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数学分析=mathematical analysis>calulas Mathematical analysis includes the following subfields.
Differential equations Real analysis, the rigorous study of derivatives and integrals of functions of real variables. This includes the study of sequences and their limits, series. Multivariable calculus Real analysis on time scales - a unification of real analysis with calculus of finite differences Measure theory - given a set, the study of how to assign to each suitable subset a number, intuitively interpreted as the size of the subset. Vector calculus Functional analysis[6] studies spaces of functions and introduces concepts such as Banach spaces and Hilbert spaces. 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. Complex analysis, the study of functions from the complex plane to itself which are complex differentiable (that is, holomorphic). Several complex variables Hypercomplex analysis or Clifford analysis 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. It is normally classed as model theory. Numerical analysis, the study of algorithms for approximating the problems of continuous mathematics. 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. 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.[7] |
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