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Mathematics
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Definition of 'Analysis'


Definition: Analysis is a branch of mathematics which studies continuous changes and includes the theories of integration, differentiation, measure, limits, analytic functions and infinite series. It is the systematic study of real and complex-valued continuous functions. It describes both the discipline of which calculus is a part and one form of the abstract logic theory.

Description: There are two broad subdivisions of analysis named Real analysis and complex analysis, which deal with the real-values and the complex-valued functions respectively. Real Analysis: Real analysis is a branch of analysis that studies concepts of sequences and their limits, continuity, differentiation, integration and sequences of functions. It focuses on the real numbers, including positive and negative infinity to form the extended real line. It deals with functions of real variables and is most commonly used to distinguish that portion of calculus. It is natural to consider differentiable, smooth or harmonic functions in the real analysis, which is more widely applicable but may lack some more powerful properties that holomorphic functions have. Complex analysis: Complex analysis is the study of complex numbers together with their manipulation, derivatives and other properties. It is an extremely powerful tool which helps in providing a way of computing difficult integrals by investigating the singularities of the function near and between the limits of integration.
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