Partial Differential Equations (PDE) for Engineers: Solution by Separation of Variables

By Prof. Sirshendu De   |   IIT Kharagpur
Learners enrolled: 1058
Modeling is essential and imperative for understanding dynamics of a large scale process. One can undertake a large number of virtual experiments based on the model equations of a process to optimize the operating conditions and/or design the system efficiently. In most of the practical processes, model equations involve more than one parameters leading to partial differential equations (PDE). Various solutions techniques are adopted by the process engineers to solve the partial differential equations. Separation of variables is one of the most robust techniques used for analytical solution of PDEs. This technique provides first hand information of process dynamics rendering it amenable for optimization of system performance. This course aims to develop the solutions techniques and hence the skills of the students to solve PDEs for any engineering applications.

INTENDED AUDIENCE :
• Elective Course
• UG/PG Course
• BE/ME/MS/BSc/MSc/PhD
PRE-REQUISITES : Basic knowledge of Mathematics
INDUSTRIES SUPPORT
• CSIR Institute & Laboratories.
• All process industries and R & D organizations.
Summary
 Course Status : Completed Course Type : Elective Duration : 4 weeks Start Date : 18 Jan 2021 End Date : 12 Feb 2021 Exam Date : 21 Mar 2021 IST Enrollment Ends : 01 Feb 2021 Category : Mathematics Credit Points : 1 Level : Undergraduate/Postgraduate

Course layout

Week 1 : Introduction, Definition & Type of PDE; Classification of various boundary condition & PDEs; Application of principle of linear superposition for PDE; Introduction of separations variables methods for solution of PDE.
Week 2 : Solution of parabolic PDE using separations variables methods ; Solution of higher dimensional PDEs.
Week 3 : Solution of Elliptic & Hyperbolic PDE using separations variables methods.
Week 4 : PDE in cylindrical and Spherical coordinate.

Books and references

• NPTEL
• S. Pushpavanam, Mathematical methods in chemical engineering

Prof. Sirshendu De

IIT Kharagpur
Dr. Sirshendu De is an Institute Chair Professor in the Department of Chemical Engineering at the Indian Institute of Technology Kharagpur. His research interests include membrane separations, adsorption, modelling of transport processes, flow through micro-channels, etc. He has over 300 international journal publications/peer reviewed articles, over 100 conference presentations (national and international). He is also the holder of 15 patents (national and international), has authored 7 books and 4 of his developed technologies have been transferred to the industry. He has received numerous awards and fellowships, including the prestigious Shanti Swarup Bhatnagar Prize in Engineering Sciences by the Council of Scientific and Industrial Research (CSIR), Govt. of India in 2011. He is also a Fellow of prestigious scientific and engineering academies like Indian National Academy of Engineering (INAE) and The National Academy of Sciences, India (NASI). He is a former INAE Chair Professor (2015-2017) and former Head of the Department of Chemical Engineering, IIT Kharagpur (2015-2017). Currently, he is a recipient of the Abdul Kalam Technology Innovation National Fellowship, awarded by INAE and SERB, DST, for the period 2018-2021.

For more details, please visit http://www.iitkgp.ac.in/department/CH/faculty/ch-sde

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: 21 March 2021 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 3 assignments out of the total 4 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