PDE AND SYSTEMS OF ODE

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, wave equation and Laplace 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.

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