Products related to Integrals:
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Irresistible Integrals : Symbolics, Analysis and Experiments in the Evaluation of Integrals
The problem of evaluating integrals is well known to every student who has had a year of calculus.It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages.In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics.The questions discussed in this book, first published in 2004, are as old as calculus itself.In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting, rather than the shortest, path to the results.Along the way, they illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics.This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.
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Theory of Stochastic Integrals
In applications of stochastic calculus, there are phenomena that cannot be analyzed through the classical Itô theory.It is necessary, therefore, to have a theory based on stochastic integration with respect to these situations. Theory of Stochastic Integrals aims to provide the answer to this problem by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales, such as Volterra Gaussian processes, or processes with bounded p-variation among which we can mention fractional Brownian motion and Riemann-Liouville fractional process. FeaturesSelf-contained treatment of the topicSuitable as a teaching or research tool for those interested in stochastic analysis and its applicationsIncludes original results.
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Theory of Stochastic Integrals
In applications of stochastic calculus, there are phenomena that cannot be analyzed through the classical Itô theory.It is necessary, therefore, to have a theory based on stochastic integration with respect to these situations. Theory of Stochastic Integrals aims to provide the answer to this problem by introducing readers to the study of some interpretations of stochastic integrals with respect to stochastic processes that are not necessarily semimartingales, such as Volterra Gaussian processes, or processes with bounded p-variation among which we can mention fractional Brownian motion and Riemann-Liouville fractional process. FeaturesSelf-contained treatment of the topicSuitable as a teaching or research tool for those interested in stochastic analysis and its applicationsIncludes original results.
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Measures, Integrals and Martingales
A concise yet elementary introduction to measure and integration theory, which are vital in many areas of mathematics, including analysis, probability, mathematical physics and finance.In this highly successful textbook, core ideas of measure and integration are explored, and martingales are used to develop the theory further.Other topics are also covered such as Jacobi's transformation theorem, the Radon–Nikodym theorem, differentiation of measures and Hardy–Littlewood maximal functions.In this second edition, readers will find newly added chapters on Hausdorff measures, Fourier analysis, vague convergence and classical proofs of Radon–Nikodym and Riesz representation theorems.All proofs are carefully worked out to ensure full understanding of the material and its background.Requiring few prerequisites, this book is suitable for undergraduate lecture courses or self-study.Numerous illustrations and over 400 exercises help to consolidate and broaden knowledge.Full solutions to all exercises are available on the author's webpage at www.motapa.de.This book forms a sister volume to René Schilling's other book Counterexamples in Measure and Integration (www.cambridge.org/9781009001625).
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What are improper integrals?
Improper integrals are integrals that cannot be evaluated using the standard methods due to one or both of the following reasons: the interval of integration is infinite, or the function being integrated is unbounded within the interval of integration. To evaluate improper integrals, we often use limits to approach the problematic points, such as infinity or a point of discontinuity, and then determine if the integral converges (has a finite value) or diverges (does not have a finite value). Improper integrals are important in various fields of mathematics and have applications in physics, engineering, and other sciences.
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What are multidimensional integrals?
Multidimensional integrals are integrals that involve functions of multiple variables. They are used to calculate the total accumulated effect of a function over a region in multiple dimensions. In other words, they represent the total "volume" or "area" of a function over a specified region in multiple dimensions. Multidimensional integrals are important in various fields such as physics, engineering, and economics, where the behavior of systems is often described by functions of multiple variables.
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What are indefinite integrals?
Indefinite integrals are a fundamental concept in calculus that represent the antiderivative of a function. They are used to find the general form of a function that, when differentiated, gives the original function. Indefinite integrals are denoted by the symbol ∫ and are used to represent the family of all possible antiderivatives of a given function. They are an essential tool in solving a wide range of problems in calculus, including finding areas under curves, determining the total change of a quantity, and solving differential equations.
