Part of the multi-volume work Analysis with MathematicaR
In the series De Gruyter Textbook
This book is devoted to applications: differential equations, elements of special functions and differential geometry of curves and surfaces with a specific focus on visualization in MathematicaR. Discusses how MathematicaR can be used as an aid in solving mathematical problems and discovering a solution. A complete tutorial provides the background needed for understanding the examples and how to compute in MathematicaR.
This book focusses on applications of Mathematica in differential geometry and differential equations. Students learn how to solve mathematical problems with a computer algebra system. Contains a vast collection of worked-out examples.
Frontmatter
Publicly Available I
Preface
Publicly Available V
Contents
Publicly Available VII
1 Graphics in MathematicaR
Requires Authentication 1
2 Regions in MathematicaR
Requires Authentication 49
3 Differential equations
Requires Authentication 71
4 Differential geometry of curves and surfaces in MathematicaR
Requires Authentication 89
5 Elements of the theory of special functions
Requires Authentication 197
6 Elliptic functions
Requires Authentication 215
7 Elements of complex analysis
Requires Authentication 241
Bibliography
Requires Authentication 263
Index
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Volume 66 in the series De Gruyter Studies in Mathematics
Noncommutative geometry studies an interplay between spatial forms and algebras with non-commutative multiplication. This book covers the key concepts of noncommutative geometry and its applications in topology, algebraic geometry, and number theory. Our presentation is accessible to the graduate students as well as nonexperts in the field. The second edition includes two new chapters on arithmetic topology and quantum arithmetic.
An authoritative introductory treatment of noncommutative geometry now in its second edition.
A novel approach using functors is presented in detail.
Covers applications of the theory in topology, algebraic geometry, and number theory.
Author information
Igor V. Nikolaev, St. John’s University, USA.
Algebra and Number Theory
Geometry and Topology
Mathematics
In the series De Gruyter Proceedings in Mathematics
This volume is dedicated to the work of three leading mathematicians in combinatoric game theory, Elwyn Berlekamp, John Conway, and Richard Guy and includes 20 contributions from colleagues reflecting on their work.
Original contributions by leading experts in combinatoric game theory.
Commemorates the work done by Professors‘ Berlekamp, Conway and Guy.
Of interest to researchers and graduate students working in combinatoric game theory
Author information
R. Nowakowski, B. Landman, F. Luca, Nathanson, J. Ne?etril, A. Robertson
Algebra and Number Theory
Combinatorics and Graph Theory
Discrete Mathematics
Mathematics
In the series De Gruyter Series in Applied and Numerical MathematicsAbout
this book
This reference contains a comprehensive summary of recent methods beyond Navier-Stokes for computation of rarefied flows in continuum-transition regimes. Coverage includes descriptions and solutions for Burnett, and Grad’s moment equations, and description and solutions of classical and generalized Boltzmann equations.
Provides a complete summary of recent methods beyond Navier-Stokes for computation of rarefied flows in continuum-transition regime.
Aeronautics & Astronautics
Applied Mathematics
Engineering
Fluid mechanics
Mathematics
Mechanical Engineering
Numerical and Computational Mathematics
Format: Paperback / softback, 294 pages, height x width: 235x155 mm, weight: 468 g, 9 Tables,
color; 9 Illustrations, color; 1 Illustrations, black and white; X, 294 p. 10 illus., 9 illus. in color.
Pub. Date: 21-Jun-2022
ISBN-13: 9783030726850
This book gives a complete spectral analysis of the non-self-adjoint Schroedinger operator with a periodic complex-valued potential. Building from the investigation of the spectrum and spectral singularities and construction of the spectral expansion for the non-self-adjoint Schroedinger operator, the book features a complete spectral analysis of the Mathieu-Schroedinger operator and the Schroedinger operator with a parity-time (PT)-symmetric periodic optical potential. There currently exists no general spectral theorem for non-self-adjoint operators; the approaches in this book thus open up new possibilities for spectral analysis of some of the most important operators used in non-Hermitian quantum mechanics and optics. Featuring detailed proofs and a comprehensive treatment of the subject matter, the book is ideally suited for graduate students at the intersection of physics and mathematics.
