Analysis

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).

Wolfram Web Resources