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1. Working with systems of ordinary differential equations and nonlinear ordinary differential equations
is also stressed.
2. Developing and understanding and appreciation of the qualitative behavior of the solution
3. To introduce wave equations, Laplace equations, Heat equations, Diffusion equations.
COs  Course outcomes  Mapping Cos with POs (High3, Medium2, Low1) 
CO1 
Solve wave equation and understand significance of transverse waves.

PO1(3), PO2(2) 
CO2 
Identify classes of nonlinear ordinary differential equations.

PO2(2), PO4(2) 
CO3 
Apply an appropriate method for the solution of nonlinear ordinary differential equations.

PO9(3) 
CO5 
Competence in solving applied problems which are linear and nonlinear form, Solve Laplace equation, Diffusion equation, heat equation.

PO2(2), PO1(3) 
Module I:
Introduction to Ordinary Differential Equations and Partial Differential Equations, First Order Non linear Ordinary differential equations such as Equations solvable for x, Equations solvable for y, Equations solvable for p.
Practice 1: Solve Ordinary Differential Equations in Python
Practice2: Solve Partial differential Equations by python
Module II:
Partial differential equation of second order with variable coefficients Monge's method and its properties
Project 1: Monge’s Method of Solution of Nonlinear Partial Differential Equations of Order Two.
Module III:
Classification of linear partial differential equation of second order, Cauchy's problem, Method of separation of variables.
Module IV
Solution of one dimensional Laplace equation by method of separation of variables and Fourier series
Project 2 : Solution of Laplace’s Equation for a Disk
Module V:
Solution of one dimensional Wave equation by method of separation of variables and Fourier series
Project 3: D’ Alembert’s solution of the wave equation
Practice 3: Solution of wave equation associated condition
u(x,0)=φ(x),u_t (x,0)=ψ(x),u(0,t)=0,xϵ(0,∞),t>0
Practice 4: Solution of wave equation associated condition
u(x,0)=φ(x),u(0,t)=a,xϵ(0,∞),t≥0
Module VI
Solution of one dimensional Diffusion equation by method of separation of variables and Fourier series
Project 4: Solution of Diffusion equation in ndimensional
Practice 5: Solution of onedimensional diffusion equation by using boundary conditions u(x,0)=φ(x),u(0,t)=a,xϵ(0,∞),t≥0
Practice 6:Solution of onedimensional diffusion equation
u(x,0)=φ(x),u(0,t)=a,u(1,t)=b,0<x0
Module VII
Solution of one dimensional Heat equation by method of separation of variables and Fourier series
Project 5: Two dimensional Heat equations Polar form
Project 6: Temperature distribution in Rectangular plate
Text Books
Reference books:
1. S.J. Farlow: An Introduction to Ordinary Differential Equations, PHI
2. M.D. Raisinghania: Ordinary and Partial Differential Equations, S. Chand & Co.
3. V. Sundarapandian: Ordinary and Partial Differential Equations, McGrawHill
Introduction to Ordinary Differential Equations and Partial Differential Equations
https://www.youtube.com/watch?v=ly4S0oi3Yz8
https://www.slideshare.net/EMDADULHAQUE13/introductiontodifferentialequations
First Order Non linear Ordinary differential equations such as Equations solvable for x
https://www.youtube.com/watch?v=p_di4Zn4wz4
https://www.slideshare.net/myaukish/formulationoffirstorderlinearandnonlinear2ndorderdifferentialequation
Nonlinear ordinary differential equations of particular forms
Youtube: Nonlinear ordinary differential equations of particular forms
Practice1 (2 hrs)
Solve Ordinary Differential Equations in Python
https://www.youtube.com/watch?v=JLtRK4Z1tEg
https://physics.nyu.edu/pine/pymanual/html/chap9/chap9_scipy.html
Practice2 (2 hrs)
Solve Partial differential Equations by python
http://csc.ucdavis.edu/~cmg/Group/readings/pythonissue_3of4.pdf
https://www.youtube.com/watch?v=mMdIxa5qC9Y
Partial differential equation of second order
https://www.youtube.com/watch?v=AXH9Xm6Rbfc
