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• Introduce students to partial differential equations.
• Introduce students to how to solve linear and nonlinear Partial Differential Equations with different methods.
• To practice heat and wave equations in 2D and 3D..
COs  Course outcomes  Mapping Cos with POs (High3, Medium2, Low1) 
CO1  Solve linear partial differential equations of both first and second order

PO1(3), PO2(2) 
CO2  Apply partial derivative equation techniques to predict the behavior of certain phenomena, apply specific methodologies, techniques and resources to conduct research.  PO1(3), PO9(3) 
CO5  Extract information from partial derivative models in order to interpret reality.

PO5(3), PO9(2) 
ModuleI(4 h + 4 h + 2 h)
Linear Homogeneous and Nonhomogeneous system of Differential Equations with constant coefficients.
Practice1
To find the general solution of linear homogeneous system of differential equations by using Matlab.
Practice2
To find the general solution of linear nonhomogeneous system of differential equations by using Matlab.
Project1
To make a report of an application of linear system of differential equation
ModuleII(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.
Practice3
To find the solution of simultaneous linear first order differential equations by using Matlab.
Practice4
To find the Solutions of system of differential equations in three Variables by using Matlab.
Project2
Tomake a report on simultaneous Linear Differential Equations.
ModuleIII(4 h + 4 h)
Introduction to first order partial differential equations, formation of first order partial differential equations, linear Partial differential equations.
Practice5
To find the solution of first order partial differential equations by using Matlab.
Practice6
To find the solution of first order Quasilinear partial differential equations by using Matlab.
ModuleIV(5 h + 4 h +2 h)
Nonlinear partial differential equations, Special types of firstorder equations, Charpit Equation, solutions of partial differential equations of first order satisfying given initial conditions.
Practice7
To find the solution of 1d Wave equation by using Matlab.
Practice8
To find the solution of 1d Heat equation by using Matlab.
Project3
Summary of Special types of partial Differential Equations.
ModuleV(4 h + 2 h + 2 h)
First order homogeneous PDE with constant coefficients, higher order homogeneous PDE with constant coefficients.
Practice9
To find the solution of first order homogeneous partial differential equations by using Matlab.
Project4
Briefly describe Homogeneous Partial differential Equations with suitable examples.
ModuleVI( 6 h + 2 h+ 2 h+)
Higher order linear Nonhomogeneous PDE with constant coefficients, general Solution of PDE by using inverse operators.
Practice10
To find the solution of 2d Wave equation by using Matlab.
Project5
Make a report on Nonhomogeneous Partial differential Equations with constant coefficients.
ModuleVII( 3 h + 4 h+ 2 h)
Solution of homogeneous and nonhomogeneous PDE with variable coefficients.
Practice11
To find the solution of 2d heat equation by using Matlab.
Practice12
To find the solution of 2d Laplace equation by using Matlab.
Project6
summary of Nonhomogeneous 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, Reprint2017
2. TynMyintU 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 EquationsMcGrawHill.
introduction to the Systems of Linear Differential Equations
https://www.slideshare.net/JDagenais/systemsofdifferentialequations
https://www.youtube.com/watch?v=p_di4Zn4wz4
Systems of Linear Differential Equations with constant coefficients
https://www.slideshare.net/pratiksudra10/lineardifferentialequation
https://www.youtube.com/watch?v=FarysWaGM9w
Homogenrous linear Systems with constant coefficients
https://www.slideshare.net/ssinghhapur/lineardifferentialequationwithconstantcoefficient
https://www.youtube.com/watch?v=XVcvOtyE7tA
Practice1
To find the general solution of linear homogeneous system of differential equations by using Matlab
>
NonHomogeneous Linear Systems with Constant Coefficients
https://player.slideplayer.com/26/8588018/#
https://www.youtube.com/watch?v=YhVb9qFspMQ
Practice2
To find the general solution of linear nonhomogeneous system of differential equations by using Matlab
https://in.mathworks.com/videos/solvingodesinmatlab8systemsofequations117652.html
Project1
To make a report of an application of linear system of differential equation
https://www.slideshare.net/shahzad_ali27/applicationsofdifferentialequations
Introduction to Simultaneous Linear First Order Equations in Three Variables
https://www.slideshare.net/shubhijain1042/simultaneousdifferentialequations
https://www.youtube.com/watch?v=3BsT85lpS4
Simultaneous Linear First Order Equations in Three Variables
https://www.slideshare.net/puniswaryparamasivam/simultaneousequation16250316
Practice3
To find the solution of simultaneous linear first order differential equations by using Matlab.
https://www.youtube.com/watch?v=G59vnBwDwqs
Methods of Solutions of Pfaffian Differential Equations in Three Variables.
pfaffian PDE
https://www.youtube.com/watch?v=FZZS91nfRgc
Practice4
To find the Solutions of system of differential equations in three Variables by using Matlab.
https://www.youtube.com/watch?v=B9FAjkeVTeI
Project2
To make a report on simultaneous Linear Differential Equations.
