Following mathematics: the theory of partial differential equation,
variational calculus, Fourier analysis, potential theory, and
vector analysis are perhaps most closely associated with mathematical physics.
These were developed intensively from the second half of the 18th century
(by, for example, D'Alembert, Euler, and Lagrange) until the 1930s.
Physical applications of these developments include hydrodynamics,
celestial mechanics, continuum mechanics, elasticity theory, acoustics,
thermodynamics, electricity, magnetism, and aerodynamics.
The theory of atomic spectra (and, later, quantum mechanics)
developed almost concurrently with some parts of the mathematical fields
of linear algebra, the spectral theory of operators, operator algebras
and more broadly, functional analysis.
Nonrelativistic quantum mechanics includes Schrödinger operators,
and it has connections to atomic and molecular physics.
Quantum information theory is another subspecialty.
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