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The intuition behind Fourier and Laplace transforms I was never taught in school

An 18-minute video by Zach Star about transforms and signals and computing mechanisms, on the Mathematics shelf. It came up in 3 Reddit threads, in r/ElectricalEngineering and r/ECE. It is pitched at intermediate level.

Zach Star, Video, 18 min, 2019, on the Mathematics shelf

Study notes

Intermediate, Visual intuition. Step 11 of 13 in The mathematics of change and signals

Helpful first

• Functions
• Exponentials
• Basic integration

What it builds

• Interpret transform integrals as real and imaginary areas.
• Relate frequency ideas to exponential behaviour.
• Compare the questions answered by Fourier and Laplace transforms.

Useful moments

• 1:00Integrals as real and imaginary areas
• 13:52Connecting to the Laplace transform

Check yourself: What new type of behaviour becomes visible when a signal is described in transform space?

Next in the path: What does the Laplace Transform really tell us? A visual explanation (plus applications)

Notes are based on metadata, Reddit context and selected English caption passages. They are not a review of every claim in the video.