Advanced Differential Equations

Teacher

Mrs. Saubhagyalaxmi Singh

Category

Core Courses

Course Attendees

Still no participant

Course Reviews

Still no reviews

Course Name : Advanced Differential Equations

Code(Credit) : CUTM1530(2-1-1)

Course Objectives

1. Working with systems of ordinary differential equations and non-linear 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.

Learning Outcomes

After successfully completing this course the expectation is that students will be able to:
1. Solve wave equation and understand significance of transverse waves.
2. Identify classes of non-linear ordinary differential equations.
3. Apply an appropriate method for the solution of non-linear ordinary differential equations.
4. solve the problems choosing the most suitable method.

5. Solve laplace equation, Diffusion equation, heat equation

5. competence in solving applied problems which are linear and nonlinear form

Course Syllabus

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
Practice-2: 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 Non-linear 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 n-dimensional
Practice 5: Solution of one-dimensional diffusion equation by using boundary conditions u(x,0)=φ(x),u(0,t)=a,xϵ(0,∞),t≥0
Practice 6:Solution of one-dimensional 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

1. Differential Equations and Their Applications, by Martin Braun, Springer, 4e, ISBN 9781111827052 (1993).
2. S. L. Ross: Differential Equations, Blaisdell Publishing Company, Londan, 1964.

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, McGraw-Hill

Session Plan

Session 1

Introduction to Ordinary Differential Equations and Partial Differential Equations
https://www.youtube.com/watch?v=ly4S0oi3Yz8

https://www.slideshare.net/EMDADULHAQUE13/introduction-to-differential-equations

Session 3

Non-linear ordinary differential equations of particular forms
Youtube: Non-linear ordinary differential equations of particular forms

Session 4

Session 5

Session 7

Session 9

Project-1 (2 hrs)
Monge’s Method of Solution of Non-linear Partial Differential Equations of Order Two
http://182.18.165.51/Fac_File/STUDY182@741319.pdf

Session 10

Classification of linear partial differential equation of second order
Classification of linear partial differential equation of second order

Session 14

One- dimensional Laplace equation by method of separation of variables and Fourier series
https://www.youtube.com/watch?v=XbCvGRjjzgg

Session 15

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/laplace-equation-78729248

Session 19

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=ck-r_qmNNG0
https://www.slideshare.net/8laddu8/fourier-series

Session 20

Project-3 (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

Session 21

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/440084-pdepe-help-boundry-condition-in-pde-solver

Session 24

Session 25

Solution of one- dimensional Diffusion equation by method of separation of variables and Fourier series
https://www.youtube.com/watch?v=WwS3CYltxqY

Session 26

Project 4(2 hrs)
Solution of Diffusion equation in n-dimensional
http://www.math.utk.edu/~freire/teaching/m435s14/HigherDimHeatEqn.pdf

Session 27

Practice 5 (2 hrs)
Solution of one-dimensional diffusion equation by using boundary conditions u(x,0)=φ(x),u(0,t)=a,xϵ(0,∞),t≥0
https://www.slideshare.net/AmrMousa12/2-dimensional-wave-equation-analytical-and-numerical-solution

Session 28

Practice 6 (2 hrs)
Solution of one-dimensional diffusion equation
u(x,0)=φ(x),u(0,t)=a,u(1,t)=b,0<x0

https://in.mathworks.com/matlabcentral/answers/440084-pdepe-help-boundry-condition-in-pde-solver

Session 30

one- dimensional Heat equation by method of separation of variables
https://www.youtube.com/watch?v=ToIXSwZ1pJU&t=147s

Session 31

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

Session 32

Project 6 (2 hrs)
Temperature distribution in Rectangular plate
http://www.math.ttu.edu/~gilliam/ttu/s10/m3351_s10/c14_2d_disk_heat.pdf

Case Studies

Case Studies

Case Studies

Case Studies

Recent Comments

    Our Main Teachers

    Mrs. Saubhagyalaxmi Singh

    Assistant Professor in School of Applied Sciences, Department of Mathematics
    VIEW PROFILE

    Mrs. Saubhagyalaxmi Singh works as an Assistant Professor, Department of Mathematics, Centurion University of Technology and Management. She has over 6 years of teaching experience with exposure to Utkal University, Bhubaneswar, Department of Mathematics. She has published 6 papers communicated to different International Journals. She has guided 7 M.Sc. projects in her area. She has […]