Udemy – Partial Differential Equations: Comprehensive Course 2024-6

Published on: 2024-12-18 23:34:34

Categories: 28

Descriptions

Partial Differential Equations: Comprehensive Course, This course is designed to provide a comprehensive understanding of how the Fourier Transform can be used as a powerful tool to solve Partial Differential Equations (PDE). The course is divided into three parts, each building on the previous one, and includes bonus sections on the mathematical derivation of the Heisenberg Uncertainty Principle.
In this part, we will start with the basics of the Fourier series and derive the Fourier Transform and its inverse. We will then apply these concepts to solve PDE’s using the Fourier Transform. Prerequisites for this section are Calculus and Multivariable Calculus, with a focus on topics related to derivatives, integrals, gradient, Laplacian, and spherical coordinates. This section introduces the heat equation and the Laplace equation in Cartesian and polar coordinates. We will solve exercises with different boundary conditions using the Separation of Variables method. This section is self-contained and independent of the first one, but prior knowledge of ODEs is recommended. This section is dedicated to the Diffusion/Heat equation, where we will derive the equation from physics principles and solve it rigorously. Bonus sections are included on the mathematical derivation of the Heisenberg Uncertainty Principle.

What you’ll learn

How to use the Fourier Trasforms to tackle the problem of solving PDE’s
Fourier Transforms in one and multiple dimensions
Method of separation of variables to solve the Heat equation (with exercises)
Method of separation of variables to solve the Laplace equation in cartesian and polar coordinates (with exercises)
How to apply the Fourier Transform to solve 2nd order ODE’s as well
How to derive the Black Scholes equation in Finance
How to derive (and in some cases solve) the Navier-Stokes equations
concept of streamlines
Mathematical tricks
How to derive Heisenberg Uncertainty Principle using concepts of Probability Theory

Who this course is for

Students who are interested in Physics and in mathematical derivations of concepts
engineers
mathematicians
physicists
data scientists
computer programmers