Introduction to first order partial differential equations,
https://www.slideshare.net/3820170034/introductionofpartialdifferentialequations
introduction to pde
Formation of first order partial differential equations,
https://www.slideshare.net/3820170034/introductionofpartialdifferentialequations
https://www.youtube.com/watch?v=ToIXSwZ1pJU
linear partial differential equations of first order
https://www.slideshare.net/vishalgohel12195/differentialequationsoffirstorder64305185
https://www.youtube.com/watch?v=IWe57vFgs3o&list=PLhSp9OSVmeyJoNnAqghUKLit3qBgfa6o&index=7
Practice5
To find the solution of first order partial differential equations by using Matlab
https://www.youtube.com/watch?v=qgh7miW8viE
Quasilinear partial differential equations of first order
https://www.slideshare.net/jayanshugundaniya9/advancedengineeringmathematicsfirstordernonlinearpartialdifferentialequationitsapplications
https://www.youtube.com/watch?v=Y_vdqYJ43xE
Practice6
To find the solution of first order Quasilinear partial differential equations by using Matlab
https://in.mathworks.com/help/matlab/math/partialdifferentialequations.html
introduction to Special types of firstorder equations
https://www.slideshare.net/aman1894/partialdifferentialequations42054204
https://www.youtube.com/watch?v=dZOTzF0YflY
nonlinear partial differential equations
https://www.slideshare.net/aman1894/partialdifferentialequations42054204
https://www.youtube.com/watch?v=N9P5i7aJ88c
Practice7
To find the solution of 1d Wave equation by using Matlab
solutions of partial differential equations of first order satisfying given conditions
https://www.slideshare.net/EnriqueValderrama4/partialdifferentialequations3simpleexamples
https://www.youtube.com/watch?v=l3T4SL6lEIE
Practice8
To find the solution of 1d Heat equation by using Matlab
solutions of PDE with initial conditions
https://www.slideshare.net/EnriqueValderrama4/partialdifferentialequations3simpleexamples
https://www.youtube.com/watch?v=l3T4SL6lEIE
Project4
Briefly describe Homogeneous Partial differential Equations with suitable examples.
Homogeneous partial differential equations with constant coefficients
https://www.slideserve.com/margot/partialdifferentialequations
https://www.youtube.com/watch?v=kuZi6SkkpGg&list=PLhSp9OSVmeyJoNnAqghUKLit3qBgfa6o&index=9
Practice9
To find the solution of first order homogeneous partial differential equations by using Matlab
https://www.youtube.com/watch?v=62Wzs0sXd8
Solution of homogeneous partial differential equations with constant coefficients
https://www.slideserve.com/margot/partialdifferentialequations
https://www.youtube.com/watch?v=995iPPGaPsg&list=PLhSp9OSVmeyJoNnAqghUKLit3qBgfa6o&index=10
Practice10
To find the solution of 2d Wave equation by using Matlab
https://www.slideshare.net/AmrMousa12/2dimensionalwaveequationanalyticalandnumericalsolution
solution of higher order homogeneous PDE with constant coefficients
https://www.slideshare.net/aman1894/partialdifferentialequations42054204
https://www.youtube.com/watch?v=TJutBkwDEFw
Project5
Make a report for the Nonhomogeneous Partial differential Equations.
solution higher order homogeneous PDE with constant coefficients.
https://www.slideshare.net/EnriqueValderrama4/partialdifferentialequations3simpleexamples
https://www.youtube.com/watch?v=TJutBkwDEFw
Higher order linear Nonhomogeneous PDE with constant coefficients
https://www.slideshare.net/EnriqueValderrama4/partialdifferentialequations3simpleexamples
https://www.youtube.com/watch?v=BmOrHZLuO7g
Higher order linear Nonhomogeneous PDE (trigonometric functions)
https://www.slideshare.net/jayanshugundaniya9/advancedengineeringmathematicsfirstordernonlinearpartialdifferentialequationitsapplications
https://www.youtube.com/watch?v=geWDVLDq8To&list=PLhSp9OSVmeyJoNnAqghUKLit3qBgfa6o&index=27
Practice11
To find the solution of 2d heat equation by using Matlab
Higher order linear Nonhomogeneous PDE (exponential shift form)
https://slideplayer.com/slide/9505473/
https://www.youtube.com/watch?v=07v6TYnpirU&list=PLhSp9OSVmeyJoNnAqghUKLit3qBgfa6o&index=28
Higher order linear Nonhomogeneous PDE (exponential form)
https://www.slideshare.net/alexkhan129/laplaceequation78729248
https://www.youtube.com/watch?v=YClMX_eYGOk&list=PL2bgr0gejLWM60EV8Njl2yyrQc4kCgGhT&index=2
Practice12
To find the solution of 2d Laplace equation by using Matlab
Project6:
summary of Nonhomogeneous Partial differential Equations with variable coefficients.
Higher order linear Nonhomogeneous PDE with inverse operators
https://www.slideshare.net/alexkhan129/laplaceequation78729248
https://www.youtube.com/watch?v=5fHrVNoaHLk&list=PL2bgr0gejLWM60EV8Njl2yyrQc4kCgGhT&index=7
Higher order linear Nonhomogeneous PDE with inverse operators
https://www.slideshare.net/alexkhan129/laplaceequation78729248
https://www.youtube.com/watch?v=5fHrVNoaHLk&list=PL2bgr0gejLWM60EV8Njl2yyrQc4kCgGhT&index=7
Solution of homogeneous PDE with variable coefficients
https://www.slideshare.net/neerajparmar68/1dwaveequation
https://www.youtube.com/watch?v=imdFhDbWDyM
Nonhomogeneous PDE with variable coefficients
https://www.slideshare.net/DhavalJalalpara/thewaveequation
https://www.youtube.com/watch?v=EJLympg3XMM
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 12 research articles in National and International refereed journals . He is continue their P.hD in the field of Fuzzy Inventory Control Models.