David S. Lim's Books

Advanced Calculus

Second Edition

By: David V. Widder

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Classic text offers exceptionally precise coverage of partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Includes exercises and selected answers.

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548

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Courier Corporation

Published Date

ISBN 10

0486134660

ISBN 13

9780486134666

Liquid Metal Alloys in Electronics

By: David J. Fisher

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Liquid Metal Alloys in Electronics

By: David J. Fisher

Liquid metal alloys are of rapidly increasing interest in electronics because they combine the high electrical conductivity of metals with the ease of manipulation and reconfiguration of liquids. The book focuses on such issues as self-assembled monolayers, energy-harvesting, reconfigurable and flexible antennae, sensors, conformable electronics, the creation of non-wetting super-hydrophobic or super-lyophobic surfaces, vacuum-assisted infiltration techniques, development of microfluidics, deformable electrodes and wearable electronics. The book references 270 original resources and includes their direct web link for in-depth reading. Keywords: Liquid Metals, Gallium-Indium Alloys, Galinstan, EGaIn, Self-Assembled Monolayers, Energy-Harvesting, Reconfigurable Antennae, Sensors, Conformable Electrodes, Stretchable Wires and Interconnects, Self-Healing Circuits, Gallium-Lyophilic Surfaces, Wettability of Liquid Metal, Substrate Topology, Selective Wetting Deposition Technique, Gallium-Indium Droplets on Thin Metal Films, Substrate Texture upon Wetting, Dielectrophoresis, Microfluidics, Deformable Electrodes, Wearable Electronics, Flexible Antennae, Surface Oxidation of Alloys.

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138

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Materials Research Forum LLC

Published Date

ISBN 10

1644900696

ISBN 13

9781644900697

AP Calculus Premium, 2024: 12 Practice Tests + Comprehensive Review + Online Practice

By: David Bock,Dennis Donovan,Shirley O. Hockett

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AP Calculus Premium, 2024: 12 Practice Tests + Comprehensive Review + Online Practice

By: David Bock,Dennis Donovan,Shirley O. Hockett

For more than 80 years, BARRON's has been helping students achieve their goals. Prep for the AP® Calculus exam with trusted review from our experts.

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673

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Simon and Schuster

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ISBN 10

1506287832

ISBN 13

9781506287836

Spectral Theory of Infinite-Area Hyperbolic Surfaces

By: David Borthwick

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Spectral Theory of Infinite-Area Hyperbolic Surfaces

By: David Borthwick

This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constants for resonance bounds. A new chapter introduces recently developed techniques for resonance calculation that illuminate the existing results and conjectures on resonance distribution. The spectral theory of hyperbolic surfaces is a point of intersection for a great variety of areas, including quantum physics, discrete groups, differential geometry, number theory, complex analysis, and ergodic theory. This book will serve as a valuable resource for graduate students and researchers from these and other related fields. Review of the first edition: "The exposition is very clear and thorough, and essentially self-contained; the proofs are detailed...The book gathers together some material which is not always easily available in the literature...To conclude, the book is certainly at a level accessible to graduate students and researchers from a rather large range of fields. Clearly, the reader...would certainly benefit greatly from it." (Colin Guillarmou, Mathematical Reviews, Issue 2008 h)

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471

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Birkhäuser

Published Date

ISBN 10

3319338773

ISBN 13

9783319338774

Cracking the AP Calculus AB & BC Exams

By: David S. Kahn,Princeton Review (Firm)

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Cracking the AP Calculus AB & BC Exams

By: David S. Kahn,Princeton Review (Firm)

Provides a review of the relevant math topics, test-taking tips, and five practice tests with answers.

