Partial Differential Equations
.Following are my notes from the "Introduction to Partial Differential Equations" (undergrad.) course completed in Spring 2016. The notes are handwritten 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 SourcesHeat 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 