Peter A. Jacobi's Books

Modular Forms: A Classical And Computational Introduction (2nd Edition)

By: Lloyd James Peter Kilford

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Modular Forms: A Classical And Computational Introduction (2nd Edition)

By: Lloyd James Peter Kilford

Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.

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252

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

1783265477

ISBN 13

9781783265473

Analytical Modelling in Parallel and Distributed Computing

By: Peter Hanuliak ,Michal Hanuliak

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Analytical Modelling in Parallel and Distributed Computing

By: Peter Hanuliak ,Michal Hanuliak

This publication examines complex performance evaluation of various typical parallel algorithms (shared memory, distributed memory) and their practical implementations. As real application examples we demonstrate the various influences during the process of modelling and performance evaluation and the consequences of their distributed parallel implementations.

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308

Publisher

Chartridge Books Oxford

Published Date

ISBN 10

1909287903

ISBN 13

9781909287907

Introduction to Heterocyclic Chemistry

By: Peter A. Jacobi

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Introduction to Heterocyclic Chemistry

By: Peter A. Jacobi

A unique approach to a core topic in organic chemistry presented by an experienced teacher to students and professionals Heterocyclic rings are present in the majority of known natural products, contributing to enormous structural diversity. In addition, they often possess significant biological activity. Medicinal chemists have embraced this last property in designing most of the small molecule drugs in use today. This book offers readers a fundamental understanding of the basics of heterocyclic chemistry and their occurrence in natural products such as amino acids, DNA, vitamins, and antibiotics. Based on class lectures that the author has developed over more than 40 years of teaching, it focuses on the chemistry of such heterocyclic substances and how they differ from carbocyclic systems. Introductory Heterocyclic Chemistry offers in-depth chapters covering naturally occurring heterocycles; properties of aromatic heterocycles; π-deficient heterocycles; π-excessive heterocycles; and ring transformations of heterocycles. It then offers an overview of 1,3-dipolar cycloadditions before finishing up with a back-to-basics section on nitriles and amidines. Presents a conversational approach to a fundamental topic in organic chemistry teaching Offers a unique look at this core organic chemistry topic via important naturally occurring and/or biologically active heterocycles Based on the author's many years of class lectures for teaching at the undergraduate and graduate level as well as pharmaceutical-industry courses Clear, concise, and accessible for advanced students of chemistry to gain a fundamental understanding of the basics of heterocyclic chemistry Introductory Heterocyclic Chemistry is an excellent text for undergraduate and graduate students as well as chemists in industrial environments in chemistry, pharmacy, medicinal chemistry, and biology.

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274

Publisher

John Wiley & Sons

Published Date

ISBN 10

1119417597

ISBN 13

9781119417590

Topics in Differential Geometry

By: Peter W. Michor

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Topics in Differential Geometry

By: Peter W. Michor

This book treats the fundamentals of differential geometry: manifolds, flows, Lie groups and their actions, invariant theory, differential forms and de Rham cohomology, bundles and connections, Riemann manifolds, isometric actions, and symplectic and Poisson geometry. It gives the careful reader working knowledge in a wide range of topics of modern coordinate-free differential geometry in not too many pages. A prerequisite for using this book is a good knowledge of undergraduate analysis and linear algebra."--BOOK JACKET.

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510

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821820036

ISBN 13

9780821820032

Extremal Riemann Surfaces

From the Proceedings of the AMS Special Session with Related Papers January 4-5, 1995, San Francisco, California

By: John R. Quine,Peter Sarnak

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Extremal Riemann Surfaces

From the Proceedings of the AMS Special Session with Related Papers January 4-5, 1995, San Francisco, California

By: John R. Quine,Peter Sarnak

Other papers deal with maximizing or minimizing functions defined by the spectrum such as the heat kernel, the zeta function, and the determinant of the Laplacian, some from the point of view of identifying an extremal metric.

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258

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American Mathematical Soc.

Published Date

ISBN 10

0821805142

ISBN 13

9780821805145

Geometric Properties Of Natural Operators Defined By The Riemann Curvature Tensor

By: Peter B Gilkey

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Geometric Properties Of Natural Operators Defined By The Riemann Curvature Tensor

By: Peter B Gilkey

A central problem in differential geometry is to relate algebraic properties of the Riemann curvature tensor to the underlying geometry of the manifold. The full curvature tensor is in general quite difficult to deal with. This book presents results about the geometric consequences that follow if various natural operators defined in terms of the Riemann curvature tensor (the Jacobi operator, the skew-symmetric curvature operator, the Szabo operator, and higher order generalizations) are assumed to have constant eigenvalues or constant Jordan normal form in the appropriate domains of definition.The book presents algebraic preliminaries and various Schur type problems; deals with the skew-symmetric curvature operator in the real and complex settings and provides the classification of algebraic curvature tensors whose skew-symmetric curvature has constant rank 2 and constant eigenvalues; discusses the Jacobi operator and a higher order generalization and gives a unified treatment of the Osserman conjecture and related questions; and establishes the results from algebraic topology that are necessary for controlling the eigenvalue structures. An extensive bibliography is provided. Results are described in the Riemannian, Lorentzian, and higher signature settings, and many families of examples are displayed.

