13 Facts About Mathematical analysis

Mathematical analysis formally developed in the 17th century during the Scientific Revolution, but many of its ideas can be traced back to earlier mathematicians.

Early results in Mathematical analysis were implicitly present in the early days of ancient Greek mathematics.

Real Mathematical analysis began to emerge as an independent subject when Bernard Bolzano introduced the modern definition of continuity in 1816, but Bolzano's work did not become widely known until the 1870s.

Much of Mathematical analysis happens in some metric space; the most commonly used are the real line, the complex plane, Euclidean space, other vector spaces, and the integers.

Real analysis is a branch of mathematical analysis dealing with the real numbers and real-valued functions of a real variable.

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Complex analysis is the branch of mathematical analysis that investigates functions of complex numbers.

Complex Mathematical analysis is particularly concerned with the analytic functions of complex variables.

Harmonic analysis is a branch of mathematical analysis concerned with the representation of functions and signals as the superposition of basic waves.

Harmonic Mathematical analysis has applications in areas as diverse as music theory, number theory, representation theory, signal processing, quantum mechanics, tidal Mathematical analysis, and neuroscience.

Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis (as distinguished from discrete mathematics).

Instead, much of numerical Mathematical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors.

Vector analysis is a branch of mathematical analysis dealing with values which have both magnitude and direction.

Scalar analysis is a branch of mathematical analysis dealing with values related to scale as opposed to direction.