Introduction to Methods of Applied Mathematics

By Prof. Mani Mehra, Prof. Vivek K. Aggarwal   |   IIT Delhi
Learners enrolled: 598
This course is aimed at final year undergraduate and graduate students in engineering, physics and applied mathematics. This will cover the very important and essential topics used by almost all branches of Science and engineering.

INTENTED AUDIENCE  : Any Interested Learners

PREREQUISITES : Some basic knowledge of Calculus, Differential Equations, Topics related to Mathematics – I, II will be an advantage.
Course Status : Completed
Course Type : Elective
Duration : 12 weeks
Category :
  • Mathematics
Credit Points : 3
Level : Undergraduate/Postgraduate
Start Date : 25 Jul 2022
End Date : 14 Oct 2022
Enrollment Ends : 08 Aug 2022
Exam Date : 29 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 :   Introduction to first order linear and non-linear ordinary differential equations (ODE), Riccati equation
Week 2 : Solving second order ODE
Week 3 : Introductions to Green’s functions for second order linear ODE
Week 4 : Introduction to Adjoint operators and their Green’s functions
Week 5 : Laplace Transforms and its properties
Week 6 : Application of Laplace Transforms to solve ODE
Week 7 : Introduction to Fourier Series
Week 8 : Fourier integrals and Fourier Transform and properties
Week 9 : Riesz bases, frames and orthonormal bases and shortcoming of Fourier Series
Week 10: Shortcomings of Fourier transforms,  Gabor transform, Window Fourier Transform, Multiresolution Analysis
Week 11: Daubechies wavelet, wavelet series and wavelet transform and different properties of wavelets
Week 12: Revision and Problem-solving sessions

Books and references

  1. Introduction to Applied Mathematics by Gilbert strang wellesly cambridge Press 
  2. Advanced topics in Applied Mathematics by Sudhakar Nair, Cambridge Press, 
  3. Wavelets theory and its applications by Mani Mehra Springer

Instructor bio

Prof. Mani Mehra

IIT Delhi
Dr. Mani Mehra is presently working as an Associate Professor in the department of Mathematics, IIT Delhi. She earned her PhD from IIT Kanpur in 2005.

Prof. Vivek K. Aggarwal

Dr. Vivek Kumar Aggarwal is presently working as an Assistant Professor dept. of Applied Mathematics, DTU Delhi. He earned his PhD in Mathematics from IIT Kanpur in 2005.

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: 29 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 Madras. 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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