Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

Books Journals

Mathematical Physics with Partial Differential Equations

2nd Edition
February 26, 2018
James Kirkwood
English
Paperback
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eBook
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Mathematical Physics with Partial Differential Equations, Second Edition, is designed for upper division undergraduate and beginning graduate students taking mathematical physics taught out by math departments. The new edition is based on the success of the first, with a continuing focus on clear presentation, detailed examples, mathematical rigor and a careful selection of topics. It presents the familiar classical topics and methods of mathematical physics with more extensive coverage of the three most important partial differential equations in the field of mathematical physics—the heat equation, the wave equation and Laplace’s equation. The book presents the most common techniques of solving these equations, and their derivations are developed in detail for a deeper understanding of mathematical applications. Unlike many physics-leaning mathematical physics books on the market, this work is heavily rooted in math, making the book more appealing for students wanting to progress in mathematical physics, with particularly deep coverage of Green’s functions, the Fourier transform, and the Laplace transform. A salient characteristic is the focus on fewer topics but at a far more rigorous level of detail than comparable undergraduate-facing textbooks. The depth of some of these topics, such as the Dirac-delta distribution, is not matched elsewhere. New features in this edition include: novel and illustrative examples from physics including the 1-dimensional quantum mechanical oscillator, the hydrogen atom and the rigid rotor model; chapter-length discussion of relevant functions, including the Hermite polynomials, Legendre polynomials, Laguerre polynomials and Bessel functions; and all-new focus on complex examples only solvable by multiple methods.

The Cognitive Basis of Institutions

1st Edition
February 16, 2018
Shinji Teraji
English
Paperback
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eBook
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The Cognitive Basis of Institutions: A Synthesis of Behavioral and Institutional Economics synthesizes modern research in behavioral economics with traditional institutional economics. This work emphasizes that institution and agent are inextricably linked, and that both cognitive and institutional processes coalesce to influence human decision-making. It integrates cognition and institution through the behavioral economics theoretical lens of bounded rationality. Methodologically, it develops game-theoretical, complexity and neuroeconomic solutions to unite study of the two areas. The work concludes by proposing general implications for the economic study of decisions using the cognitive-institutional approach, also providing specific recommendations for public policy.

Advances in Computers

1st Edition
Volume 108
February 14, 2018
Atif Memon
English
Hardback
9 7 8 0 1 2 8 1 5 1 1 9 8
eBook
9 7 8 0 1 2 8 1 5 1 2 0 4

Advances in Computers, Volume 108, the latest volume in a series published since 1960, presents detailed coverage of innovations in computer hardware, software, theory, design and applications. This book provides contributors with a medium in which they can explore subjects in greater depth and breadth than similar topics in journal articles allow.

A Contemporary Study of Iterative Methods

1st Edition
February 13, 2018
A. Alberto Magrenan + 1 more
English
Paperback
9 7 8 0 1 2 8 0 9 2 1 4 9
eBook
9 7 8 0 1 2 8 0 9 4 9 3 8

A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand.

Nonlinear Differential Problems with Smooth and Nonsmooth Constraints

1st Edition
February 5, 2018
Dumitru Motreanu
English
Paperback
9 7 8 0 1 2 8 1 3 3 8 6 6
eBook
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Nonlinear Differential Problems with Smooth and Nonsmooth Constraints systematically evaluates how to solve boundary value problems with smooth and nonsmooth constraints. Primarily covering nonlinear elliptic eigenvalue problems and quasilinear elliptic problems using techniques amalgamated from a range of sophisticated nonlinear analysis domains, the work is suitable for PhD and other early career researchers seeking solutions to nonlinear differential equations. Although an advanced work, the book is self-contained, requiring only graduate-level knowledge of functional analysis and topology. Whenever suitable, open problems are stated and partial solutions proposed. The work is accompanied by end-of-chapter problems and carefully curated references.

Fundamentals of Advanced Mathematics V2

1st Edition
January 17, 2018
Henri Bourles
English
Hardback
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eBook
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The three volumes of this series of books, of which this is the second, put forward the mathematical elements that make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. Whereas the first volume focused on the formal conditions for systems of linear equations (in particular of linear differential equations) to have solutions, this book presents the approaches to finding solutions to polynomial equations and to systems of linear differential equations with varying coefficients. Fundamentals of Advanced Mathematics, Volume 2: Field Extensions, Topology and Topological Vector Spaces, Functional Spaces, and Sheaves begins with the classical Galois theory and the theory of transcendental field extensions. Next, the differential side of these theories is treated, including the differential Galois theory (Picard-Vessiot theory of systems of linear differential equations with time-varying coefficients) and differentially transcendental field extensions. The treatment of analysis includes topology (using both filters and nets), topological vector spaces (using the notion of disked space, which simplifies the theory of duality), and the radon measure (assuming that the usual theory of measure and integration is known). In addition, the theory of sheaves is developed with application to the theory of distributions and the theory of hyperfunctions (assuming that the usual theory of functions of the complex variable is known). This volume is the prerequisite to the study of linear systems with time-varying coefficients from the point-of-view of algebraic analysis and the algebraic theory of nonlinear systems.

Ulam Stability of Operators

1st Edition
January 4, 2018
Janusz Brzdek + 3 more
English
Paperback
9 7 8 0 1 2 8 0 9 8 2 9 5
eBook
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Ulam Stability of Operators presents a modern, unified, and systematic approach to the field. Focusing on the stability of functional equations across single variable, difference equations, differential equations, and integral equations, the book collects, compares, unifies, complements, generalizes, and updates key results. Whenever suitable, open problems are stated in corresponding areas. The book is of interest to researchers in operator theory, difference and functional equations and inequalities, differential and integral equations.

Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces

1st Edition
January 4, 2018
Abraham Ungar
English
Paperback
9 7 8 0 1 2 8 1 1 7 7 3 6
eBook
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Beyond Pseudo-Rotations in Pseudo-Euclidean Spaces presents for the first time a unified study of the Lorentz transformation group SO(m, n) of signature (m, n), m, n ∈ N, which is fully analogous to the Lorentz group SO(1, 3) of Einstein’s special theory of relativity. It is based on a novel parametric realization of pseudo-rotations by a vector-like parameter with two orientation parameters. The book is of interest to specialized researchers in the areas of algebra, geometry and mathematical physics, containing new results that suggest further exploration in these areas.

Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations

1st Edition
January 2, 2018
Gemma Robles + 1 more
English
Paperback
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eBook
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Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De Morgan negations. This book provides research on particular features of intuitionistic-type of negations in RM-semantics, while also defining the basic systems and many of their extensions by using models with or without a set of designated points.

Statistical Inference in Financial and Insurance Mathematics with R

1st Edition
November 22, 2017
Alexandre Brouste
English
Hardback
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eBook
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Finance and insurance companies are facing a wide range of parametric statistical problems. Statistical experiments generated by a sample of independent and identically distributed random variables are frequent and well understood, especially those consisting of probability measures of an exponential type. However, the aforementioned applications also offer non-classical experiments implying observation samples of independent but not identically distributed random variables or even dependent random variables. Three examples of such experiments are treated in this book. First, the Generalized Linear Models are studied. They extend the standard regression model to non-Gaussian distributions. Statistical experiments with Markov chains are considered next. Finally, various statistical experiments generated by fractional Gaussian noise are also described. In this book, asymptotic properties of several sequences of estimators are detailed. The notion of asymptotical efficiency is discussed for the different statistical experiments considered in order to give the proper sense of estimation risk. Eighty examples and computations with R software are given throughout the text.

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