This course aims to teach students about Partial Differential Equations (PDEs) and their applications. By the end of the course, learners will be able to understand the basics of PDEs, solve simple and first-order PDEs using various methods such as the characteristic, coordinate, and transform methods. They will also learn about the wave equation, D'Alembert formula, energy method, heat equation, Fourier series, separation of variables, Laplace equation, and more. The teaching method involves a combination of theoretical explanations, problem-solving sessions, and practical applications. This course is intended for individuals interested in deepening their knowledge of PDEs and their real-world implications.
Overview
Syllabus
What is a PDE ?.
Simple PDE.
First Order PDE.
Characteristic Method.
Coordinate Method.
Transform Method.
Wave equation.
D Alembert formula.
Factoring Method.
Energy Method.
Heat Equation.
Monster Integral.
Energy Decay.
Maximum Principle.
Half Heat Equation.
Another monster integral.
Reflection of waves.
Fourier series.
Fourier cosine and sine series.
Sum of 1/n^2.
Sum of 1/n^2+1.
Sum 1/n^6.
Odd sum two ways.
Separation of Variables.
Separation of Variables.
Rotation invariance.
Laplace Equation.
The hardest question on the hardest calc 3 test.
Taught by
Dr Peyam
