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Analysis 𓆩⚪𓆪｜Definition｜1st｜20251119205401-00-⌔
Mathematical analysis - Wikipedia
Mathematical analysis
Mathematical analysis is the branch of mathematics concerned with the quantitative study of change, motion, functions, and limiting processes.1 It grew out of calculus, especially the use of derivatives and integrals to study variable quantities, and in the 19th century its foundations were reformulated with greater rigor. Basic objects of study in mathematical analysis include the real numbers, functions, sequences, series, and limits. Analysis has remained closely connected with applications in the sciences, where it is used to study equations, approximate one object by another, and estimate the accuracy of such approximations.
Modern analysis studies these questions in many settings, including Euclidean spaces, metric spaces, topological spaces, measure spaces, and function spaces. Its major areas include complex analysis, functional analysis, measure theory, harmonic analysis, and the theory of ordinary and partial differential equations.
Printed 2026-06-28.
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Link to original Footnotes
Lavrent’ev, M. A.; Nikol’skii, S. M. (1963). “Analysis”. In Aleksandrov, A. D.; Kolmogorov, A. N.; Lavrent’ev, M. A. (eds.). Mathematics: Its Content, Methods, and Meaning. Vol. 1. Translated by Gould, S. H.; Bartha, T. Cambridge, Massachusetts: MIT Press. pp. 65–180. ↩
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