Fourier Series as Basis Functions
How the Fourier Series act as Basis Functions in Function Space $L^2[-\pi,\pi]$
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Math
8 Lessons
No Holes Allowed! What's a Complete Space?
When Cauchy Sequences Converge we get no Holes!
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Closed, Open, Clopen
What's a Clopen? Open Sets, Closure, Closed Sets, Clopen Sets, & Connected Sets
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Metric Space vs Inner Product Space
Introductory Comparison & Definitions of a Metric Space vs an Inner Product Space
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The Euler–Lagrange Equation, Derived
From Shortest Paths to a General Optimization Principle for Functionals
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Derivatives of Functions vs. Derivatives of Functionals
How do you take a derivative of a functional? $dF[f]$
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Fun with Functionals
Introduction to Functionals: $F: f \rightarrow F[f] \in \mathbb{R}$
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