Heat Equation Courses and Certifications

Steve Brunton

Deriving the Heat Equation - A Parabolic Partial Differential Equation for Heat Energy Conservation

Derive the one-dimensional heat equation from thermal-energy conservation and Fourier’s law for heat conduction in a thin metal rod.

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

Steve Brunton

Fourier Transform to Solve PDEs - 1D Heat Equation on Infinite Domain

Learn how the Fourier transform turns the 1D heat equation on an infinite rod into frequency-domain damping and spatial Gaussian smoothing.

• YouTube
• 43 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

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

Tom Rocks Maths

Oxford Calculus: How to Solve the Heat Equation

An undergraduate introduction to solving the heat equation through separable solutions.

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

Tom Rocks Maths

Oxford Calculus - Heat Equation Derivation

Derives the heat equation by balancing energy and heat flow in a thin rod, then extends the result to two and three dimensions.

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

Steve Brunton

Deriving the Heat Equation in 2D and 3D and in N Dimensions with Control Volumes and Vector Calculus

Derive the heat equation in two, three, and N dimensions using control volumes, Gauss’s theorem, and vector calculus.

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

Steve Brunton

Solving PDEs with the Laplace Transform - The Heat Equation

Solve the heat equation on a semi-infinite domain by transforming it in time with the Laplace transform, then enforcing initial and boundary conditions.

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

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

3Blue1Brown

But What Is a Fourier Series? From Heat Flow to Drawing With Circles

An animated introduction to complex Fourier series, showing how rotating vectors combine to draw shapes and connect to the heat equation.

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

3Blue1Brown

Differential Equations - A Tourist's Guide

Discover the fundamentals of differential equations through visual explanations, covering partial differential equations, heat equations, Fourier series, and Laplace transforms.

• YouTube
• 3 hours 17 minutes
• Self-Paced
• Free Video

Advanced Heat Conduction

Advanced analytical and numerical methods for modeling and solving steady and transient heat conduction problems across complex geometries, materials, and source conditions.

• Swayam
• 12 weeks
• Available until Oct 9, 2026
• Free Online Course

Let's Code Physics

Introduction to Difference Equations - Computational Quantum Mechanics Part 1

See how a differential equation can be recast as a difference equation for computer study, using the heat equation as an example.

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

Stochastic Calculus and Stochastic Differential Equations - Lecture 25

Explore Itô's formula and stochastic differential equations, covering Black-Scholes derivation, geometric Brownian motion, and Ornstein-Uhlenbeck processes in finance.

• YouTube
• 1 hour 21 minutes
• Self-Paced
• Free Video

Wolfram

Computational Egg-cellence - Nutritional Analysis, PDE Modeling and LLM Recipe Tools Using Eggs

Explore the intersection of food science and mathematics through egg cooking analysis, combining nutritional data, PDE modeling, and AI-powered recipe optimization using Wolfram Language.

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