Dive into the world of Partial Differential Equations (PDEs) through this comprehensive 8-hour course. Begin with the fundamentals, exploring what PDEs are and examining simple examples. Progress to first-order PDEs, mastering various solution methods including Characteristic, Coordinate, and Transform techniques. Delve into specific equations such as the Wave equation, applying D'Alembert's formula, Factoring Method, and Energy Method. Tackle the Heat Equation, grappling with monster integrals and exploring energy decay and the Maximum Principle. Investigate Fourier series, including cosine and sine series, and solve challenging summation problems. Apply the Separation of Variables technique to various scenarios and explore rotation invariance. Conclude with the Laplace Equation and confront the most challenging problems in advanced calculus.
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