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895

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Princeton Review

Published Date

ISBN 10

0375429158

ISBN 13

9780375429156

A Basic Course in Complex Variables

By: David C. Kay

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A Basic Course in Complex Variables

By: David C. Kay

The calculus of real numbers can be extended to complex numbers, where the definitions and techniques one learns in calculus carry over to complex variables. David C. Kay, who has written several books geared for college students, explains this development in his new book. A short review of basic concepts from real variable calculus appears with each new topic. Differentiation and integration in complex variables is clearly explained, with numerical examples. Other topics include infinite series of complex variables, uniform convergence, the Taylor and Laurent series, and methods for evaluating difficult integrals. Charts, tables, and drawings throughout the book make even tough concepts easy to understand, and problems have been carefully crafted to cover the main concepts while maintaining your interest. Whether you're an educator seeking to provide an additional resource for your students or a student seeking a self-help guide to understand complex variables, the developmental in this book is a refreshing treatment that can be a stand-alone tutorial or companion guide to another textbook.

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207

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iUniverse

Published Date

ISBN 10

1491742666

ISBN 13

9781491742662

Classical Potential Theory

By: David H. Armitage,Stephen J. Gardiner

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Classical Potential Theory

By: David H. Armitage,Stephen J. Gardiner

A long-awaited, updated introductory text by the world leaders in potential theory. This essential reference work covers all aspects of this major field of mathematical research, from basic theory and exercises to more advanced topological ideas. The largely self-contained presentation makes it basically accessible to graduate students.

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343

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Springer Science & Business Media

Published Date

ISBN 10

1447102339

ISBN 13

9781447102335

Basic Partial Differential Equations

By: David. Bleecker

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Basic Partial Differential Equations

By: David. Bleecker

Methods of solution for partial differential equations (PDEs) used in mathematics, science, and engineering are clarified in this self-contained source. The reader will learn how to use PDEs to predict system behaviour from an initial state of the system and from external influences, and enhance the success of endeavours involving reasonably smooth, predictable changes of measurable quantities. This text enables the reader to not only find solutions of many PDEs, but also to interpret and use these solutions. It offers 6000 exercises ranging from routine to challenging. The palatable, motivated proofs enhance understanding and retention of the material. Topics not usually found in books at this level include but examined in this text: the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks convergence of numerical solutions of PDEs and implementation on a computer convergence of Laplace series on spheres quantum mechanics of the hydrogen atom solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.

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765

Publisher

CRC Press

Published Date

ISBN 10

1351078534

ISBN 13

9781351078535

Spectral Theory on the S-Spectrum for Quaternionic Operators

By: Fabrizio Colombo,Jonathan Gantner,David P. Kimsey

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Spectral Theory on the S-Spectrum for Quaternionic Operators

By: Fabrizio Colombo,Jonathan Gantner,David P. Kimsey

The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.

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357

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Springer

Published Date

ISBN 10

3030030741

ISBN 13

9783030030742

Lévy Processes and Stochastic Calculus

By: David Applebaum

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Lévy Processes and Stochastic Calculus

By: David Applebaum

Lévy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Lévy processes, then leading on to develop the stochastic calculus for Lévy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

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461

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Cambridge University Press

Published Date

ISBN 10

1139477986

ISBN 13

9781139477987

Numerical Range of Holomorphic Mappings and Applications

By: Mark Elin,Simeon Reich,David Shoikhet

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Numerical Range of Holomorphic Mappings and Applications

By: Mark Elin,Simeon Reich,David Shoikhet

This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L. A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.

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238

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Springer

Published Date

ISBN 10

3030050203

ISBN 13

9783030050207

The Convolution Transform

By: Isidore Isaac Hirschman,David V. Widder

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The Convolution Transform

By: Isidore Isaac Hirschman,David V. Widder

In studies of general operators of the same nature, general convolution transforms are immediately encountered as the objects of inversion. The relation between differential operators and integral transforms is the basic theme of this work. Discusses finite and non-finite kernels, variation diminishing transforms, asymptotic behavior of kernels, real inversion theory, representation theory, the Weierstrass transform, and complex inversion theory.

