X

PDE AND SYSTEMS OF ODE

By Dr. Vijitha Mukundan   |   Sacred Heart College, Chalakudy
Learners enrolled: 306
This course provides a comprehensive understanding of partial differential equations(pde) and systems of ordinary differential equations(ode). It enables us to understand the different types of pde and methods to solve first order and second order partial differential equations. It helps in understanding methods of characteristics, relevance of heat equation and wave equation. It also provides some methods to solve systems of ode and approximate methods to solve first order ordinary differential equations.
The primary learning outcome for this course is efficiently solving partial differential equations of first and second order, and systems of ode. Students will also be able to find approximate solutions to some first order ode.

The resource person for this course are:
1. Dr. Vijitha Mukundan (Course Coordinator)
Assistant Professor, Department of Mathematics, Sacred Heart College Chalakudy.
2. Ms. Smitha Davis , HoD, Department of Mathematics, Sacred Heart College Chalakudy
3. Dr. Lejo J Manavalan, Assistant Professor,
Department of Mathematics, Little Flower College, Guruvayoor.
Summary
Course Status : Completed
Course Type : Core
Language for course content : English
Duration : 12 weeks
Category :
  • Mathematics
Credit Points : 4
Level : Undergraduate
Start Date : 31 Jul 2023
End Date : 31 Oct 2023
Enrollment Ends : 31 Aug 2023
Exam Date :

Page Visits



Course layout

Weeks Weekly Lecture Topics (Module Titles)

1 Day 1 Module 1 : Introductions To Partial Differential Equations And Mathematical Problems
Day 2 Module 2 : First Order PDE: Classification And Constructions – Part 1
Day 3 Module 3 : First Order PDE: Classification And Constructions –  Part 2
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

2 Day 1 Module 4 : Integral Surface of PDE – Problems
Day 2 Module 5 : First Order PDE : Geometrical Interpretation
Day 3 Module 6 : General Solutions And Method Of Characteristics –  Part 1
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

3 Day 1 Module 7 : General Solutions And Method Of Characteristics – Part 2 (Cauchy Problem For First Order PDE and Method of Characteristics ) 
Day 2 Module 8 : General Solutions And Method Of Characteristics – Part 3
Day 3 Module 9 : Canonical Forms And First Order PDE
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments


4 Day 1 Module 10 : Separation Of Variables 
Day 2 Module 11 : The Vibrating String
Day 3 Module 12 : Conduction Of Heat In Solids / Derivation of Heat Equation and Laplace Equation 
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

5 Day 1 Module 13 : Second Order Equations In Two Independent Variables & Canonical Forms Part 1 
Day 2 Module 14 : Canonical Forms Part 2 
Day 3 Module 15 : Canonical Forms Part 3
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

6 Day 1 Module 16 : Problems Related to Canonical Forms
Day 2 Module 17 : General Solutions
Day 3 Module 18 : Cauchy Problem And Cauchy-Kowaleewsky Theorem 
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

7 Day 1 Module 19 : Cauchy Problem And Infinite String Part 1
Day 2 Module 20 : Cauchy Problem And Infinite String Part 2
Day 3 Module 21 : Cauchy Problem For An Infinite String-Part 3 and Generalized Solution
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

8 Day 1 Module 22 : Initial-Value Problems : Semi-Infinite String With A Fixed End
Day 2 Module 23:Initial-Value Problems : Semi-Infinite String With A Free End 
Day 3 Module 24 : Equations With Non-Homogeneous Boundary Conditions and NonHomogeneous Wave Equation - Part 1
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

9 Day 1 Module 25 : Non-Homogeneous Wave Equation - Part 2
Day 2 Module 26 : Method Of Separation Of Variables
Day 3 Module 27: Vibrating String Problem – Part 1
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

10 Day 1 Module 28 : Vibrating String Problem – Part 2
Day 2 Module 29 : Heat Conduction Problem – Part 1
Day 3 Module 30 : Heat Conduction Problem – Part 2
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

11 Day 1 Module 31 : Types Of Linear Systems 
Day 2 Module 32 : An Operator Method For Linear Systems With Constant Coefficient
Day 3 Module 33: An Alternative Procedure For The Solution System Of ODE With Constant Coefficients (Basic Theory Of Linear Systems In Normal Forms Part 1)
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

12 Day 1 Module 34 : Basic Theory Of Linear Systems In Normal Forms Part 2
Day 2 Module 35 : Basic Theory Of Linear Systems In Normal Forms Part 3
Day 3 Module 36 : Homogeneous Linear Systems With Constant Coefficients - Part 1 
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

13 Day 1 Module 37 : Homogeneous Linear Systems With Constant Coefficients - Part 2 
Day 2 Module 38 : Homogeneous Linear Systems With Constant Coefficients - Part 3 
Day 3 Module 39 : The Method Of Successive Approximations
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

 15 Day 1 Module 40 : Euler Method
Day 2 Module 41 : Modified Euler Method
Day 3 Module 42 : Runge - Kutta Method
Day 4 Interactions based on the three modules covered
Day 5 Deadline for submitting Assignments

 16 Day 1 Module 43 : Problems on Numerical Method to Solve Ist Order Ordinary Differential Equations
Day 2
Day 3
Day 4
Day 5

Books and references

• Linear Partial Differential Equations for Scientists and Engineers,
Tyn Myint-U and Lokenath Debnath, Fourth edition, Springer
Science & Business Media, 2007.

• An elementary course in Partial Differential Equations, T.
Amaranath, Second edition, Narosa Publishing House, 2003.

• Elements of partial differential equations, Ian N. Sneddon , Courier
Corporation, 2006.

• Partial Differential Equations: Classical Theory with a Modern
Touch, Nandakumaran A.K. and Datti P.S., Cambridge University
Press 2020.

Instructor bio

Dr. Vijitha Mukundan

Sacred Heart College, Chalakudy
Dr. Vijitha Mukundan is Assistant professor in Department of Mathematics, Sacred Heart College Chalakudy. She received her Bachelor’s degree in Mathematics from Vimala College, Thrissur and Masters from St. Thomas’ College, Thrissur. She has  qualified for GATE and CSIR-UGC NET. She has  ten  years of extensive teaching experience in Colleges.  She received her Ph. D from the Department of Mathematics, National Institute of Technology Calicut under the guidance of Dr. Ashish Awasthi in 2018. She has published several research papers in national and international journals and participated in several conferences and workshops. Her research interests include numerical analysis, modeling, simulation, computational methods for ODE and PDE, and perturbation theory. She has delivered invited lectures at many institutions.


Course certificate

30 Marks will be allocated for Internal Assessment and 70 Marks will be allocated for end term proctored examination
Securing 40% in both separately is mandatory to pass the course and get Credit Certificate.


MHRD logo Swayam logo

DOWNLOAD APP

Goto google play store

FOLLOW US