Uploaded March 2025 | Updated September 2026, 1 week ago
Fourier transform miracle
Welcome to the most important property of the Fourier transform. Namely the Fourier transform turns differentiation into multiplication, and therefore turns partial differential equations (hard) into algebra equations (much easier). Here we prove the derivative rule using a simple u-substitution and in a future video we will use this to solve the heat equation. This is similar in spirit to the Laplace transform, which helped us solve ordinary differential equations. This is a must-see for mathematicians, physicists, and engineers!
Fourier transform playlist: youtube.com/playlist?list=PLJb1qAQIrmmCgatSUjpLQWk1AmeZ0B5MI
What is the Fourier transform: youtu.be/o5jovJ4mkwI
Solving the heat equation: youtu.be/KpQTkHCfioY
Subscribe to my channel: youtube.com/drpeyam
Instagram: instagram.com/peyamstagram
Teespring merch: dr-peyam.creator-spring.com/?
Fourier transform miracle
Welcome to the most important property of the Fourier transform. Namely the Fourier transform turns differentiation into multiplication, and therefore turns partial differential equations (hard) into algebra equations (much easier). Here we prove the derivative rule using a simple u-substitution and in a future video we will use this to solve the heat equation. This is similar in spirit to the Laplace transform, which helped us solve ordinary differential equations. This is a must-see for mathematicians, physicists, and engineers!
Fourier transform playlist: youtube.com/playlist?list=PLJb1qAQIrmmCgatSUjpLQWk1AmeZ0B5MI
What is the Fourier transform: youtu.be/o5jovJ4mkwI
Solving the heat equation: youtu.be/KpQTkHCfioY
Subscribe to my channel: youtube.com/drpeyam
Instagram: instagram.com/peyamstagram
Teespring merch: dr-peyam.creator-spring.com/?