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Gaussian Integrals and their Applications
Gaussian Integrals form an integral part of many subfields of applied mathematics and physics, especially in topics such as probability theory, statistics, statistical mechanics, quantum mechanics and so on.They are essential in computing quantities such as the statistical properties of normal random variables, solving partial differential equations involving diffusion processes, and gaining insight into the properties of particles.In Gaussian Integrals and their Applications, the author has condensed the material deemed essential for undergraduate and graduate students of physics and mathematics, such that for those who are very keen would know what to look for next if their appetite for knowledge remains unsatisfied by the time they finish reading this book. FeaturesA concise and easily digestible treatment of the essentials of Gaussian IntegralsSuitable for advanced undergraduates and graduate students in mathematics, physics, and statisticsThe only prerequisites are a strong understanding of multivariable calculus and linear algebra. Supplemented by numerous exercises (with fully worked solutions) at the end, which pertain to various levels of difficulty and are inspired by different fields in which Gaussian integrals are used.
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Table of Integrals, Series, and Products
The eighth edition of the classic Gradshteyn and Ryzhik is an updated completely revised edition of what is acknowledged universally by mathematical and applied science users as the key reference work concerning the integrals and special functions.The book is valued by users of previous editions of the work both for its comprehensive coverage of integrals and special functions, and also for its accuracy and valuable updates.Since the first edition, published in 1965, the mathematical content of this book has significantly increased due to the addition of new material, though the size of the book has remained almost unchanged.The new 8th edition contains entirely new results and amendments to the auxiliary conditions that accompany integrals and wherever possible most entries contain valuable references to their source.
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Elliptic and Hyperelliptic Integrals and Allied Theory
Originally published in 1938, this book focuses on the area of elliptic and hyperelliptic integrals and allied theory.The text was a posthumous publication by William Westropp Roberts (1850–1935), who held the position of Vice-Provost at Trinity College, Dublin from 1927 until shortly before his death.This book will be of value to anyone with an interest in the history of mathematics.
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Quantum Field Theory : From Operators to Path Integrals
A new, updated and enhanced edition of the classic work, which was welcomed for its general approach and self-sustaining organization of the chapters. Written by a highly respected textbook writer and researcher, this book has a more general scope and adopts a more practical approach than other books.It includes applications of condensed matter physics, first developing traditional concepts, including Feynman graphs, before moving on to such key topics as functional integrals, statistical mechanics and Wilson's renormalization group.The author takes care to explain the connection between the latter and conventional perturbative renormalization.Due to the rapid advance and increase in importance of low dimensional systems, this second edition fills a gap in the market with its added discussions of low dimensional systems, including one-dimensional conductors. All the chapters have been revised, while more clarifying explanations and problems have been added.A FREE SOLUTIONS MANUAL is available for lecturers from www.wiley-vch.de/textbooks.
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How do you complete integrals?
To complete integrals, you first need to identify the function you want to integrate. Then, you apply the rules of integration to find the antiderivative of the function. Once you have the antiderivative, you can evaluate it at the upper and lower limits of integration and subtract the lower limit value from the upper limit value to find the definite integral. If you are finding an indefinite integral, you simply add the constant of integration to the antiderivative.
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What are integrals in mathematics?
Integrals in mathematics are a fundamental concept in calculus that represent the accumulation of quantities over a continuous interval. They are used to find the area under a curve, the total change in a quantity, and the net accumulation of a function. Integrals can be calculated using various techniques such as Riemann sums, definite and indefinite integrals, and the fundamental theorem of calculus. They are essential for solving problems in physics, engineering, economics, and many other fields.
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What are parameters and integrals?
Parameters are variables that are used to represent specific values in a mathematical equation or model. They are often used to define the characteristics or properties of a system or function, and can be adjusted to analyze different scenarios or outcomes. Integrals, on the other hand, are mathematical tools used to calculate the area under a curve or the accumulation of a quantity over a given interval. They are a fundamental concept in calculus and are used to solve a wide range of problems in physics, engineering, and other fields. Integrals can be used to find the total distance traveled, the total amount of a substance in a system, or the total work done by a force, among other applications.
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How do indefinite integrals work?
Indefinite integrals are a way to find the antiderivative of a function. This means that we are looking for a function whose derivative is the original function we are integrating. When we find the indefinite integral of a function, we add a constant of integration (usually denoted as "+C") to account for all possible antiderivatives. This constant represents the family of functions that have the same derivative. In notation, the indefinite integral of a function f(x) is denoted as ∫f(x)dx, and it represents the set of all antiderivatives of f(x).
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