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290

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Courier Corporation

Published Date

ISBN 10

048644175X

ISBN 13

9780486441757

Fundamentals of Modern Mathematics

A Practical Review

By: David B. MacNeil

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Fundamentals of Modern Mathematics

A Practical Review

By: David B. MacNeil

Students and others wishing to know more about the practical side of mathematics will find this volume a highly informative resource. Accessible explanations of important concepts feature worked examples and diagrams. 1963 edition.

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322

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Courier Corporation

Published Date

ISBN 10

0486316149

ISBN 13

9780486316147

An Introduction to the Theory of Point Processes

Volume II: General Theory and Structure

By: D.J. Daley,David Vere-Jones

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An Introduction to the Theory of Point Processes

Volume II: General Theory and Structure

By: D.J. Daley,David Vere-Jones

This is the second volume of the reworked second edition of a key work on Point Process Theory. Fully revised and updated by the authors who have reworked their 1988 first edition, it brings together the basic theory of random measures and point processes in a unified setting and continues with the more theoretical topics of the first edition: limit theorems, ergodic theory, Palm theory, and evolutionary behaviour via martingales and conditional intensity. The very substantial new material in this second volume includes expanded discussions of marked point processes, convergence to equilibrium, and the structure of spatial point processes.

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591

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Springer Science & Business Media

Published Date

ISBN 10

0387498354

ISBN 13

9780387498355

The Theory of Algebraic Number Fields

By: David Hilbert

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The Theory of Algebraic Number Fields

By: David Hilbert

A translation of Hilberts "Theorie der algebraischen Zahlkörper" best known as the "Zahlbericht", first published in 1897, in which he provides an elegantly integrated overview of the development of algebraic number theory up to the end of the nineteenth century. The Zahlbericht also provided a firm foundation for further research in the theory, and can be seen as the starting point for all twentieth century investigations into the subject, as well as reciprocity laws and class field theory. This English edition further contains an introduction by F. Lemmermeyer and N. Schappacher.

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360

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Springer Science & Business Media

Published Date

ISBN 10

3662035456

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9783662035450

Advanced Calculus for Mathematical Modeling in Engineering and Physics

With Discrete and Numerical Analogies

By: David Stapleton

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Advanced Calculus for Mathematical Modeling in Engineering and Physics

With Discrete and Numerical Analogies

By: David Stapleton

Advanced Calculus for Mathematical Modeling in Engineering and Physics introduces the principles and methods of advanced calculus for mathematical modeling, through a balance of theory and application using a state space approach with elementary functional analysis. This framework facilitates a deeper understanding of the nature of mathematical models and of the behavior of their solutions. The work provides a variety of advanced calculus models for mathematical, physical science, and engineering audiences, with discussion of how calculus-based models and their discrete analogies are generated. This valuable textbook offers scientific computations driven by Octave/MATLAB script, in recognition of the rising importance of associated numerical models. - Adopts a state space/functional analysis approach to advanced calculus-based models to provide a better understanding of the development of models and the behaviors of their solutions - Uniquely includes discrete analogies to calculus-based models, as well as the derivation of many advanced calculus models of physics and engineering– instead of only seeking solutions to the models - Offers online teaching support for qualified instructors (for selected solutions) and study materials for students (MATLAB/Octave scripts)

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882

Publisher

Elsevier

Published Date

ISBN 10

0443222886

ISBN 13

9780443222887

Asymptotics of Elliptic and Parabolic PDEs

and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics

By: David Holcman,Zeev Schuss

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Asymptotics of Elliptic and Parabolic PDEs

and their Applications in Statistical Physics, Computational Neuroscience, and Biophysics

By: David Holcman,Zeev Schuss

This is a monograph on the emerging branch of mathematical biophysics combining asymptotic analysis with numerical and stochastic methods to analyze partial differential equations arising in biological and physical sciences. In more detail, the book presents the analytic methods and tools for approximating solutions of mixed boundary value problems, with particular emphasis on the narrow escape problem. Informed throughout by real-world applications, the book includes topics such as the Fokker-Planck equation, boundary layer analysis, WKB approximation, applications of spectral theory, as well as recent results in narrow escape theory. Numerical and stochastic aspects, including mean first passage time and extreme statistics, are discussed in detail and relevant applications are presented in parallel with the theory. Including background on the classical asymptotic theory of differential equations, this book is written for scientists of various backgrounds interested in deriving solutions to real-world problems from first principles.

