This course covers the following learning outcomes and goals: understanding Laplace, Poisson, heat, transport, wave, and porous medium equations; mastering techniques like convolution, dominated convergence theorem, Green's function, and calculus of variations; and applying concepts such as normal derivative, polar coordinates, and separation of variables. The course teaches skills in solving partial differential equations and emphasizes theoretical foundations. It is designed for learners interested in advanced mathematics and physics concepts related to differential equations.
Overview
Syllabus
Laplace equation.
Laplace Derivation.
Laplace Applications.
Convolution.
Dominated Convergence Theorem.
Polar Coordinates Formula.
Normal Derivative.
Integrate by parts like a pro.
Poisson equation.
Laplace Mean Value Formula.
Mollifiers.
Green's Function.
Poisson formula on half plane.
Poisson Formula on a ball.
Calculus of Variations.
A Taste of Calculus of Variations.
Heat equation.
Heat Equation Initial Condition.
What is Convexity?.
Transport equation.
Wave equation.
the Euler Poisson Darboux equation.
Kirchhoff Formula.
Separation of Variables.
Porous Medium Equation .
Heat-Wave Equation.
Taught by
Dr Peyam
