Jan Mikusinski's Books

An Introduction To Analysis

By: Piotr Mikusinski,Jan Mikusinski

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The book contains a rigorous exposition of calculus of a single real variable. It covers the standard topics of an introductory analysis course, namely, functions, continuity, differentiability, sequences and series of numbers, sequences and series of functions, and integration. A direct treatment of the Lebesgue integral, based solely on the concept of absolutely convergent series, is presented, which is a unique feature of a textbook at this level. The standard material is complemented by topics usually not found in comparable textbooks, for example, elementary functions are rigorously defined and their properties are carefully derived and an introduction to Fourier series is presented as an example of application of the Lebesgue integral.The text is for a post-calculus course for students majoring in mathematics or mathematics education. It will provide students with a solid background for further studies in analysis, deepen their understanding of calculus, and provide sound training in rigorous mathematical proof.

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Page Count

318

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9813202637

ISBN 13

9789813202634

Operational Calculus

By: Jan Mikusinski

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Operational Calculus

By: Jan Mikusinski

Pure and Applied Mathematics, Volume 109: Operational Calculus, Second Edition. Volume I presents the foundations of operational calculus and its applications to physics and engineering. This book introduces the operators algebraically as a kind of fractions. Organized into three parts, this volume begins with an overview of the concept as well as the characteristics of a convolution of continuous functions. This text then examines the transitivity, associativity, and distributivity of convolution with regard to addition. Other parts consider the methods of solving other difference equations, particularly in the field of electrical engineering, in which the variable runs over integer values only. This book discusses as well the solution of differential equations under given initial conditions. The final part deals with the characteristic properties of a derivative and provides the definition of algebraic derivative to any operators. This book is a valuable resource for physicists, electrical engineers, mathematicians, and research workers.

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324

Publisher

Elsevier

Published Date

ISBN 10

148327893X

ISBN 13

9781483278933

Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications (Second Edition)

By: Jan-frederik Mai,Matthias Scherer

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Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications (Second Edition)

By: Jan-frederik Mai,Matthias Scherer

The book remains a valuable tool both for statisticians who are already familiar with the theory of copulas and just need to develop sampling algorithms, and for practitioners who want to learn copulas and implement the simulation techniques needed to exploit the potential of copulas in applications.'Mathematical ReviewsThe book provides the background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for graduate and advanced undergraduate students with a firm background in stochastics. Besides the theoretical foundation, ready-to-implement algorithms and many examples make the book a valuable tool for anyone who is applying the methodology.

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Page Count

357

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#N/A

Published Date

ISBN 10

9813149264

ISBN 13

9789813149267

Simulating Copulas

Stochastic Models, Sampling Algorithms, and Applications

By: Jan-Frederik Mai,Matthias Scherer

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Simulating Copulas

Stochastic Models, Sampling Algorithms, and Applications

By: Jan-Frederik Mai,Matthias Scherer

This book provides the reader with a background on simulating copulas and multivariate distributions in general. It unifies the scattered literature on the simulation of various families of copulas (elliptical, Archimedean, Marshall-Olkin type, etc.) as well as on different construction principles (factor models, pair-copula construction, etc.). The book is self-contained and unified in presentation and can be used as a textbook for advanced undergraduate or graduate students with a firm background in stochastics. Alongside the theoretical foundation, ready-to-implement algorithms and many examples make this book a valuable tool for anyone who is applying the methodology.Errata(s)Errata (128 KB)

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Page Count

310

Publisher

World Scientific

Published Date

ISBN 10

1848168748

ISBN 13

9781848168749

Stochastic Geometry

Selected Topics

By: Viktor Benes,Jan Rataj

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Stochastic Geometry

Selected Topics

By: Viktor Benes,Jan Rataj

Stochastic geometry, based on current developments in geometry, probability and measure theory, makes possible modeling of two- and three-dimensional random objects with interactions as they appear in the microstructure of materials, biological tissues, macroscopically in soil, geological sediments etc. In combination with spatial statistics it is used for the solution of practical problems such as the description of spatial arrangements and the estimation of object characteristics. A related field is stereology, which makes possible inference on the structures, based on lower-dimensional observations. Unfolding problems for particle systems and extremes of particle characteristics are studied. The reader can learn about current developments in stochastic geometry with mathematical rigor on one hand and find applications to real microstructure analysis in natural and material sciences on the other hand.

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Page Count

231

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402081030

ISBN 13

9781402081033

Operational Calculus

By: Jan Mikusinski

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Operational Calculus

By: Jan Mikusinski

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324

Publisher

Elsevier

Published Date

ISBN 10

148327893X

ISBN 13

9781483278933

An Introduction to Analysis

From Number to Integral

By: Jan Mikusiński,Piotr Mikusiński

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An Introduction to Analysis

From Number to Integral

By: Jan Mikusiński,Piotr Mikusiński

Based on the lifetime work of leading teacher and researcher Jan Mikusiński, this classroom-tested book provides a thorough grounding in mathematical analysis, calculus and mathematical proofing. It introduces natural numbers through a new mathematical approach; replaces the Riemann integral with the more general Lebesgue integral; and rigorously develops the real number system from four simple axioms of natural numbers. Additional features include a wider range of problems than other texts--including simple and routine as well as problems requiring more in depth creativity, answers to common questions, a new approach to the concept of equivalence relation which simplifies the construction of real numbers, and a large number of computational applications.

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Page Count

290

Published Date

ISBN 10

0471599778

ISBN 13

9780471599777

Book's by Jan Mikusinski

An Introduction To Analysis

An Introduction To Analysis

Operational Calculus

Operational Calculus

Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications (Second Edition)

Simulating Copulas: Stochastic Models, Sampling Algorithms, And Applications (Second Edition)

Simulating Copulas

Simulating Copulas

Stochastic Geometry

Stochastic Geometry

Operational Calculus

Operational Calculus

An Introduction to Analysis

An Introduction to Analysis

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