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456

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Springer

Published Date

ISBN 10

3319768956

ISBN 13

9783319768953

AP Calculus Premium, 2022-2023: 12 Practice Tests + Comprehensive Review + Online Practice

By: David Bock,Dennis Donovan,Shirley O. Hockett

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AP Calculus Premium, 2022-2023: 12 Practice Tests + Comprehensive Review + Online Practice

By: David Bock,Dennis Donovan,Shirley O. Hockett

Be prepared for exam day with Barron’s. Trusted content from AP experts! Barron’s AP Calculus Premium: 2022-2023 includes in-depth content review and online practice for the AB and BC exams. It’s the only book you’ll need to be prepared for exam day. Written by Experienced Educators Learn from Barron’s--all content is written and reviewed by AP experts Build your understanding with comprehensive review tailored to the most recent exams Get a leg up with tips, strategies, and study advice for exam day--it’s like having a trusted tutor by your side Be Confident on Exam Day Sharpen your test-taking skills with 12 full-length practice tests--4 AB practice tests and 4 BC practice tests in the book, including a diagnostic AB test and a diagnostic BC test to target your studying--and 2 more AB practice tests and 2 more BC practice tests online Strengthen your knowledge with in-depth review covering all Units on the AP Calculus AB and BC Exams Reinforce your learning with multiple-choice practice questions at the end of each chapter Enhance your problem-solving skills with new and revised multiple-choice and free-response practice questions throughout the book, including a chapter filled with multiple-choice questions and a chapter devoted to free-response practice exercises Online Practice Continue your practice with 2 full-length AB practice tests and 2 full-length BC practice tests on Barron’s Online Learning Hub Simulate the exam experience with a timed test option Deepen your understanding with detailed answer explanations and expert advice Gain confidence with scoring to check your learning progress

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673

Publisher

Simon and Schuster

Published Date

ISBN 10

1506279597

ISBN 13

9781506279596

An Invitation to Variational Methods in Differential Equations

By: David G. Costa

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An Invitation to Variational Methods in Differential Equations

By: David G. Costa

This textbook introduces variational methods and their applications to differential equations to graduate students and researchers interested in differential equations and nonlinear analysis. It serves as a sampling of topics in critical point theory. Coverage includes: minimizations, deformations results, the mountain-pass and saddle-point theorems, critical points under constraints, and issues of compactness. Applications immediately follow each result for easy assimilation by the reader. This straightforward and systematic presentation includes many exercises and examples to motivate the study of variational methods.

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141

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Springer Science & Business Media

Published Date

ISBN 10

0817645365

ISBN 13

9780817645366

Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences

Theoretical Predictions Compared with Data

By: David J. Wollkind,Bonni J. Dichone

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Comprehensive Applied Mathematical Modeling in the Natural and Engineering Sciences

Theoretical Predictions Compared with Data

By: David J. Wollkind,Bonni J. Dichone

This text demonstrates the process of comprehensive applied mathematical modeling through the introduction of various case studies. The case studies are arranged in increasing order of complexity based on the mathematical methods required to analyze the models. The development of these methods is also included, providing a self-contained presentation. To reinforce and supplement the material introduced, original problem sets are offered involving case studies closely related to the ones presented. With this style, the text’s perspective, scope, and completeness of the subject matter are considered unique. Having grown out of four self-contained courses taught by the authors, this text will be of use in a two-semester sequence for advanced undergraduate and beginning graduate students, requiring rudimentary knowledge of advanced calculus and differential equations, along with a basic understanding of some simple physical and biological scientific principles.