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316

Publisher

World Scientific

Published Date

ISBN 10

9814490091

ISBN 13

9789814490092

The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds

By: Peter B. Gilkey

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The Geometry of Curvature Homogeneous Pseudo-Riemannian Manifolds

By: Peter B. Gilkey

Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and StanilovOCoTsankovOCoVidev theory.

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389

Publisher

Imperial College Press

Published Date

ISBN 10

1860948588

ISBN 13

9781860948589

Riemannian Geometry

By: Peter Petersen

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Riemannian Geometry

By: Peter Petersen

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with positive curvature; presentation of a new simplifying approach to the Bochner technique for tensors with application to bound topological quantities with general lower curvature bounds. From reviews of the first edition: "The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type." ―Bernd Wegner, ZbMATH

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512

Publisher

Springer

Published Date

ISBN 10

3319266543

ISBN 13

9783319266541

Weighted Polynomial Approximation and Numerical Methods for Integral Equations

By: Peter Junghanns,Giuseppe Mastroianni,Incoronata Notarangelo

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Weighted Polynomial Approximation and Numerical Methods for Integral Equations

By: Peter Junghanns,Giuseppe Mastroianni,Incoronata Notarangelo

The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.

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662

Publisher

Springer Nature

Published Date

ISBN 10

303077497X

ISBN 13

9783030774974

Exploring Numerical Methods

An Introduction to Scientific Computing Using MATLAB

By: Peter Linz,Richard Wang

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Exploring Numerical Methods

An Introduction to Scientific Computing Using MATLAB

By: Peter Linz,Richard Wang

Advanced Mathematics

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494

Publisher

Jones & Bartlett Learning

Published Date

ISBN 10

0763714992

ISBN 13

9780763714994

Computational Science - ICCS 2003. Part 3.

International Conference, Melbourne, Australia and St. Petersburg, Russia, June 2-4, 2003, Proceedings,

By: Peter Sloot

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Computational Science - ICCS 2003. Part 3.

International Conference, Melbourne, Australia and St. Petersburg, Russia, June 2-4, 2003, Proceedings,

By: Peter Sloot

The four-volume set LNCS 2657, LNCS 2658, LNCS 2659, and LNCS 2660 constitutes the refereed proceedings of the Third International Conference on Computational Science, ICCS 2003, held concurrently in Melbourne, Australia and in St. Petersburg, Russia in June 2003. The four volumes present more than 460 reviewed contributed and invited papers and span the whole range of computational science, from foundational issues in computer science and algorithmic mathematics to advanced applications in virtually all application fields making use of computational techniques. These proceedings give a unique account of recent results in the field.

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1183

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Springer Science & Business Media

Published Date

ISBN 10

3540401962

ISBN 13

9783540401964

Aspects of Differential Geometry I

By: Peter Gilkey,JeongHyeong Park,Ramón Vázquez-Lorenzo

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Aspects of Differential Geometry I

By: Peter Gilkey,JeongHyeong Park,Ramón Vázquez-Lorenzo

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. In Book I, we focus on preliminaries. Chapter 1 provides an introduction to multivariable calculus and treats the Inverse Function Theorem, Implicit Function Theorem, the theory of the Riemann Integral, and the Change of Variable Theorem. Chapter 2 treats smooth manifolds, the tangent and cotangent bundles, and Stokes' Theorem. Chapter 3 is an introduction to Riemannian geometry. The Levi-Civita connection is presented, geodesics introduced, the Jacobi operator is discussed, and the Gauss-Bonnet Theorem is proved. The material is appropriate for an undergraduate course in the subject. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the Chern-Gauss-Bonnet Theorem for pseudo-Riemannian manifolds with boundary is new. Table of Contents: Preface / Acknowledgments / Basic Notions and Concepts / Manifolds / Riemannian and Pseudo-Riemannian Geometry / Bibliography / Authors' Biographies / Index

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140

Publisher

Springer Nature

Published Date

ISBN 10

3031024079

ISBN 13

9783031024078

The Riemann Hypothesis in Characteristic p in Historical Perspective

By: Peter Roquette

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The Riemann Hypothesis in Characteristic p in Historical Perspective

By: Peter Roquette

This book tells the story of the Riemann hypothesis for function fields (or curves) starting with Artin's 1921 thesis, covering Hasse's work in the 1930s on elliptic fields and more, and concluding with Weil's final proof in 1948. The main sources are letters which were exchanged among the protagonists during that time, found in various archives, mostly the University Library in Göttingen. The aim is to show how the ideas formed, and how the proper notions and proofs were found, providing a particularly well-documented illustration of how mathematics develops in general. The book is written for mathematicians, but it does not require any special knowledge of particular mathematical fields.

