Advanced Engineering Mathematics

By Prof. P. N. Agarwal   |   IIT Roorkee
Learners enrolled: 1805
This course is a basic course offered to UG/PG students of Engineering/Science background. It contains Analytic Functions, applications to the problems of potential flow, Harmonic functions, Harmonic conjugates, Milne’s method, Complex integration, sequences and series, uniform convergence, power series, Hadamard’s formula for the radius of convergence, Taylor and Laurent series, zeros and poles of a function, meromorphic function, the residue at a singularity, Residue theorem, the argument principle and Rouche’s theorem, contour integration and its applications to evaluation of a real integral, integration through a branch cut, conformal mapping, application to potential theory, review of unilateral and bilateral Z-transforms and their properties, application of calculus of residues for the inversion formula of Z- transforms and Laplace transforms, review of Fourier integrals and Fourier transforms, Finite Fourier transforms, discrete Fourier transforms and applications, basic concepts of probability, Bayes theorem, probability networks, discrete and continuous probability distribution, joint distribution, correlation coefficient, applications to problems of reliability, queueing theory, service time for a customer in a facility and life testing, testing of hypotheses. This course has tremendous applications in diverse fields of Engineering and Sciences such as Signal processing, Potential theory, Bending of beams etc.

INTENDED AUDIENCE  : UG and PG students of technical institutions/ universities/colleges.
Course Status : Completed
Course Type : Core
Duration : 12 weeks
Category :
  • Mathematics
Credit Points : 3
Level : Undergraduate
Start Date : 25 Jul 2022
End Date : 14 Oct 2022
Enrollment Ends : 08 Aug 2022
Exam Date : 30 Oct 2022 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:  Analytic Functions, Cauchy-Riemann Equations, Harmonic Functions, Harmonic Conjugates and Milne’s Method, Applications to the problems of potential flow-I, Applications to the problems of potential flow-II
Week 2 : Complex integration, Cauchy’s theorem-I, Cauchy’s theorem-II , Cauchy’s Integral Formula for the Derivatives of an Analytic Function , Morera’s theorem, Liouville’s theorem and Fundamental Theorem of Algebra
Week 3 :  Winding Number and Maximum Modulus Principle, Sequences and Series, Uniform Convergence of Series, Power Series, Taylor series
Week 4:Laurent Series,Zeros and Singularities of an Analytic Function,Residue at a Singularity,Residue Theorem,Meromorphic Functions
Week 5 :  Evaluation of real integrals using residues-I, Evaluation of real integrals using residues-II , Evaluation of real integrals using residues-III, Evaluation of real integrals using residues-IV, Evaluation of real integrals using residues-V
Week 6 :  Bilinear Transformations, Cross ratio, Conformal Mapping-I, Conformal Mapping-II, Conformal mappings from half plane to disk and half plane to half plane-I
Week 7:  Conformal mappings from disk to disk and angular region to disk, Application of Conformal mapping to potential theory, Review of Z-transforms-I, Review of Z-transforms-II, Review of Z-transforms-III
Week 8:  Review of bilateral Z-transforms, Finite Fourier transforms, Fourier integrals and Fourier transforms, Fourier Series, Discrete Fourier transforms-I
Week 9: Discrete Fourier transforms-II, Basic concepts of probability, Conditional probability, Bayes theorem and Probability networks, Discrete probability distribution
Week 10:  Binomial distribution, Negative binomial distribution and Poisson distribution, Continuous probability distribution, Poisson Process, Exponential distribution
Week 11:  Normal distribution , Joint distribution-I, Joint probability distribution-III, Joint probability distribution-III, Correlation and regression-I
Week 12:  Correlation and regression-II, Testing of hypotheses-I, Testing of hypotheses-II, Testing of hypotheses-III, Application to Queueing Theory and Reliablility Theory

Books and references

Kreyszig, E., “Advanced Engineering Mathematics”, Wiley, New York.2. Jain, R.K. and Iyenger, S.R.K., Advanced Engineering Mathematics, 2nd Edition, Narosa Publishing House.3. Churchill, J. W. and Brown, R. V., “Complex Analysis”, McGraw Hill.4. Ahlfors, L. V., "Complex Analysis", McGraw Hill.5. Conway, J. B., "Functions of One Complex Variable", Narosa Publishing House.6. Debnath, L., Bhatta, D., “Integral Transforms and Their Tpplications”, Chapman & Hall/CRC (2nd edition)7. Miller, I. and Miller, M: “John E. Freund’s Mathematical Statistics with Applications”, 7th Edition, Prentice Hall.8. Mayer, P. L., “Introductory Probability and Statistical Applications”, Oxford & IBH Publishing Co. Pvt. Ltd. 

Instructor bio

Prof. P. N. Agarwal

IIT Roorkee
Dr. P. N. Agarwal is a Professor in the Department of Mathematics, IIT Roorkee. His area of research includes approximation Theory and Complex Analysis. He delivered 13 video lectures on Engineering Mathematics in NPTEL Phase I and recently completed Pedagogy project on Engineering Mathematics jointly with Dr. Uaday Singh in the same Department. Further he has completed online certification course “Mathematical methods and its applications” jointly with Dr. S.K. Gupta of the same department. He taught the course on “Integral equations and calculus of variations” several times to MSc (Industrial Mathematics and Informatics) students. He has supervised nine Ph.D. theses and has published more than 187 research papers in reputed international journals of the world. Currently, he is supervising eight research students.

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 October 2022 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 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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