Heat Equation Courses and Certifications

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

Tom Rocks Maths

Oxford Calculus: How to Solve the Heat Equation

Learn to solve the Heat Equation, a fundamental PDE in calculus, with Oxford mathematician Dr Tom Crawford. Includes practice questions, interactive worksheets, and a free calculator app for comprehensive understanding.

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

Tom Rocks Maths

Oxford Calculus - Heat Equation Derivation

Comprehensive derivation of the Heat Equation from physical principles, including Liebniz Rule and Fourier's Law. Extends to 2D and 3D applications with interactive exercises for practice.

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

Steve Brunton

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

Comprehensive derivation of the heat equation, exploring its mathematical foundations and physical principles in thermal energy conservation and transfer.

• YouTube
• 24 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

Solving PDEs with the Laplace Transform - The Heat Equation

Learn to solve the heat equation using Laplace Transforms. Explore problem setup, transform application, ODE solutions, and boundary conditions. Gain insights into frequency and time domain solutions.

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

ICTP-SAIFR

Heat Equation: Introduction - Class 24

Dive into the heat equation with analytical and numerical tools in this comprehensive lecture by Oscar Reula, exploring fundamental concepts and applications.

• YouTube
• 1 hour 35 minutes
• On-Demand
• Free Video

Centrum Fizyki Teoretycznej PAN

Solutions of Heat Equation on Unitary Groups: Relation Between ϵ-nets and Approximate Unitary t-designs

Explore the improved relation between ϵ-nets and approximate unitary t-designs through heat equation solutions on unitary groups, with applications in quantum computation, information, and black hole physics.

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

Mathematical Methods for Engineers II

Explore advanced numerical methods for engineers, covering differential equations, network flows, and optimization. Gain practical skills in solving complex mathematical problems.

• MIT OpenCourseWare
• On-Demand
• Free Online Course

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

Dive into differential equations with MIT's Gilbert Strang and MathWorks' Cleve Moler, covering theory, MATLAB applications, and real-world examples from linear systems to chaos.

• MIT OpenCourseWare
• On-Demand
• Free Online Course

Steve Brunton

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

Explore solving the 1D heat equation on an infinite domain using Fourier transforms. Learn key concepts, inverse transforms, and physical properties in engineering mathematics.

• YouTube
• 43 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

3Blue1Brown

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

Explore Fourier series through heat flow and circular drawings, understanding complex mathematical concepts with engaging animations and clear explanations.

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

Steve Brunton

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

Explore the derivation of the heat equation in multiple dimensions using Gauss's theorem, control volumes, and vector calculus techniques for a comprehensive understanding of heat transfer.

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