PDE for Engineers: Separation of Variables Course | IIT Kharagpur NPTEL
Course Details
| Exam Registration | 93 |
|---|---|
| Course Status | Ongoing |
| Course Type | Elective |
| Language | English |
| Duration | 4 weeks |
| Categories | Mathematics |
| Credit Points | 1 |
| Level | Undergraduate/Postgraduate |
| Start Date | 19 Jan 2026 |
| End Date | 13 Feb 2026 |
| Enrollment Ends | 02 Feb 2026 |
| Exam Registration Ends | 16 Feb 2026 |
| Exam Date | 29 Mar 2026 IST |
| NCrF Level | 4.5 — 8.0 |
Master Engineering Modeling with Partial Differential Equations (PDEs)
In the world of engineering, from designing efficient chemical reactors to optimizing heat exchangers, the ability to model and predict system behavior is paramount. At the heart of these advanced models often lie Partial Differential Equations (PDEs). For engineers, moving from ordinary to partial differential equations is a significant leap, unlocking the ability to model systems where key parameters like temperature, concentration, or pressure vary in both space and time.
One of the most powerful and elegant analytical techniques for tackling these complex equations is the Method of Separation of Variables. This foundational method provides deep, first-hand insight into process dynamics, making it an indispensable tool for system optimization and design.
About the Course Instructor: Prof. Sirshendu De
This specialized course is taught by Prof. Sirshendu De, an Institute Chair Professor in the Department of Chemical Engineering at the prestigious Indian Institute of Technology (IIT) Kharagpur.
Prof. De is a distinguished scholar and practitioner with exceptional credentials:
- Research Expertise: Membrane separations, adsorption, transport process modeling, micro-channel flow.
- Prolific Contributor: Over 300 international journal publications and 100+ conference presentations.
- Innovator: Holder of 15 national and international patents; 4 technologies transferred to industry.
- Award-Winning: Recipient of the prestigious Shanti Swarup Bhatnagar Prize (2011) and the Abdul Kalam Technology Innovation National Fellowship.
- Author & Leader: Authored 7 books and former Head of the Department of Chemical Engineering at IIT Kharagpur.
- Fellow of the Indian National Academy of Engineering (INAE) and The National Academy of Sciences, India (NASI).
Learning PDE solution techniques from an instructor of this caliber ensures you are gaining knowledge grounded in both deep theoretical understanding and real-world industrial application.
Course Overview: What Will You Learn?
This is a 4-week, undergraduate/postgraduate level course designed to build a strong, practical foundation in solving PDEs using the separation of variables method.
Intended Audience: BE/ME/MS/BSc/MSc/PhD students and professionals in Chemical, Mechanical, Civil, and related engineering fields, as well as applied scientists.
Pre-requisites: A basic knowledge of calculus and ordinary differential equations is recommended.
Detailed Course Layout
| Week | Topics Covered |
|---|---|
| Week 1 | Introduction to PDEs, Definitions & Types; Classification of Boundary Conditions & PDEs; Principle of Linear Superposition; Introduction to the Separation of Variables Method. |
| Week 2 | Solution of Parabolic PDEs (e.g., Heat/Diffusion Equation) using Separation of Variables; Extension to Higher Dimensional Problems. |
| Week 3 | Solution of Elliptic PDEs (e.g., Laplace's Equation) and Hyperbolic PDEs (e.g., Wave Equation) using Separation of Variables. |
| Week 4 | Solving PDEs in Cylindrical and Spherical Coordinate Systems – essential for modeling real-world geometries like pipes and reactors. |
Why is This Course Important for Engineers?
- Bridge Theory & Practice: Move from abstract mathematics to solving tangible engineering problems like transient heat transfer, contaminant diffusion, and vibration analysis.
- Robust Analytical Skills: The separation of variables method provides exact solutions, offering unparalleled insight into how different parameters affect your system, which is crucial for sensitivity analysis and optimization.
- Foundation for Advanced Methods: A solid grasp of this analytical technique is the perfect springboard for understanding more complex numerical methods (like Finite Element Analysis) used when analytical solutions are not possible.
- Industry Relevance: The skills taught are directly applicable in R&D and core process industries (supported by organizations like CSIR labs), making you a more effective and versatile engineer.
Recommended Textbook
To complement the video lectures, the course references the NPTEL book "Mathematical Methods in Chemical Engineering" by S. Pushpavanam, providing a cohesive learning resource.
Who Should Enroll?
This course is ideal for:
- Engineering students (UG/PG) wanting to strengthen their applied mathematics skills.
- PhD researchers and R&D professionals needing to build or interpret process models.
- Engineers in process, chemical, mechanical, or civil fields involved in design and simulation.
- Any professional aiming to add powerful analytical modeling techniques to their toolkit.
By the end of this 4-week journey with Prof. Sirshendu De, you will not just learn a mathematical technique; you will acquire a fundamental skill set to model, analyze, and optimize complex engineering systems with confidence. Enroll to transform your approach to engineering problem-solving.
Enroll Now →