# Transform Calculus and Its Applications In Differential Equations

By Prof. Adrijit Goswami   |   IIT Kharagpur
Learners enrolled: 1110
For undergraduate students in the discipline of Mathematics, the course on Transform Calculus has become an integral part. This course is designed to train students with the basic Integral Transform techniques.Application of these transforms techniques in solving ordinary differential equations and partial differential equations will be discussed. We will also introduce some higher level concepts that will prepare them for future research and development projects. The course outline is given for each week. We will introduce each topic and give an overview of the topic and underlying theory. This will be followed by some solved numerical examples on each topic for their better understanding. Weekly assignments will be provided and graded

INTENDED AUDIENCE : MATHEMATICS(Any student with a course in Mathematics in their curriculum)
PREREQUISITES : NONE
INDUSTRY SUPPORT : NONE
Summary
 Course Status : Completed Course Type : Core Duration : 12 weeks Category : Mathematics Credit Points : 3 Level : Postgraduate Start Date : 24 Jan 2022 End Date : 15 Apr 2022 Enrollment Ends : 07 Feb 2022 Exam Date : 24 Apr 2022 IST

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

### Course layout

Week 1  :  Introduction to Laplace transform: Definition and properties
Week 2  :  Laplace Transform of derivatives and integrals
Week 3  :  Laplace Transform of some special functions
Week 4  :  Inverse Laplace Transform
Week 5  :  Application of Laplace Transform to Ordinary Differential Equationsand Integral Equations
Week 6  :  Fourier Series
Week 7  :  Introduction to Fourier Transforms: Definition and properties
Week 8  :  Fourier Sine and Cosine transforms of different functions
Week 9  :  Parsevalâ€™s Identity for Fourier Sine and Cosine Transforms
Week 10  :  Application of Fourier Transform to Ordinary Differential Equations and Integral Equations
Week 11  :  Application of Fourier Transform to Partial Differential Equations
Week 12  :  Finite Fourier transform and its application to Boundary ValuedProblems.

NILL

### Instructor bio

IIT Kharagpur
Adrijit Goswami joined the Institute as a Faculty member in 1992. He received his M.Sc. and Ph.D. degree from Jadavpur University, India in 1985 and 1991 respectively. His research interest and publications have been on Operations Research and Theoretical Computer Science. His initial interest has been in developing mathematical models in Inventory Control under deterministic, probabilistic and fuzzy environment. For the past several years he has been involved in various aspects of database systems, data mining and cryptography and computer network as a researcher. Professor Goswami has guided 14 research scholars in their Ph.D. programs and at present guiding 7 students. He is author and co-author of more than 90 research publications in major International journals in the area of Operations Research and Theoretical Computer Science. He is also member of the editorial board of several International/National research journals. His current interests and publications have been on Production Planning and Control, Supply Chain management, Data Mining, Cryptography, Hierarchial access Control and Network security.

### 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: 24 April 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.

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

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