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Partial Differential Equations (PDE) for Engineers

Partial Differential Equations (PDE) for Engineers. Instructor: Prof. Sirshendu De, Department of Chemical Engineering, IIT Kharagpur. 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. (from nptel.ac.in)

Introduction


Lecture 01 - Introduction to Partial Differential Equations
Lecture 02 - Classification of Partial Differential Equations
Lecture 03 - Principle of Linear Superposition
Lecture 04 - Standard Eigenvalue Problem and Special ODEs
Lecture 05 - Adjoint Operator
Lecture 06 - Generalized Sturm-Liouville Problem
Lecture 07 - Properties of Adjoint Operator
Lecture 08 - Separation of Variables: Rectangular Coordinate Systems
Lecture 09 - Solution of 3 Dimensional Parabolic Problem
Lecture 10 - Solution of 4 Dimensional Parabolic Problem
Lecture 11 - Solution of 4 Dimensional Parabolic Problem (cont.)
Lecture 12 - Solution of Elliptic Partial Differential Equation
Lecture 13 - Solution of Hyperbolic Partial Differential Equation
Lecture 14 - Orthogonality of Bessel Function and 2 Dimensional Cylindrical Coordinate System
Lecture 15 - Cylindrical Coordinate System - 3 Dimensional Problem
Lecture 16 - Spherical Polar Coordinate System
Lecture 17 - Spherical Polar Coordinate System (cont.)
Lecture 18 - Examples of Generalized 3 Dimensional Problem
Lecture 19 - Examples of Application Oriented Problems
Lecture 20 - Examples of Application Oriented Problems (cont.)

References
Partial Differential Equations (PDE) for Engineers
Instructor: Prof. Sirshendu De, Department of Chemical Engineering, IIT Kharagpur. Modeling is essential and imperative for understanding dynamics of a large scale process.