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Calculus of variations deals with extremizing functionals, as opposed to ordinary calculus which deals with functions. Harmonic analysis deals with Fourier series and their abstractions. Geometric analysis involves the use of geometrical methods in the study of partial differential equations and the application of the theory of partial differential equations to geometry. Clifford analysis, the study of Clifford valued functions that are annihilated by Dirac or Dirac-like operators, termed in general as monogenic or Clifford analytic functions. p-adic analysis, the study of analysis within the context of p-adic numbers, which differs in some interesting and surprising ways from its real and complex counterparts. Non-standard analysis, which investigates the hyperreal numbers and their functions and gives a rigorous treatment of infinitesimals and infinitely large numbers. Computable analysis, the study of which parts of analysis can be carried out in a computable manner. Stochastic calculus – analytical notions developed for stochastic processes. Set-valued analysis – applies ideas from analysis and topology to set-valued functions. Convex analysis, the study of convex sets and functions. Tropical analysis (or idempotent analysis) – analysis in the context of the semiring of the max-plus algebra where the lack of an additive inverse is compensated somewhat by the idempotent rule A + A = A. When transferred to the tropical setting, many nonlinear problems become linear.[18] |
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