Storm-Louville Series | Expansion of a Function in a Series of Orthonormal Function (1)

In this video we bring the Sturm-Liouville series together — we use the orthonormal eigenfunctions we built in Part 3 to expand an arbitrary function f(x) as a generalised Fourier series.

This is where the theory pays off. Once you have an orthonormal system, computing the expansion coefficients becomes a clean inner product calculation. We walk through the full process with a detailed worked example.

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WHAT YOU'LL LEARN IN THIS VIDEO
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✦ Representing f(x) as a series: f(x) = ∑ cₙ φₙ(x)
✦ Deriving the expansion coefficients: cₙ = ∫ f(x) φₙ(x) w(x) dx
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PREREQUISITES
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• Part 1: Solving a Sturm-Liouville Problem
• Part 2: Orthogonal Systems
• Part 3: Orthonormal Systems (watch first)

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STURM-LIOUVILLE SERIES
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Part 1 → Solving a Sturm-Liouville Problem
Part 2 → Orthogonal Systems
Part 3 → Orthonormal Systems
Part 4 → You are here
More series coming soon — subscribe so you don't miss it.

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ABOUT THIS CHANNEL
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Math with Algephile is dedicated to university-level mathematics — Calculus, Algebra, Geometry, Number Theory, and Statistics. Every video is built around deep understanding, not just exam tricks.

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Видео Storm-Louville Series | Expansion of a Function in a Series of Orthonormal Function (1) канала Math With Algephile