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606

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Springer

Published Date

ISBN 10

3319735187

ISBN 13

9783319735184

Media Theory

Interdisciplinary Applied Mathematics

By: David Eppstein,Jean-Claude Falmagne,Sergei Ovchinnikov

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Media Theory

Interdisciplinary Applied Mathematics

By: David Eppstein,Jean-Claude Falmagne,Sergei Ovchinnikov

This book presents a mathematical structure modeling a physical or biological system that can be in any of a number of states. Each state is characterized by a set of binary features, and differs from some other neighbor state or states by just one of those features. The book considers the evolution of such a system over time and analyzes such a structure from algebraic and probabilistic (stochastic) standpoints.

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330

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Springer Science & Business Media

Published Date

ISBN 10

3540716971

ISBN 13

9783540716976

A Simple Definition of the Feynman Integral, with Applications

By: Robert Horton Cameron,David Arne Storvick

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A Simple Definition of the Feynman Integral, with Applications

By: Robert Horton Cameron,David Arne Storvick

This memoir presents a simple sequential definition of the Feynman integral which is applicable to a rather large class of functionals.

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American Mathematical Soc.

Published Date

ISBN 10

0821822888

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9780821822883

Spectral Theory

Basic Concepts and Applications

By: David Borthwick

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Spectral Theory

Basic Concepts and Applications

By: David Borthwick

This textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.

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339

Publisher

Springer Nature

Published Date

ISBN 10

3030380025

ISBN 13

9783030380021

Theory of Games and Statistical Decisions

By: David A. Blackwell,M. A. Girshick

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Theory of Games and Statistical Decisions

By: David A. Blackwell,M. A. Girshick

Evaluating statistical procedures through decision and game theory, as first proposed by Neyman and Pearson and extended by Wald, is the goal of this problem-oriented text in mathematical statistics. First-year graduate students in statistics and other students with a background in statistical theory and advanced calculus will find a rigorous, thorough presentation of statistical decision theory treated as a special case of game theory. The work of Borel, von Neumann, and Morgenstern in game theory, of prime importance to decision theory, is covered in its relevant aspects: reduction of games to normal forms, the minimax theorem, and the utility theorem. With this introduction, Blackwell and Professor Girshick look at: Values and Optimal Strategies in Games; General Structure of Statistical Games; Utility and Principles of Choice; Classes of Optimal Strategies; Fixed Sample-Size Games with Finite Ω and with Finite A; Sufficient Statistics and the Invariance Principle; Sequential Games; Bayes and Minimax Sequential Procedures; Estimation; and Comparison of Experiments. A few topics not directly applicable to statistics, such as perfect information theory, are also discussed. Prerequisites for full understanding of the procedures in this book include knowledge of elementary analysis, and some familiarity with matrices, determinants, and linear dependence. For purposes of formal development, only discrete distributions are used, though continuous distributions are employed as illustrations. The number and variety of problems presented will be welcomed by all students, computer experts, and others using statistics and game theory. This comprehensive and sophisticated introduction remains one of the strongest and most useful approaches to a field which today touches areas as diverse as gambling and particle physics.

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388

Publisher

Courier Corporation

Published Date

ISBN 10

0486150895

ISBN 13

9780486150895

One Thousand Exercises in Probability

By: Geoffrey Grimmett,David Stirzaker

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One Thousand Exercises in Probability

By: Geoffrey Grimmett,David Stirzaker

This guide provides a wide-ranging selection of illuminating, informative and entertaining problems, together with their solution. Topics include modelling and many applications of probability theory.

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452

Publisher

Oxford University Press

Published Date

ISBN 10

0198572212

ISBN 13

9780198572213

Stochastic Mechanics of Discrete Media

By: David R. Axelrad

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Stochastic Mechanics of Discrete Media

By: David R. Axelrad

For the past three decades the mechanics of structured media, frequently called micromechanics, has been recognized as an important new approach in the analysis of material behaviour. This book discusses the modern use of mathematical analysis to the stochastic mechanics of discrete media. The theoretical study is therefore based on set and measure theory and the application of point processes.

