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Mathematical analysis This article is about a branch of mathematics. The words "mathematical analysis" are also used to mean: the process or result of modeling and analyzing a phenomenon using mathematical techniques in general. Analysis is the branch of mathematics most explicitly concerned with the limit process or the concept of convergence. It includes the theories of differentiation integration and measure, infinite series , and analytic functions. These topics are often studied in the context of real numbers complex numbers , and their functions . However, they can also be defined and studied in any space of mathematical objects that is equipped with a definition of "nearness" (a topological space) or more specifically "distance" (a metric space). Mathematical analysis has its beginnings in the rigorous formulation of calculus History Greek mathematicians such as Eudoxus and Archimedes made informal use of the concepts of limits and convergence when they used the method of exhaustion to compute the area and volume of regions and solids. In India, the 12th century mathematician Bhaskara conceived of differential calculus, and gave examples of the

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Mathematical analysis Fnd Analysis is that branch of mathematics which deals with the real numbers and complex numbers and their functions . It has its beginnings in the rigorous formulation of calculus and studies concepts such as continuity integration and differentiability in general settings. The study of real analysis usually starts with simple proofs in elementary set theory , a clean definition of the concept of function, and an introduction to the natural numbers and the important proof technique of mathematical induction . Then the real numbers are either introduced axiomatically, or they are constructed from sequences of rational numbers . Initial consequences are derived, most importantly the properties of the absolute value such as the triangle inequality. The concept of convergence , central to analysis, is introduced via limits of sequences. Several laws governing the limiting process can be derived, and several limits can be computed. Infinite series , which are special sequences, are also studied at this point. Power series serve to cleanly define several central functions, such as the

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