https://www.slideshare.net/3820170034/introductionofpartialdifferentialequations
Partial differential equation of second order with variable coefficients
https://www.youtube.com/watch?v=3lHbafzc6a8
https://www.slideshare.net/aman1894/partialdifferentialequations42054204
Monge's method and its properties
https://www.youtube.com/watch?v=AXH9Xm6Rbfc
https://www.slideshare.net/alibhalli43/differentialequations48242801
Project1 (2 hrs)
Monge’s Method of Solution of Nonlinear Partial Differential Equations of Order Two
http://182.18.165.51/Fac_File/[email protected]
Classification of linear partial differential equation of second order
Classification of linear partial differential equation of second order
Method of separation of variables
https://www.youtube.com/watch?v=aolvx8bWFDA
https://www.slideshare.net/JuanApolinarioReyes/separationofvariables
one dimensional Laplace equation
https://www.youtube.com/watch?v=EW08rDGFh0
https://nptel.ac.in/content/storage2/courses/115101005/downloads/lecturesdoc/Lecture14.pdf
One dimensional Laplace equation by method of separation of variables and Fourier series
https://www.youtube.com/watch?v=XbCvGRjjzgg
Solution of one dimensional Laplace equation by method of separation of variables and Fourier series
https://www.youtube.com/watch?v=6cMn1F6bNPU
https://www.youtube.com/watch?v=WWphCZkdByA
https://www.slideshare.net/alexkhan129/laplaceequation78729248
Project2 (2 hrs)
Solution of Laplace’s Equation for a Disk
https://math.okstate.edu/people/binegar/4263/4263l15.pdf
https://www.youtube.com/watch?v=MCoe3HFu9Yk
one dimensional Wave equation
https://www.youtube.com/watch?v=0Rfushlee0U
https://www.slideshare.net/DhavalJalalpara/thewaveequation
Solution of one dimensional Wave equation by method of separation of variables and Fourier series
https://www.youtube.com/watch?v=9TQCKWWAVjM&t=17s
https://www.youtube.com/watch?v=imdFhDbWDyM
https://www.slideshare.net/neerajparmar68/1dwaveequation
one dimensional Wave equation by method of separation of variables and Fourier series
https://www.youtube.com/watch?v=k2TuJfNQ9s
https://www.youtube.com/watch?v=ckr_qmNNG0
https://www.slideshare.net/8laddu8/fourierseries
Project3 (2 hrs)
D’ Alembert’s solution of the wave equation
https://www.youtube.com/watch?v=j2G91naZ8bo
D’ Alembert’s solution of the wave equation
Practice 3 (2 hrs)
Solution of wave equation associated condition
u(x,0)=φ(x),u_t (x,0)=ψ(x),u(0,t)=0,xϵ(0,∞),t>0
https://in.mathworks.com/matlabcentral/answers/440084pdepehelpboundryconditioninpdesolver
Practice 4 (2 hrs)
Solution of wave equation associated condition
u(x,0)=φ(x),u(0,t)=a,xϵ(0,∞),t≥0
https://www.slideshare.net/AmrMousa12/2dimensionalwaveequationanalyticalandnumericalsolution
one dimensional Diffusion equation by method of separation of variables
https://www.youtube.com/watch?v=jco8ygBA8LY
https://www.slideshare.net/EnriqueValderrama4/partialdifferentialequations3simpleexamples
Solution of one dimensional Diffusion equation by method of separation of variables and Fourier series
https://www.youtube.com/watch?v=WwS3CYltxqY
Project 4(2 hrs)
Solution of Diffusion equation in ndimensional
http://www.math.utk.edu/~freire/teaching/m435s14/HigherDimHeatEqn.pdf
Practice 5 (2 hrs)
Solution of onedimensional diffusion equation by using boundary conditions u(x,0)=φ(x),u(0,t)=a,xϵ(0,∞),t≥0
https://www.slideshare.net/AmrMousa12/2dimensionalwaveequationanalyticalandnumericalsolution
Practice 6 (2 hrs)
Solution of onedimensional diffusion equation
u(x,0)=φ(x),u(0,t)=a,u(1,t)=b,0<x0
https://in.mathworks.com/matlabcentral/answers/440084pdepehelpboundryconditioninpdesolver
one dimensional Heat equation by method of separation of variables
https://www.youtube.com/watch?v=ToIXSwZ1pJU&t=147s
Project 5 (2 hrs)
Two dimensional Heat equations Polar form
http://www.math.ttu.edu/~gilliam/ttu/s10/m3351_s10/c14_2d_disk_heat.pdf
Project 6 (2 hrs)
Temperature distribution in Rectangular plate
http://www.math.ttu.edu/~gilliam/ttu/s10/m3351_s10/c14_2d_disk_heat.pdf