Laplace's Equation Courses and Certifications

Steve Brunton

PDE 101 - Separation of Variables or How I Learned to Stop Worrying and Solve Laplace's Equation

Solve 2D Laplace’s equation for steady-state heat on a rectangular plate using separation of variables and Fourier coefficients.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Steve Brunton

Potential Flow and Laplace's Equation

Explore how Laplace’s equation models potential fluid flows through vector fields, particle motion, and applications to airfoils, cylinders, and ocean gyres.

• YouTube
• 46 minutes
• Self-Paced
• Free Video

Steve Brunton

Numerical Solution to Laplace's Equation in Matlab - Intro to Fourier Series

Solve Laplace's equation numerically in MATLAB while introducing Fourier series.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Steve Brunton

Analytic Solution to Laplace's Equation in 2D - On Rectangle

Derive an analytic solution to the two-dimensional Laplace equation on a rectangular domain.

• YouTube
• 48 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

The Laplace Equation: Dirichlet and Neumann Boundary Conditions - Lecture 67

Explore Dirichlet and Neumann boundary conditions for the Laplace Equation, enhancing understanding of partial differential equations and their applications.

• YouTube
• 29 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

The Laplace Equation in Spherical Coordinates: Solution - Lecture 71

Solve the Laplace equation in spherical coordinates, exploring methods and techniques for finding solutions to this fundamental partial differential equation.

• YouTube
• 12 minutes
• Self-Paced
• Free Video

NPTEL-NOC IITM

The Laplace Equation in Spherical Coordinates: Illustrative Examples - Lecture 72

Explore illustrative examples of the Laplace Equation in spherical coordinates, enhancing understanding of this fundamental concept in mathematical physics.

• YouTube
• 13 minutes
• Self-Paced
• Free Video

Steve Brunton

Heat Equation- Derivation and Equilibrium Solution in 1D - Laplace's Equation

Derives the one-dimensional heat equation from conservation laws and Fourier’s law, then solves its equilibrium form under common and insulated boundary conditions.

• YouTube
• 49 minutes
• Self-Paced
• Free Video

Steve Brunton

Complex Analysis - Analytic Functions Solve Laplace's Equation

Analytic complex functions yield harmonic solutions to Laplace's equation through their real and imaginary parts.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler

Learn to analyze differential equations with Fourier series, Laplace transforms, phase planes, and MATLAB’s ODE suite, including ODE45 and stiff solvers.

• MIT OpenCourseWare
• Self-Paced
• Free Online Course

Steve Brunton

Canonical Linear PDEs- Wave Equation, Heat Equation, and Laplace's Equation

An introduction to canonical linear PDEs, using the wave, heat, and Laplace equations to compare oscillation, diffusion, and steady-state behavior.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Steve Brunton

Engineering Math - Crash Course in Complex Analysis

Master complex analysis fundamentals from arithmetic to residues, exploring Euler's formula, analytic functions, and Cauchy integrals for differential equations modeling.

• YouTube
• 6 hours 28 minutes
• Self-Paced
• Free Video

Steve Brunton

Potential Flow Part 2 - Details and Examples

Explore contour integrals and examples of potential flows, showing how Laplace’s equation establishes idealized fluid-flow vector fields.

• YouTube
• 26 minutes
• Self-Paced
• Free Video

Steve Brunton

Heat Equation in 2D and 3D - 2D Laplace Equation on Rectangle

Explore heat equations in two and three dimensions alongside the 2D Laplace equation on a rectangle.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Pretty Much Physics

Electrodynamics - Electricity and Magnetism

Explore fundamental concepts of electricity and magnetism through electrostatics, electrodynamics, Maxwell equations, electric fields, magnetic fields, and Coulomb's law.

• YouTube
• 23 minutes
• Self-Paced
• Free Video