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BARAKA ALLAH FIKA
Analysis
has its beginnings in the rigorous formulation of calculus. It is the branch of mathematics most explicitly concerned with the notion of a limit, whether the limit of a sequence or the limit of a function.[1] It also includes the theories of differentiation, integration and measure, infinite series[2], and analytic functions. These theories are often studied in the context of real numbers, complex numbers, and real and complex 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 includes the following subfields
Real analysis
the rigorous study of derivatives and integrals of functions of real variables. This includes the study of sequences and their limits, series, and measures.
Functional analysis
studies spaces of functions and introduces concepts such as Banach spaces and Hilbert spaces.
Harmonic analysis
deals with Fourier series and their abstractions.
Complex analysis
the study of functions from the complex plane to the complex plane which are complex differentiable.
Differential geometry and topology, the application of calculus to abstract mathematical spaces that possess a complicated internal structure.
p-adic analysis
the study of analysis within the context of p-adic numbers, which differs in some interesting and surprising ways from its real and complex counterparts.
Non-standard analysis
which investigates the hyperreal numbers and their functions and gives a rigorous treatment of infinitesimals and infinitely large numbers. It is normally classed as model theory.
Numerical analysis
the study of algorithms for approximating the problems of continuous mathematics.
Classical analysis would normally be understood as any work not using functional analysis techniques, and is sometimes also called hard analysis; it also naturally refers to the more traditional topics. The study of differential equations is now shared with other fields such as dynamical systems, though the overlap with conventional analysis is large
رد : Analysis and some books
Real Analysis
(3rd Edition)
by Halsey RoydenThe publisher, Prentice-Hall Engineering/Science/MathematicsThis is the classic introductory graduate text. Product DetailsHardcover: 434 pages Publisher: Prentice Hall; 3 edition(February 12, 1988) Language: English ISBN-10: 0024041513 ISBN-13: 978-0024041517 Product Dimensions: 9.3 x 6.3 x 1.6 inches Shipping Weight: 2.1 pounds
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