Titlebook: Real Analysis; Series, Functions of Miklós Laczkovich,Vera T. Sós Textbook 2017 Springer Science+Business Media LLC 2017 Continuity of func

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https://doi.org/10.1007/978-1-4939-7369-9Continuity of functions; History of Fourier series; History of infinite series; Limit of functions; Real

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Functions from , to ,,Consider a function ., where . is an arbitrary set, and let the coordinates of the vector .(.) be denoted by . for every .. In this way we define the functions ., where . for every .. We call . the .th . or . of ..

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The Jordan Measure,One of the main goals of mathematical analysis, besides applications in physics, is to compute the measure of sets (arc length, area, surface area, and volume).

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,Integrals of Multivariable Functions?I,The concept of the integral of a multivariable function arose as an attempt to solve some problems in mathematics, physics, and in science in general, similarly to the case of the integral of a single-variable function. We give an example from physics.

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,Integrals of Multivariable Functions?II,The notion of the line integral was motivated by some problems in physics. One of these problems is the computation of the work done by a force that changes while moving a point. The mathematical model describing the situation is the following.

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Miklós Laczkovich,Vera T. SósCorresponds to a second course in real analysis to follow the authors‘ book Real Analysis: Foundations and Functions of One Variable.Motivates ideas and results in analysis by exploring concepts and a

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