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346

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Springer Science & Business Media

Published Date

ISBN 10

3642514855

ISBN 13

9783642514852

Nonlinear Time Series

Theory, Methods and Applications with R Examples

By: Randal Douc,Eric Moulines,David Stoffer

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Nonlinear Time Series

Theory, Methods and Applications with R Examples

By: Randal Douc,Eric Moulines,David Stoffer

This text emphasizes nonlinear models for a course in time series analysis. After introducing stochastic processes, Markov chains, Poisson processes, and ARMA models, the authors cover functional autoregressive, ARCH, threshold AR, and discrete time series models as well as several complementary approaches. They discuss the main limit theorems for Markov chains, useful inequalities, statistical techniques to infer model parameters, and GLMs. Moving on to HMM models, the book examines filtering and smoothing, parametric and nonparametric inference, advanced particle filtering, and numerical methods for inference.

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548

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CRC Press

Published Date

ISBN 10

1466502347

ISBN 13

9781466502345

Stochastic Analysis of Biochemical Systems

By: David F. Anderson,Thomas G. Kurtz

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Stochastic Analysis of Biochemical Systems

By: David F. Anderson,Thomas G. Kurtz

This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other areas of science and technology. These notes are based in part on lectures given by Professor Anderson at the University of Wisconsin – Madison and by Professor Kurtz at Goethe University Frankfurt.

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Springer

Published Date

ISBN 10

3319168959

ISBN 13

9783319168951

Statistical Mechanics

Rigorous Results

By: David Ruelle

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Statistical Mechanics

Rigorous Results

By: David Ruelle

This classic book marks the beginning of an era of vigorous mathematical progress in equilibrium statistical mechanics. Its treatment of the infinite system limit has not been superseded, and the discussion of thermodynamic functions and states remains basic for more recent work. The conceptual foundation provided by the Rigorous Results remains invaluable for the study of the spectacular developments of statistical mechanics in the second half of the 20th century.

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240

Publisher

World Scientific

Published Date

ISBN 10

9810238622

ISBN 13

9789810238629

The Ricci Flow: Techniques and Applications

Techniques and Applications. Geometric-analytic aspects

By: Bennett Chow,Sun-Chin Chu,David Glickenstein,Christine Guenther,James Isenberg,Tom Ivey,Dan Knopf,Peng Lu,Feng Luo,Lei Ni

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The Ricci Flow: Techniques and Applications

Techniques and Applications. Geometric-analytic aspects

By: Bennett Chow,Sun-Chin Chu,David Glickenstein,Christine Guenther,James Isenberg,Tom Ivey,Dan Knopf,Peng Lu,Feng Luo,Lei Ni

The Ricci flow uses methods from analysis to study the geometry and topology of manifolds. With the third part of their volume on techniques and applications of the theory, the authors give a presentation of Hamilton's Ricci flow for graduate students and mathematicians interested in working in the subject, with an emphasis on the geometric and analytic aspects. The topics include Perelman's entropy functional, point picking methods, aspects of Perelman's theory of $\kappa$-solutions including the $\kappa$-gap theorem, compactness theorem and derivative estimates, Perelman's pseudolocality theorem, and aspects of the heat equation with respect to static and evolving metrics related to Ricci flow. In the appendices, we review metric and Riemannian geometry including the space of points at infinity and Sharafutdinov retraction for complete noncompact manifolds with nonnegative sectional curvature. As in the previous volumes, the authors have endeavored, as much as possible, to make the chapters independent of each other. The book makes advanced material accessible to graduate students and nonexperts. It includes a rigorous introduction to some of Perelman's work and explains some technical aspects of Ricci flow useful for singularity analysis. The authors give the appropriate references so that the reader may further pursue the statements and proofs of the various results.

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542

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American Mathematical Soc.

Published Date

ISBN 10

0821846612

ISBN 13

9780821846612

Elementary Probability

By: David Stirzaker

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Elementary Probability

By: David Stirzaker

Now available in a fully revised and updated second edition, this well established textbook provides a straightforward introduction to the theory of probability. The presentation is entertaining without any sacrifice of rigour; important notions are covered with the clarity that the subject demands. Topics covered include conditional probability, independence, discrete and continuous random variables, basic combinatorics, generating functions and limit theorems, and an introduction to Markov chains. The text is accessible to undergraduate students and provides numerous worked examples and exercises to help build the important skills necessary for problem solving.

