Learn how to solve Partial Differential Equations (PDEs) using Laplace Transforms, focusing on the heat equation on a semi-infinite domain. The course covers the Laplace Transform with respect to time, solving ODEs with forcing, handling homogeneous and particular solutions, initial and boundary conditions, and transitioning between frequency and time domains. The teaching method involves a step-by-step explanation with practical examples. This course is intended for learners interested in advanced mathematics, particularly in the field of solving PDEs using Laplace Transforms.
Overview
Syllabus
Overview and Problem Setup
How Classic Methods e.g., Laplace Relate to Modern Problems
Laplace Transform with respect to Time
Solving ODE with Forcing: Homogeneous and Particular Solution
The Particular Solution and Initial Conditions
The Homogeneous Solution and Boundary Conditions
The Solution in Frequency and Time Domains
Taught by
Steve Brunton
Related Courses
-
18.03x Differential Equations
-
Differential Equations for Engineers
4.9 -
Modeling of Feedback Systems
-
PDE 101 - Separation of Variables or How I Learned to Stop Worrying and Solve Laplace's Equation
-
Solving the Wave Equation with Separation of Variables and Guitar String Physics
-
Transform Calculus and Its Applications in Differential Equations
