The term analysis is used in two ways in mathematics. It describes both the discipline of which calculus is a part and one form of abstract
logic theory.

Analysis is the systematic study of real and complex-valued continuous functions. Important subfields of analysis include calculus,
differential equations, and functional
analysis. The term is generally reserved for advanced topics which are not encountered
in an introductory calculus sequence, although many ideas from those courses, such
as derivatives, integrals,
and series are studied in more detail. Real
analysis and complex analysis are two broad
subdivisions of analysis which deal with real-values and complex-valued functions,
respectively.

Derbyshire (2004, p. 16) describes analysis as "the study of limits."

Logicians often call second-order arithmetic "analysis." Unfortunately, this term conflicts with the more usual definition of analysis as the study of functions. This terminology problem is discussed briefly by Enderton (1972, p. 287).