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

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

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

IISER Pune;  NPTEL

Probabilistic Methods in PDE

Explore probabilistic methods in PDEs, bridging pure and applied mathematics. Learn stochastic calculus, Ito's formula, Feynman-Kac formula, and applications to finance and physics. Ideal for advanced researchers and doctoral students.

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

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

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

Mathematics III

Explore advanced mathematical concepts including ODEs, improper integrals, series solutions, Bessel functions, Laplace transformations, and partial differential equations.

• YouTube
• 18 hours
• On-Demand
• Free Video

Partial Differential Equations

Explore partial differential equations through various methods, including characteristic, coordinate, and transform approaches. Learn to solve wave and heat equations using advanced techniques.

• YouTube
• 8 hours
• On-Demand
• Free Video

Partial Differential Equations

Explore advanced mathematical concepts including Laplace equations, convolution, polar coordinates, and more. Master techniques for solving complex differential equations and their applications.

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

Let's Code Physics

Introduction to Difference Equations - Computational Quantum Mechanics Part 1

Transform differential equations into difference equations for computer-based quantum mechanics study. Explore this process using the heat equation and learn to create visualizations with VPython.

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

Hausdorff Center for Mathematics

A Gradient Flow Approach to Kinetic Equations

Gradient flow approach to linear kinetic equations, exploring entropy dissipation inequality and large deviation principles. Discusses potential extensions to non-linear cases and connections to Markov chains.

• YouTube
• 58 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