Partial Differential Equations And System of Ordinary Differential Equations
Teacher
Dr.Balaji Padhy
Category
Core Courses
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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
| COs | Course outcomes | Mapping Cos with POs (High-3, Medium-2, Low-1) |
| 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) |
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
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
Session 2
Systems of Linear Differential Equations with constant coefficients
https://www.slideshare.net/pratiksudra10/linear-differential-equation
https://www.youtube.com/watch?v=FarysWaGM9w
Session 3
Homogenrous linear Systems with constant coefficients
https://www.slideshare.net/ssinghhapur/linear-differential-equation-with-constant-coefficient
https://www.youtube.com/watch?v=XVcvOtyE7tA
Session 4 & 5
Practice-1
To find the general solution of linear homogeneous system of differential equations by using 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 12
Simultaneous Linear First Order Equations in Three Variables
https://www.slideshare.net/puniswaryparamasivam/simultaneous-equation-16250316
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 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
Introduction to first order partial differential equations,
https://www.slideshare.net/3820170034/introduction-of-partial-differential-equations
introduction to pde
Session 22
Formation of first order partial differential equations,
https://www.slideshare.net/3820170034/introduction-of-partial-differential-equations
https://www.youtube.com/watch?v=ToIXSwZ1pJU
Session 23
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
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 26
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
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 31
introduction to Special types of first-order equations
https://www.slideshare.net/aman1894/partial-differential-equations-42054204
https://www.youtube.com/watch?v=dZOTzF0YflY
Session 32
non-linear partial differential equations
https://www.slideshare.net/aman1894/partial-differential-equations-42054204
https://www.youtube.com/watch?v=N9P5i7aJ88c
Session 33 & 34
Practice-7
To find the solution of 1-d Wave equation by using Matlab
Session 36
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
Session 37 & 38
Practice-8
To find the solution of 1-d Heat equation by using Matlab
Session 39
solutions of PDE with initial conditions
https://www.slideshare.net/EnriqueValderrama4/partial-differential-equations-3-simple-examples
https://www.youtube.com/watch?v=l3T4SL6lEIE
Session 40 & 41
Project-4
Briefly describe Homogeneous Partial differential Equations with suitable examples.
Session 42
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
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 45
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
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
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
Session 50 & 51
Project-5
Make a report for the Non-homogeneous Partial differential Equations.
Session 52
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
Session 53
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
Session 54
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
Session 55 & 56
Practice-11
To find the solution of 2-d heat equation by using Matlab
Session 57
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
Session 58
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
Session 59 & 60
Practice-12
To find the solution of 2-d Laplace equation by using Matlab
Session 61 & 62
Project-6:
summary of Non-homogeneous Partial differential Equations with variable coefficients.
Session 63
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
Session 64
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
Session 65
Solution of homogeneous PDE with variable coefficients
https://www.slideshare.net/neerajparmar68/1-d-wave-equation
https://www.youtube.com/watch?v=imdFhDbWDyM
Session 66
Non-homogeneous PDE with variable coefficients
https://www.slideshare.net/DhavalJalalpara/the-wave-equation
https://www.youtube.com/watch?v=EJLympg3XMM
Case Studies
Case Studies
Our Main Teachers
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.