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239

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Springer

Published Date

ISBN 10

3319990675

ISBN 13

9783319990675

A Mathematician and His Mathematical Work

Selected Papers of S.S. Chern

By: Shiing-Shen Chern,G. Tian,Peter Li

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A Mathematician and His Mathematical Work

Selected Papers of S.S. Chern

By: Shiing-Shen Chern,G. Tian,Peter Li

This volume is about the life and work of Shiing-Shen Chern (1911-), one of the leading mathematicians of this century. The book contains personal accounts by some friends, together with a summary of the mathematical works by Chern himself. Besides a selection of the mathematical papers the book also contains all his papers published after 1988.

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734

Publisher

World Scientific

Published Date

ISBN 10

9810223854

ISBN 13

9789810223854

The Geometry of Walker Manifolds

By: Peter Gilkey,Miguel Brozos-Vázquez,Eduardo Garcia-Rio,Stana Nikcevic

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The Geometry of Walker Manifolds

By: Peter Gilkey,Miguel Brozos-Vázquez,Eduardo Garcia-Rio,Stana Nikcevic

This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts: classical cosmological models (general relativity) and string theory to name but two. Walker manifolds appear naturally in numerous physical settings and provide examples of extremal mathematical situations as will be discussed presently. To describe the geometry of a pseudo-Riemannian manifold, one must first understand the curvature of the manifold. We shall analyze a wide variety of curvature properties and we shall derive both geometrical and topological results. Special attention will be paid to manifolds of dimension 3 as these are quite tractable. We then pass to the 4 dimensional setting as a gateway to higher dimensions. Since the book is aimed at a very general audience (and in particular to an advanced undergraduate or to a beginning graduate student), no more than a basic course in differential geometry is required in the way of background. To keep our treatment as self-contained as possible, we shall begin with two elementary chapters that provide an introduction to basic aspects of pseudo-Riemannian geometry before beginning on our study of Walker geometry. An extensive bibliography is provided for further reading. Math subject classifications : Primary: 53B20 -- (PACS: 02.40.Hw) Secondary: 32Q15, 51F25, 51P05, 53B30, 53C50, 53C80, 58A30, 83F05, 85A04 Table of Contents: Basic Algebraic Notions / Basic Geometrical Notions / Walker Structures / Three-Dimensional Lorentzian Walker Manifolds / Four-Dimensional Walker Manifolds / The Spectral Geometry of the Curvature Tensor / Hermitian Geometry / Special Walker Manifolds

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159

Publisher

Springer Nature

Published Date

ISBN 10

3031023978

ISBN 13

9783031023972

Aspects of Differential Geometry II

By: Peter Gilkey,JeongHyeong Park,Ramón Vázquez-Lorenzo

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Aspects of Differential Geometry II

By: Peter Gilkey,JeongHyeong Park,Ramón Vázquez-Lorenzo

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups and the Peter--Weyl Theorem are treated. In Chapter 7, material concerning homogeneous spaces and symmetric spaces is presented. Book II concludes in Chapter 8 where the relationship between simplicial cohomology, singular cohomology, sheaf cohomology, and de Rham cohomology is established. We have given some different proofs than those that are classically given and there is some new material in these volumes. For example, the treatment of the total curvature and length of curves given by a single ODE is new as is the discussion of the total Gaussian curvature of a surface defined by a pair of ODEs.

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143

Publisher

Springer Nature

Published Date

ISBN 10

3031024087

ISBN 13

9783031024085

Introduction to Parallel Computing

A practical guide with examples in C

By: Wesley Petersen,Peter Arbenz

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Introduction to Parallel Computing

A practical guide with examples in C

By: Wesley Petersen,Peter Arbenz

In the last few years, courses on parallel computation have been developed and offered in many institutions in the UK, Europe and US as a recognition of the growing significance of this topic in mathematics and computer science. There is a clear need for texts that meet the needs of students and lecturers and this book, based on the author's lecture at ETH Zurich, is an ideal practical student guide to scientific computing on parallel computers working up from a hardware instruction level, to shared memory machines, and finally to distributed memory machines. Aimed at advanced undergraduate and graduate students in applied mathematics, computer science, and engineering, subjects covered include linear algebra, fast Fourier transform, and Monte-Carlo simulations, including examples in C and, in some cases, Fortran. This book is also ideal for practitioners and programmers.