1. Spectral Theory for the Schroedinger Operator with a Complex-Valued Periodic Potential.-
2. On the Special Potentials.-
3. On the Matheiu-Schroedinger Operator.-
4. PT-Symmetric Periodic Optical Potential.- Index.
Format: Hardback, 595 pages, height x width: 235x155 mm, 31 Illustrations, black and white; VIII, 595 p. 31 illus.,
Pub. Date: 26-Sep-2022
ISBN-13: 9783031098970
This book gathers, in a beautifully structured way, recent findings on chain conditions in commutative algebra that were previously only available in papers. The majority of chapters are self-contained, and all include detailed proofs, a wealth of examples and solved exercises, and a complete reference list. The topics covered include S-Noetherian, S-Artinian, Nonnil-Noetherian, and Strongly Hopfian properties on commutative rings and their transfer to extensions such as polynomial and power series rings, and more. Though primarily intended for readers with a background in commutative rings, modules, polynomials and power series extension rings, the book can also be used as a reference guide to support graduate-level algebra courses, or as a starting point for further research.
Preface.- S-Noetherian Modules and Rings.- S-Artininian Rings and Modules.- Almost Principal Polynomial Rings.- The SFT and t-SFT rings.- Nonnil-Noetherian Rings.- Strongly Hopfian, Endo-Noetherian and Isonoetherian Rings.- Index.
Format: Hardback, 232 pages, height x width: 235x155 mm, 16 Illustrations, black and white; VIII, 232 p. 16 illus.,
Pub. Date: 11-Oct-2022
ISBN-13: 9783031105975
This textbook describes selected topics in functional analysis as powerful tools of immediate use in many fields within applied mathematics, physics and engineering. It follows a very reader-friendly structure, with the presentation and the level of exposition especially tailored to those who need functional analysis but don’t have a strong background in this branch of mathematics. For every tool, this work emphasizes the motivation, the justification for the choices made, and the right way to employ the techniques. Proofs appear only when necessary for the safe use of the results.
The book gently starts with a road map to guide reading. A subsequent chapter recalls definitions and notation for abstract spaces and some function spaces, while Chapter 3 enters dual spaces. Tools from Chapters 2 and 3 find use in Chapter 4, which introduces distributions. The Linear Functional Analysis basic triplet makes up Chapter 5, followed by Chapter 6, which introduces the concept of compactness. Chapter 7 brings a generalization of the concept of derivative for functions defined in normed spaces, while Chapter 8 discusses basic results about Hilbert spaces that are paramount to numerical approximations. The last chapter brings remarks to recent bibliographical items. Elementary examples included throughout the chapters foster understanding and self-study.
By making key, complex topics more accessible, this book serves as a valuable resource for researchers, students, and practitioners alike that need to rely on solid functional analysis but don’t need to delve deep into the underlying theory.
Road Map.- Basic Concepts.- Dual of a Normed Space.- Sobolev Spaces, Distributions.- The Three Basic Principles.- Compactness.- Function Derivatives in Normed Spaces.- Hilbert Bases and Approximations.
Format: Hardback, 580 pages, height x width: 235x155 mm, weight: 1051 g, 32 Illustrations, color; XVI, 580 p. 32 illus. in color.,
Series: Springer Series in Computational Mathematics 58
Pub. Date: 24-Jul-2022
ISBN-13: 9783031099502
Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.
Introduction.- Integration of Smooth Periodic Functions.- Constructions of Lattice Rules.- Modified Construction Schemes.- Discrepancy of Lattice Point Sets.- Extensible Lattice Point Sets.- Lattice Rules for Nonperiodic Integrands.- Intrgration with Respect to Probability Measures.- Integration of Analytic Functions.- Korobov's p-Sets.- Lattice Rules in the Randomized Setting.- Stability of Lattice Rules.- L2-Approximation Using Lattice Rules.- L -Approximation Using Lattice Rules.- Multiple Rank-1 Lattice Point Sets.- Fast QMC Matrix-Vector Multiplication.- Partial Diffeential Equations With Random Coefficients.- Numerical Experiments for Lattice Rule Construction Algorithms.- References.- Index.