A tutorial introduction to functional analysis for scientists and engineers
By
[Submitted on 2 Apr 2019 (v1), last revised 12 Apr 2019 (this version, v2)]
A good honest bake. Not flashy, but you'll finish the whole bagel.
Summary
This is a tutorial introduction to functional analysis mathematics tailored for scientists and engineers. It covers essential topics from sets and sequences of real numbers through Hilbert spaces, compact operators, Hilbert-Schmidt operators, eigenfunctions, and singular-value decomposition. The article aims to provide a readable, self-contained, and mathematically complete treatment that bridges the gap between rigorous mathematical theory and practical application in physical problems such as waves in continuous media. Longer proofs are relegated to a separate section to maintain narrative flow and motivation.
Key quotes
· 5 pulledFunctional analysis takes us beyond finite matrices, allowing us to work with infinite sets of continuous functions.
It resolves important issues, such as whether, why and how we can practically reduce such problems to finite matrix approximations.
It is, however, difficult to find a readable introduction that is efficient and comprehensible for scientists and engineers.
This article is written in a style that is complementary to that of standard mathematical treatments; by relegating longer proofs to a separate section, I have attempted to retain a clear narrative flow and motivation in developing the mathematical structure.
Hopefully, the result is useful to a broader readership who need to understand this mathematics, especially in physical science and engineering.
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