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278

Publisher

OUP Oxford

Published Date

ISBN 10

019151361X

ISBN 13

9780191513619

The Convenient Setting of Global Analysis

By: Andreas Kriegl,Peter W. Michor

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The Convenient Setting of Global Analysis

By: Andreas Kriegl,Peter W. Michor

This book lays the foundations of differential calculus in infinite dimensions and discusses those applications in infinite dimensional differential geometry and global analysis not involving Sobolev completions and fixed point theory. The approach is simple: a mapping is called smooth if it maps smooth curves to smooth curves. Up to Fr‚chet spaces, this notion of smoothness coincides with all known reasonable concepts. In the same spirit, calculus of holomorphic mappings (including Hartogs' theorem and holomorphic uniform boundedness theorems) and calculus of real analytic mappings are developed. Existence of smooth partitions of unity, the foundations of manifold theory in infinite dimensions, the relation between tangent vectors and derivations, and differential forms are discussed thoroughly. Special emphasis is given to the notion of regular infinite dimensional Lie groups. Many applications of this theory are included: manifolds of smooth mappings, groups of diffeomorphisms, geodesics on spaces of Riemannian metrics, direct limit manifolds, perturbation theory of operators, and differentiability questions of infinite dimensional representations.

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631

Publisher

American Mathematical Society

Published Date

ISBN 10

1470478935

ISBN 13

9781470478933

Applications of Affine and Weyl Geometry

By: Eduardo García-Río,Peter Gilkey,Stana Nikčević,Ramón Vázquez-Lorenzo

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Applications of Affine and Weyl Geometry

By: Eduardo García-Río,Peter Gilkey,Stana Nikčević,Ramón Vázquez-Lorenzo

Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannian extensions, and Kähler--Weyl geometry from this viewpoint. This book is intended to be accessible to mathematicians who are not expert in the subject and to students with a basic grounding in differential geometry. Consequently, the first chapter contains a comprehensive introduction to the basic results and definitions we shall need---proofs are included of many of these results to make it as self-contained as possible. Para-complex geometry plays an important role throughout the book and consequently is treated carefully in various chapters, as is the representation theory underlying various results. It is a feature of this book that, rather than as regarding para-complex geometry as an adjunct to complex geometry, instead, we shall often introduce the para-complex concepts first and only later pass to the complex setting. The second and third chapters are devoted to the study of various kinds of Riemannian extensions that associate to an affine structure on a manifold a corresponding metric of neutral signature on its cotangent bundle. These play a role in various questions involving the spectral geometry of the curvature operator and homogeneous connections on surfaces. The fourth chapter deals with Kähler--Weyl geometry, which lies, in a certain sense, midway between affine geometry and Kähler geometry. Another feature of the book is that we have tried wherever possible to find the original references in the subject for possible historical interest. Thus, we have cited the seminal papers of Levi-Civita, Ricci, Schouten, and Weyl, to name but a few exemplars. We have also given different proofs of various results than those that are given in the literature, to take advantage of the unified treatment of the area given herein.

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152

Publisher

Springer Nature

Published Date

ISBN 10

3031024052

ISBN 13

9783031024054

Guide to Scientific Computing

By: Peter R. Turner

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Guide to Scientific Computing

By: Peter R. Turner

This book introduces the reader to many of the problems of scientific computing and the wide variety of methods used for their solutions. It discusses basic approaches and stimulates an appreciation of the need for numerical methods in solving different types of problems. For each of the problems presented, the author provides some mathematical justification and examples. These serve as practical evidence and motivation for the reader to follow. Practical justification of the methods is provided through computer examples and exercises. The book includes an introduction to MATLAB, but the code used is not intended to exemplify sophisticated or robust pieces of software; it is purely illustrative of the method under discussion.

