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But what is a Fourier series? From heat flow to drawing with circles | DE4

A 25-minute video by 3Blue1Brown about transforms and signals, computing mechanisms and mathematical reasoning, on the Mathematics shelf. It came up in 2 Reddit threads, in r/ElectricalEngineering. It is pitched at intermediate level.

3Blue1Brown, Video, 25 min, 2019, on the Mathematics shelf

Fourier series, from the heat equation epicycles.

Study notes

Intermediate, Derivation. Step 9 of 13 in The mathematics of change and signals

Helpful first

• Sine and cosine
• Basic derivatives

What it builds

• Build complicated behaviour from rotating vectors.
• Treat sine-wave decomposition as a special case.
• Use linearity to solve the heat equation with simple solutions.

Useful moments

• 1:31Drawing with rotating vectors
• 2:11Context in the heat-equation series
• 3:10Why linear equations combine solutions

Check yourself: Why does linearity let simple solutions combine into a solution of the heat equation?

Next in the path: But what is a convolution?

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