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Integral Equations and Integral Transforms
This comprehensive textbook on linear integral equations and integral transforms is aimed at senior undergraduate and graduate students of...
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Indefinite Integral
The concepts of the antiderivative and the indefinite integral are introduced. Integration methods (by substitution, by parts and by decomposition...
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Definite Integral
The definite integral is defined and examples of definite integration by substitution are given. Integration of even, odd and periodic functions is...
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Integral Equations
Integral equations appear in the descriptions of the processes in electrical circuits, in the models of materials deformation, and in the theory of...
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Riemann- und Lebesgue-Integral
Im vorliegenden Kapitel wird ein gewisser Abschluss der eindimensionalen Analysis erreicht. Das Riemann-Integral wird definiert und seine...
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Das Integral
Das Integral einer nichtnegativen Funktion beschreibt den Inhalt der Fläche zwischen dem Graphen der Funktion und der reellen Achse. Wir definieren...
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The Lebesgue Integral
The previous chapters concerned what one may call the basic “calculus of probability”, that is, the acquisition of the skills that suffice to deal...
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Abel Integral Equations
The simplest form of the Abel integral equation is given by $$\int _{0}^{x}\frac{\phi...
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Integral Representations and Integral Identities
Working in the complex plane, in §1.1 we prove versions of the classical Cauchy-Pompeiu integral representation formula, Morera’s Theorem, the...
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Das Lebesgue-Integral
Kapitel 8 ist dem (mehrdimensionalen) Lebesgue-Integral gewidmet. Nach den Vorarbeiten des fünften Kapitels kommt es sehr schnell zu den typisch...
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The Integral
In this chapter we extend the theory of the integral to functions of several variables defined on subsets of...
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Das Riemannsche Integral
Die Integration ist neben der Differentiation die wichtigste Anwendung des Grenzwertbegriffs in der Analysis. Wir definieren das Integral zunächst...
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Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters
Derivatives with respect to the parameters of the integral Mittag-Leffler function and the integral Wright function, recently introduced by us, are...
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Das Riemann-Integral
In diesem Kapitel wollen wir das Riemann-Integral einer Funktion f : [a; b] → ℝ einführen.
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Quaternionic Integral Transforms A Machine-Generated Literature Overview
This book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which...
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New types of general single/multiple integral inequalities
By introducing some concepts such as multiple integral inner product (MIIP) and multiple integral inner product space (MIIPS), new series of...
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Solvability of Quasilinear Integral–Algebraic Equations
We study quasilinear systems of integral equations that are linear with respect to the principal part and nonlinear with respect to the integral...
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The Stochastic Integral
In this chapter, Itô’s stochastic integral and some of its basic properties are carefully introduced. The essential role of martingale theory is made...
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Hypercomplex Cauchy-Type Integral
In this chapter, we consider a certain hypercomplex Cauchy-type integral taking values in a three-dimensional harmonic algebra with two-dimensional...