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314

Publisher

CRC Press

Published Date

ISBN 10

0849312426

ISBN 13

9780849312427

Applied Scientific Computing

With Python

By: Peter R. Turner,Thomas Arildsen,Kathleen Kavanagh

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Applied Scientific Computing

With Python

By: Peter R. Turner,Thomas Arildsen,Kathleen Kavanagh

This easy-to-understand textbook presents a modern approach to learning numerical methods (or scientific computing), with a unique focus on the modeling and applications of the mathematical content. Emphasis is placed on the need for, and methods of, scientific computing for a range of different types of problems, supplying the evidence and justification to motivate the reader. Practical guidance on coding the methods is also provided, through simple-to-follow examples using Python. Topics and features: provides an accessible and applications-oriented approach, supported by working Python code for many of the methods; encourages both problem- and project-based learning through extensive examples, exercises, and projects drawn from practical applications; introduces the main concepts in modeling, python programming, number representation, and errors; explains the essential details of numerical calculus, linear, and nonlinear equations, including the multivariable Newton method; discusses interpolation and the numerical solution of differential equations, covering polynomial interpolation, splines, and the Euler, Runge–Kutta, and shooting methods; presents largely self-contained chapters, arranged in a logical order suitable for an introductory course on scientific computing. Undergraduate students embarking on a first course on numerical methods or scientific computing will find this textbook to be an invaluable guide to the field, and to the application of these methods across such varied disciplines as computer science, engineering, mathematics, economics, the physical sciences, and social science.

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280

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Springer

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ISBN 10

3319895753

ISBN 13

9783319895758

Hypergeometric Orthogonal Polynomials and Their q-Analogues

By: Roelof Koekoek,Peter A. Lesky,René F. Swarttouw

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Hypergeometric Orthogonal Polynomials and Their q-Analogues

By: Roelof Koekoek,Peter A. Lesky,René F. Swarttouw

The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969–1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).

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584

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364205014X

ISBN 13

9783642050145

Log-Gases and Random Matrices (LMS-34)

By: Peter J. Forrester

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Log-Gases and Random Matrices (LMS-34)

By: Peter J. Forrester

Random matrix theory, both as an application and as a theory, has evolved rapidly over the past fifteen years. Log-Gases and Random Matrices gives a comprehensive account of these developments, emphasizing log-gases as a physical picture and heuristic, as well as covering topics such as beta ensembles and Jack polynomials. Peter Forrester presents an encyclopedic development of log-gases and random matrices viewed as examples of integrable or exactly solvable systems. Forrester develops not only the application and theory of Gaussian and circular ensembles of classical random matrix theory, but also of the Laguerre and Jacobi ensembles, and their beta extensions. Prominence is given to the computation of a multitude of Jacobians; determinantal point processes and orthogonal polynomials of one variable; the Selberg integral, Jack polynomials, and generalized hypergeometric functions; Painlevé transcendents; macroscopic electrostatistics and asymptotic formulas; nonintersecting paths and models in statistical mechanics; and applications of random matrix theory. This is the first textbook development of both nonsymmetric and symmetric Jack polynomial theory, as well as the connection between Selberg integral theory and beta ensembles. The author provides hundreds of guided exercises and linked topics, making Log-Gases and Random Matrices an indispensable reference work, as well as a learning resource for all students and researchers in the field.

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808

Publisher

Princeton University Press

Published Date

ISBN 10

1400835410

ISBN 13

9781400835416

Volterra-hamilton Models In The Ecology And Evolution Of Colonial Organisms

By: Peter L Antonelli

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Volterra-hamilton Models In The Ecology And Evolution Of Colonial Organisms

By: Peter L Antonelli

This book begins with the modeling of evolutionary constraints on morphological diversity in ecology and then extends to development and evolution. The authors have used tractable, traditional models and mathematics, and carefully linked traditional ecological equations with production and consumption. This book contains new, more powerful models and has applied them, for example, in chemical ecology of coral reef. The production space serves as an appropriate background space from which the environmentally induced curvature in the allometric relations of superorganisms such as siphonophores, polymorphic bryozoans and ants can be measured. Projective differential geometry is used to formula dynamical models of evolution by heterochrony and by symbiosis and a theory of stable and weakly chaotic production, important in ecology and in modeling the evolution of individuality is developed.

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227

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World Scientific

Published Date

ISBN 10

9814499706

ISBN 13

9789814499705

Interpolation Of Functions

By: J Szabados,Peter Vertesi

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Interpolation Of Functions

By: J Szabados,Peter Vertesi

This book gives a systematic survey on the most significant results of interpolation theory in the last forty years. It deals with Lagrange interpolation including lower estimates, fine and rough theory, interpolatory proofs of Jackson and Teliakovski-Gopengauz theorems, Lebesgue function, Lebesgue constant of Lagrange interpolation, Bernstein and Erdös conjecture on the optimal nodes, the almost everywhere divergence of Lagrange interpolation for arbitrary system of nodes, Hermite-Fejer type and lacunary interpolation and other related topics.

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Page Count

320

Publisher

World Scientific

Published Date

ISBN 10

9814507377

ISBN 13

9789814507370

Book's by Peter A. Jacobi

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