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# PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES

Duration: 9:45:00
Lectures: 20
Level: Beginner 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.

1
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 01 : Introduction to PDE
30:32
2
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 02 : Classification of PDE
29:50
3
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 03 : Principle of Linear Superposition
27:03
4
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 04 : Standard Eigen Value Problem and Special ODEs
30:31
5
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 05 : Adjoint Operator
28:
6
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 07 : Properties of Adjoint Operator
34:06
7
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 06 : Generalized Sturm – Louiville Problem
30:16
8
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 08 : Separation of Variables: Rectangular Coordinate Systems
28:25
9
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 09 : Solution of 3 Dimensional Parabolic Problem
32:41
10
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 10 :Solution of 4 Dimensional Parabolic problem
28:12
11
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 11 : Solution of 4 Dimensional Parabolic Problem (Contd.)
28:33
12
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 12 : Solution of Elliptical PDE
31:31
13
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 13 : Solution of Hyperbolic PDE
28:54
14
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 14 : Orthogonality of Bessel Function and 2 Dimensional Cylindrical Coordinate System
28:00
15
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 15 : Cylindrical Co-ordinate System – 3 Dimensional Problem
32:49
16
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 16 : Spherical Polar Coordinate System
27:56
17
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 17 : Spherical Polar Coordinate System (Contd.)
27:52
18
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 18 : Example of Generalized 3 Dimensional Problem
31:37
19
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 19 : Example of Application Oriented Problems
29:27
20
PARTIAL DIFFERENTIAL EQUATIONS (PDE) FOR ENGINEERS: SOLUTION BY SEPARATION OF VARIABLES -Lecture 20 : Examples of Application Oriented Problems (Contd.)
31:43