005.

Instructor bio

Prof. Hari Shankar Mahato

IIT Kharagpur
Prof. Hari Shankar Mahato is currently working as an Assistant Professor in the Department of Mathematics at the Indian Institute of Technology Kharagpur. Before joining here, he worked as a postdoc at the University of Georgia, USA. He did his PhD from the University of Bremen, Germany and then he worked as a Postdoc at the University of Erlangen-Nuremberg and afterwards at the Technical University of Dortmund, both located in Germany. His research expertise are Partial Differential Equations, Applied Analysis, Variational Methods, Homogenization Theory and very recently he has started working on Mathematical Biology. He can be able to teach (both online and offline) any undergraduate courses from pre to advanced calculus, mechanics, ordinary differential equations, up to advanced graduate courses like linear and nonlinear PDEs, functional analysis, topology, mathematical modeling, fluid mechanics and homogenization theory

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: 30 April 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 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

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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