Partial Differential Equations (PDE) For Engineers: Solution By Separation Of Variables

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 MathematicsINDUSTRIES SUPPORT :

• CSIR Institute & Laboratories.
• All process industries and R & D organizations.

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.