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540

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Cambridge University Press

Published Date

ISBN 10

1139441035

ISBN 13

9781139441032

Automorphisms and Equivalence Relations in Topological Dynamics

By: David B. Ellis,Robert Ellis

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Automorphisms and Equivalence Relations in Topological Dynamics

By: David B. Ellis,Robert Ellis

A lucid and self-contained treatment of many key ideas in topological dynamics, achieved by focusing on equivalence relations and automorphisms.

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283

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Cambridge University Press

Published Date

ISBN 10

1107633222

ISBN 13

9781107633223

Malliavin Calculus in Finance

Theory and Practice

By: Elisa Alos,David Garcia Lorite

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Malliavin Calculus in Finance

Theory and Practice

By: Elisa Alos,David Garcia Lorite

Malliavin Calculus in Finance: Theory and Practice aims to introduce the study of stochastic volatility (SV) models via Malliavin Calculus. Malliavin calculus has had a profound impact on stochastic analysis. Originally motivated by the study of the existence of smooth densities of certain random variables, it has proved to be a useful tool in many other problems. In particular, it has found applications in quantitative finance, as in the computation of hedging strategies or the efficient estimation of the Greeks. The objective of this book is to offer a bridge between theory and practice. It shows that Malliavin calculus is an easy-to-apply tool that allows us to recover, unify, and generalize several previous results in the literature on stochastic volatility modeling related to the vanilla, the forward, and the VIX implied volatility surfaces. It can be applied to local, stochastic, and also to rough volatilities (driven by a fractional Brownian motion) leading to simple and explicit results. Features Intermediate-advanced level text on quantitative finance, oriented to practitioners with a basic background in stochastic analysis, which could also be useful for researchers and students in quantitative finance Includes examples on concrete models such as the Heston, the SABR and rough volatilities, as well as several numerical experiments and the corresponding Python scripts Covers applications on vanillas, forward start options, and options on the VIX. The book also has a Github repository with the Python library corresponding to the numerical examples in the text. The library has been implemented so that the users can re-use the numerical code for building their examples. The repository can be accessed here: https://bit.ly/2KNex2Y.

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350

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CRC Press

Published Date

ISBN 10

1000403513

ISBN 13

9781000403510

One-Dimensional Ergodic Schrödinger Operators

I. General Theory

By: David Damanik,Jake Fillman

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One-Dimensional Ergodic Schrödinger Operators

I. General Theory

By: David Damanik,Jake Fillman

The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from dynamical systems, topology, and analysis. Additionally, this setting includes many models of physical interest, including those operators that model crystals, disordered media, or quasicrystals. This field has seen substantial progress in recent decades, much of which has yet to be discussed in textbooks. Beginning with a refresher on key topics in spectral theory, this volume presents the basic theory of discrete one-dimensional Schrödinger operators with dynamically defined potentials. It also includes a self-contained introduction to the relevant aspects of ergodic theory and topological dynamics. This text is accessible to graduate students who have completed one-semester courses in measure theory and complex analysis. It is intended to serve as an introduction to the field for junior researchers and beginning graduate students as well as a reference text for people already working in this area. It is well suited for self-study and contains numerous exercises (many with hints).

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464

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American Mathematical Society

Published Date

ISBN 10

1470456060

ISBN 13

9781470456061

Bounded and Compact Integral Operators

By: David E. Edmunds,V.M Kokilashvili,Alexander Meskhi

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Bounded and Compact Integral Operators

By: David E. Edmunds,V.M Kokilashvili,Alexander Meskhi

The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).

