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• 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..

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.

**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.

introduction to the Systems of Linear Differential Equations

https://www.slideshare.net/JDagenais/systems-of-differential-equations

https://www.youtube.com/watch?v=p_di4Zn4wz4

Systems of Linear Differential Equations with constant coefficients

https://www.slideshare.net/pratiksudra10/linear-differential-equation

https://www.youtube.com/watch?v=FarysWaGM9w

Homogenrous linear Systems with constant coefficients

https://www.slideshare.net/ssinghhapur/linear-differential-equation-with-constant-coefficient

https://www.youtube.com/watch?v=XVcvOtyE7tA

**Practice-1**

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

>

Non-Homogeneous Linear Systems with Constant Coefficients

https://player.slideplayer.com/26/8588018/#

https://www.youtube.com/watch?v=YhVb9qFspMQ

**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

**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

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

Simultaneous Linear First Order Equations in Three Variables

https://www.slideshare.net/puniswaryparamasivam/simultaneous-equation-16250316

**Practice-3**

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

**Practice-4**

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

https://www.youtube.com/watch?v=B9FAjkeVTeI

**Project-2**

To make a report on simultaneous Linear Differential Equations.

Introduction to first order partial differential equations,

https://www.slideshare.net/3820170034/introduction-of-partial-differential-equations

introduction to pde

Formation of first order partial differential equations,

https://www.slideshare.net/3820170034/introduction-of-partial-differential-equations

https://www.youtube.com/watch?v=ToIXSwZ1pJU

linear partial differential equations of first order

https://www.slideshare.net/vishalgohel12195/differential-equations-of-first-order-64305185

https://www.youtube.com/watch?v=IWe57vFgs3o&list=PLhSp9OSVmeyJoNnAqghUK-Lit3qBgfa6o&index=7

**Practice-5**

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

https://www.youtube.com/watch?v=qgh7miW8viE

Quasi-linear partial differential equations of first order

https://www.slideshare.net/jayanshugundaniya9/advanced-engineering-mathematics-first-order-nonlinear-partial-differential-equation-its-applications

https://www.youtube.com/watch?v=Y_vdqYJ43xE

**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

introduction to Special types of first-order equations

https://www.slideshare.net/aman1894/partial-differential-equations-42054204

https://www.youtube.com/watch?v=dZOTzF0YflY

non-linear partial differential equations

https://www.slideshare.net/aman1894/partial-differential-equations-42054204

https://www.youtube.com/watch?v=N9P5i7aJ88c

**Practice-7**

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

solutions of partial differential equations of first order satisfying given conditions

https://www.slideshare.net/EnriqueValderrama4/partial-differential-equations-3-simple-examples

https://www.youtube.com/watch?v=l3T4SL6lEIE

**Practice-8**

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

solutions of PDE with initial conditions

https://www.slideshare.net/EnriqueValderrama4/partial-differential-equations-3-simple-examples

https://www.youtube.com/watch?v=l3T4SL6lEIE

**Project-4**

Briefly describe Homogeneous Partial differential Equations with suitable examples.

Homogeneous partial differential equations with constant coefficients

https://www.slideserve.com/margot/partial-differential-equations

https://www.youtube.com/watch?v=kuZi6SkkpGg&list=PLhSp9OSVmeyJoNnAqghUK-Lit3qBgfa6o&index=9

**Practice-9**

To find the solution of first order homogeneous partial differential equations by using Matlab

https://www.youtube.com/watch?v=6-2Wzs0sXd8

Solution of homogeneous partial differential equations with constant coefficients

https://www.slideserve.com/margot/partial-differential-equations

https://www.youtube.com/watch?v=995iPPGaPsg&list=PLhSp9OSVmeyJoNnAqghUK-Lit3qBgfa6o&index=10

**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

solution of higher order homogeneous PDE with constant coefficients

https://www.slideshare.net/aman1894/partial-differential-equations-42054204

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

**Project-5**

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

solution higher order homogeneous PDE with constant coefficients.

https://www.slideshare.net/EnriqueValderrama4/partial-differential-equations-3-simple-examples

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

Higher order linear Non-homogeneous PDE with constant coefficients

https://www.slideshare.net/EnriqueValderrama4/partial-differential-equations-3-simple-examples

https://www.youtube.com/watch?v=BmOrHZLuO7g

Higher order linear Non-homogeneous PDE (trigonometric functions)

https://www.slideshare.net/jayanshugundaniya9/advanced-engineering-mathematics-first-order-nonlinear-partial-differential-equation-its-applications

https://www.youtube.com/watch?v=geWDVLDq8To&list=PLhSp9OSVmeyJoNnAqghUK-Lit3qBgfa6o&index=27

**Practice-11**

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

Higher order linear Non-homogeneous PDE (exponential shift form)

https://slideplayer.com/slide/9505473/

https://www.youtube.com/watch?v=07v6TYnpirU&list=PLhSp9OSVmeyJoNnAqghUK-Lit3qBgfa6o&index=28

Higher order linear Non-homogeneous PDE (exponential form)

https://www.slideshare.net/alexkhan129/laplace-equation-78729248

https://www.youtube.com/watch?v=YClMX_eYGOk&list=PL2bgr0gejLWM60EV8Njl2yyrQc4kCgGhT&index=2

**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.

Higher order linear Non-homogeneous PDE with inverse operators

https://www.slideshare.net/alexkhan129/laplace-equation-78729248

https://www.youtube.com/watch?v=5fHrVNoaHLk&list=PL2bgr0gejLWM60EV8Njl2yyrQc4kCgGhT&index=7

https://www.slideshare.net/alexkhan129/laplace-equation-78729248

https://www.youtube.com/watch?v=5fHrVNoaHLk&list=PL2bgr0gejLWM60EV8Njl2yyrQc4kCgGhT&index=7

Solution of homogeneous PDE with variable coefficients

https://www.slideshare.net/neerajparmar68/1-d-wave-equation

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

Non-homogeneous PDE with variable coefficients

https://www.slideshare.net/DhavalJalalpara/the-wave-equation

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 5 research articles in National and International refereed journals . He is continue their P.hD in the field of Fuzzy Inventory Control Models.

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