Partial Differential Equations
.Following are my notes from the "Introduction to Partial Differential Equations" (undergrad.) course completed in Spring 2016. The notes are hand-written and as I revise them later, I will formalise them using LaTeX. Those written formally are tagged with "#formal". Topics covered in each lecture are tagged with a '#'.
Course Book: Partial Differential Equations - An Introduction (Second Edition) by Walter A. Strauss.
Most of the following notes are adapted from the book.
Most of the following notes are adapted from the book.
Introduction to PDEs |
#formal |
|
# Wave Equation
# Examples of ODEs # Complex Numbers # Linear Differential Operators | ||
First Order Linear Equations |
#formal |
|
# Derivatives as Local Operators
# The Constant Coefficient Equation # The Variable Coefficient Equation # Example PDE solutions | ||
The Wave Equation |
#formal |
|
# The Wave Equation
# Initial Value Problem # Solved Example | ||
The Wave Equation II
|
#formal# Causality
# Energy # Solved Example | ||
The Diffusion Equation
| The Diffusion Equation |
The Diffusion Equation II
| The Diffusion Equation II |
Diffusion on the Whole Line I
| Diffusion on the Whole Line I |
Diffusion on the Whole Line II
| Diffusion on the Whole Line II |
Reflection and Sources-Heat Equation
| Reflection and Sources- Heat Equation |
Reflection of Waves
| Reflection of Waves |
Diffusion with a Source
| Diffusion with a Source |
Heat Equation with Source
| Heat Equation with Source |
Waves and Sources
| Waves and Sources |
Boundary Conditions
| Boundary Conditions |
Fourier Series
| Fourier Series |
Convergence |
#formal |
|
# Pointwise Convergence
# Uniform Convergence # L^2 Convergence # Examples | ||
L^2 Theory
| L^2 Theory |
Poisson's Formula
| Poisson Formula |
