Partial Differential Equations And System of Ordinary Differential Equations

Teacher

Balaji Padhy

Category

Core Courses

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Partial Differential Equations And System of Ordinary Differential Equations

Code(Credit) : CUTM1517(3-2-1)

Course Objectives

• Introduce students to partial differential equations.
• Introduce students to how to solve linear and non-linear Partial Differential Equations with different methods.
• To practice heat and wave equations in 2D and 3D..

Learning Outcomes

Upon successful completion of this course, students will be able to:
• solve linear partial differential equations of both first and second order
• apply partial derivative equation techniques to predict the behavior of certain phenomena.
• apply specific methodologies, techniques and resources to conduct research and produce innovative results in the area of specialization.
• extract information from partial derivative models in order to interpret reality.

Course Syllabus

Module-I(4 h + 4 h + 2 h)

Linear Homogeneous and Non-homogeneous system of Differential Equations with constant coefficients.

Practice-1

To find the general solution of linear homogeneous system of differential equations by using Matlab.

Practice-2

To find the general solution of linear non-homogeneous system of differential equations by using Matlab.

Project-1
To make a report of an application of linear system of differential equation

Module-II(4 h+ 4 h + 2 h )

Simultaneous linear first order differential equations in three variables, Pfaffian differential equations, Methods of Solutions of Pfaffian differential equations in three variables.

Practice-3
To find the solution of simultaneous linear first order differential equations by using Matlab.

Practice-4
To find the Solutions of system of differential equations in three Variables by using Matlab.

Project-2
Tomake a report on simultaneous Linear Differential Equations.

Module-III(4 h + 4 h)

Introduction to first order partial differential equations, formation of first order partial differential equations, linear Partial differential equations.

Practice-5
To find the solution of first order partial differential equations by using Matlab.

Practice-6
To find the solution of first order Quasi-linear partial differential equations by using Matlab.

Module-IV(5 h + 4 h +2 h)

Non-linear partial differential equations, Special types of first-order equations, Charpit Equation, solutions of partial differential equations of first order satisfying given initial conditions.
Practice-7

To find the solution of 1-d Wave equation by using Matlab.
Practice-8

To find the solution of 1-d Heat equation by using Matlab.

Project-3

Summary of Special types of partial Differential Equations.

Module-V(4 h + 2 h + 2 h)

First order homogeneous PDE with constant coefficients, higher order homogeneous PDE with constant coefficients.

Practice-9
To find the solution of first order homogeneous partial differential equations by using Matlab.

Project-4

Briefly describe Homogeneous Partial differential Equations with suitable examples.

Module-VI( 6 h + 2 h+ 2 h+)

Higher order linear Non-homogeneous PDE with constant coefficients, general Solution of PDE by using inverse operators.

Practice-10
To find the solution of 2-d Wave equation by using Matlab.

Project-5

Make a report on Non-homogeneous Partial differential Equations with constant coefficients.

Module-VII( 3 h + 4 h+ 2 h)

Solution of homogeneous and non-homogeneous PDE with variable coefficients.

Practice-11
To find the solution of 2-d heat equation by using Matlab.

Practice-12
To find the solution of 2-d Laplace equation by using Matlab.

Project-6

summary of Non-homogeneous Partial differential Equations with variable coefficients.

Text Book:

1. J. Sinha Roy and S. Padhy, A course on ordinary and partial differential equation, Kalyani Publisers, New Delhi, Ludhiana, 2012.

Reference Books:
1. Loknath Sahoo, Calculus and ordinary differential equations, Kalyani Publication, Reprint-2017
2. TynMyint-U and Lokenath Debnath, Linear Partial differential Equations for Scientists and Engineers, 4th Edition, Springer, Indian reprint, 2006
3. S.L. Ross, Differential Equations, 3rd Ed., John Wiley and Sons, India, 2004

4.Paul DuChateau, David W. Zachmann - Schaum’s Outline of Theory and Problems of Partial Differential Equations-McGraw-Hill.

Session Plan

Session 1

Session 2

Session 4 & 5

Practice-1

To find the general solution of linear homogeneous system of differential equations by using Matlab

https://in.mathworks.com/matlabcentral/answers/301863-how-to-solve-a-system-of-first-order-differential-equation-in-matlab

>

Session 6

Non-Homogeneous Linear Systems with Constant Coefficients
https://player.slideplayer.com/26/8588018/#
https://www.youtube.com/watch?v=YhVb9qFspMQ

Session 7 & 8

Practice-2

To find the general solution of linear non-homogeneous system of differential equations by using Matlab
https://in.mathworks.com/videos/solving-odes-in-matlab-8-systems-of-equations-117652.html

Session 9 & 10

Project-1

To make a report of an application of linear system of differential equation

https://www.slideshare.net/shahzad_ali27/applications-of-differential-equations

Session 11

Introduction to Simultaneous Linear First Order Equations in Three Variables
https://www.slideshare.net/shubhijain1042/simultaneous-differential-equations
https://www.youtube.com/watch?v=3BsT85-lpS4

Session 13 & 14

Practice-3

To find the solution of simultaneous linear first order differential equations by using Matlab.
https://www.youtube.com/watch?v=G59vnBwDwqs

Session 15

Session 16

Methods of Solutions of Pfaffian Differential Equations in Three Variables.
pfaffian PDE
https://www.youtube.com/watch?v=FZZS91nfRgc

Session 17 & 18

Practice-4

To find the Solutions of system of differential equations in three Variables by using Matlab.
https://www.youtube.com/watch?v=B9FAjkeVTeI

Session 19 & 20

Project-2

To make a report on simultaneous Linear Differential Equations.

Session 21

Session 24 & 25

Practice-5

To find the solution of first order partial differential equations by using Matlab
https://www.youtube.com/watch?v=qgh7miW8viE

Session 27 & 28

Practice-6

To find the solution of first order Quasi-linear partial differential equations by using Matlab

https://in.mathworks.com/help/matlab/math/partial-differential-equations.html

Session 29 & 30

Project-3

Summary of Special types of partial Differential Equations.

Assignment-2

Session 33 & 34

Practice-7

To find the solution of 1-d Wave equation by using Matlab

https://in.mathworks.com/help/pde/ug/wave-equation.html

Session 36

Session 37 & 38

Session 40 & 41

Project-4

Briefly describe Homogeneous Partial differential Equations with suitable examples.

Assignment-3

Session 43 & 44

Practice-9

To find the solution of first order homogeneous partial differential equations by using Matlab
https://www.youtube.com/watch?v=6-2Wzs0sXd8

Session 46 & 47

Practice-10

To find the solution of 2-d Wave equation by using Matlab

https://www.slideshare.net/AmrMousa12/2-dimensional-wave-equation-analytical-and-numerical-solution

Session 48 & 49

Session 50 & 51

Project-5

Make a report for the Non-homogeneous Partial differential Equations.

Session 55 & 56

Practice-11

To find the solution of 2-d heat equation by using Matlab

https://www.youtube.com/watch?v=f4VXKPoHbTE

Session 59 & 60

Practice-12

To find the solution of 2-d Laplace equation by using Matlab

https://www.youtube.com/watch?v=PE7oiOq_xig

Session 61 & 62

Project-6:

summary of Non-homogeneous Partial differential Equations with variable coefficients.

Session 65

Case Studies

Case Studies

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    Assistant Professor ,School of Applied Sciences, Centurion University of Technology and Management, Paralakhemundi, Odisha, India. He has over 11 years of teaching experiences. He has published 5 research articles in National and International refereed journals . He is continue their P.hD in the field of Fuzzy Inventory Control Models.