What area of Math do the following fall under?
1) Systems of ODEs and Phase planes
2) Laplace Transforms
3) Fourier series
4) PDEs with grad, div, curl, flux
2026-04-05 20:39:59.1775421599
Categorising types of Mathematics
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The links below are to the Mathematical Atlas. Most of these fall under the large area called analysis.
1) and 4) are (surprisingly?) differential equations. Maybe someone else can provide more insight than I can? As for div and curl, these can be studied in more generality in differential geometry.
2) The Laplace transform is a technique that is used both in differential equations as well as in probability theory.
3) Following the theme, Fourier series can be used in differential equations, but if you want to look deeper, Fourier analysis and harmonic analysis deal with the more theoretical questions like convergence criteria, existence/uniqueness, figuring out in which function spaces will the Fourier transform work, etc.