Laplace's Equation Courses and Certifications

Steve Brunton

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

Explore numerical solutions to Laplace's Equation using MATLAB and get introduced to Fourier Series in this engineering mathematics lecture, with practical code examples and comprehensive notes provided.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Steve Brunton

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

Explore the analytic solution to Laplace's equation in 2D on a rectangle, enhancing your understanding of engineering mathematics and partial differential equations.

• YouTube
• 48 minutes
• On-Demand
• Free Video

Steve Brunton

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

Explore the powerful Separation of Variables technique for solving PDEs, focusing on Laplace's equation in 2D for steady-state heat distribution, with applications in physics and engineering.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Steve Brunton

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

Explore fundamental linear PDEs: wave, heat, and Laplace's equations. Gain insights into their properties, applications, and mathematical foundations in engineering and physics.

• YouTube
• 50 minutes
• On-Demand
• Free Video

Steve Brunton

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

Explore the derivation and equilibrium solution of the heat equation in 1D, including Laplace's equation, boundary conditions, and practical applications in engineering mathematics.

• YouTube
• 49 minutes
• On-Demand
• Free Video

Steve Brunton

Potential Flow and Laplace's Equation

Explore potential flow and Laplace's equation in engineering mathematics, covering vector fields, heat conduction, and practical applications in fluid dynamics and thermodynamics.

• YouTube
• 46 minutes
• On-Demand
• Free Video

Steve Brunton

Complex Analysis - Analytic Functions Solve Laplace's Equation

Explore how analytic complex functions' real and imaginary parts solve Laplace's equation, introducing harmonic functions in this in-depth mathematical analysis.

• YouTube
• 41 minutes
• On-Demand
• Free Video

IISc Bangalore;  NPTEL

First Course on Partial Differential Equations - I

Explore fundamental concepts of partial differential equations, including first-order equations, Laplace and Poisson equations, and 1D heat and wave equations. Ideal for mathematics, science, and engineering students.

• Swayam
• 8 weeks
• On-Demand
• Free Online Course

NPTEL;  IIT Bombay

Electromagnetic Theory

Comprehensive exploration of electromagnetic theory, covering fields, potentials, Maxwell's equations, waves, and applications in waveguides and radiation. Ideal for advanced physics students.

• YouTube
• 1 day 10 hours
• On-Demand
• Free Video

Steve Brunton

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

Explore multidimensional heat equations and the 2D Laplace equation on rectangles, advancing your understanding of engineering mathematics and partial differential equations.

• YouTube
• 47 minutes
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• 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
• On-Demand
• Free Video

Hausdorff Center for Mathematics

The Regularity Problem for the Laplace Equation in Rough Domains

Explores recent advances in Boundary Value Problems for the Laplace operator in rough domains, focusing on the equivalence between Dirichlet and regularity problem solvability.

• YouTube
• 42 minutes
• On-Demand
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities

Explore recent advancements in positive mass theorem for asymptotically flat manifolds with isolated conical singularities, covering spin and non-spin settings, analysis techniques, and Geroch-type results.

• YouTube
• 45 minutes
• On-Demand
• Free Video