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Last updated:

September 23, 2023

Duration:

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FREE

This course includes:

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Description

Partial Differential Equations (PDE) for Engineers. Instructor: Prof. Sirshendu De, Department of Chemical Engineering, IIT Kharagpur. Modeling is essential and imperative for understanding the 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)

Course Curriculum

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

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