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655

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Springer Science & Business Media

Published Date

ISBN 10

940159922X

ISBN 13

9789401599221

A First Course in Fourier Analysis

By: David W. Kammler

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A First Course in Fourier Analysis

By: David W. Kammler

This book provides a meaningful resource for applied mathematics through Fourier analysis. It develops a unified theory of discrete and continuous (univariate) Fourier analysis, the fast Fourier transform, and a powerful elementary theory of generalized functions and shows how these mathematical ideas can be used to study sampling theory, PDEs, probability, diffraction, musical tones, and wavelets. The book contains an unusually complete presentation of the Fourier transform calculus. It uses concepts from calculus to present an elementary theory of generalized functions. FT calculus and generalized functions are then used to study the wave equation, diffusion equation, and diffraction equation. Real-world applications of Fourier analysis are described in the chapter on musical tones. A valuable reference on Fourier analysis for a variety of students and scientific professionals, including mathematicians, physicists, chemists, geologists, electrical engineers, mechanical engineers, and others.

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Cambridge University Press

Published Date

ISBN 10

1139469037

ISBN 13

9781139469036

Elements of Applied Probability

For Engineering, Mathematics and Systems Science

By: David McDonald

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Elements of Applied Probability

For Engineering, Mathematics and Systems Science

By: David McDonald

This book has been designed for senior engineering, mathematics and systems science students. In addition, the author has used the optional, advanced sections as the basis for graduate courses in quality control and queueing. It is assumed that the students have taken a first course in probability but that some need a review. Discrete models are emphasized and examples have been chosen from the areas of quality control and telecommunications. The book provides correct, modern mathematical methods and at the same time conveys the excitement of real applications.

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380

Publisher

World Scientific

Published Date

ISBN 10

9812387404

ISBN 13

9789812387400

Laplace Transform (PMS-6)

By: David Vernon Widder

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Laplace Transform (PMS-6)

By: David Vernon Widder

Book 6 in the Princeton Mathematical Series. Originally published in 1941. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

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417

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Princeton University Press

Published Date

ISBN 10

1400876451

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9781400876457

Time Series

Data Analysis and Theory

By: David R. Brillinger

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Time Series

Data Analysis and Theory

By: David R. Brillinger

This text employs basic techniques of univariate and multivariate statistics for the analysis of time series and signals.

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556

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SIAM

Published Date

ISBN 10

0898715016

ISBN 13

9780898715019

Counting Processes and Survival Analysis

By: Thomas R. Fleming,David P. Harrington

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Counting Processes and Survival Analysis

By: Thomas R. Fleming,David P. Harrington

The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "The book is a valuable completion of the literature in this field. It is written in an ambitious mathematical style and can be recommended to statisticians as well as biostatisticians." -Biometrische Zeitschrift "Not many books manage to combine convincingly topics from probability theory over mathematical statistics to applied statistics. This is one of them. The book has other strong points to recommend it: it is written with meticulous care, in a lucid style, general results being illustrated by examples from statistical theory and practice, and a bunch of exercises serve to further elucidate and elaborate on the text." -Mathematical Reviews "This book gives a thorough introduction to martingale and counting process methods in survival analysis thereby filling a gap in the literature." -Zentralblatt für Mathematik und ihre Grenzgebiete/Mathematics Abstracts "The authors have performed a valuable service to researchers in providing this material in [a] self-contained and accessible form. . . This text [is] essential reading for the probabilist or mathematical statistician working in the area of survival analysis." -Short Book Reviews, International Statistical Institute Counting Processes and Survival Analysis explores the martingale approach to the statistical analysis of counting processes, with an emphasis on the application of those methods to censored failure time data. This approach has proven remarkably successful in yielding results about statistical methods for many problems arising in censored data. A thorough treatment of the calculus of martingales as well as the most important applications of these methods to censored data is offered. Additionally, the book examines classical problems in asymptotic distribution theory for counting process methods and newer methods for graphical analysis and diagnostics of censored data. Exercises are included to provide practice in applying martingale methods and insight into the calculus itself.

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466

Publisher

John Wiley & Sons

Published Date

ISBN 10

0471769886

ISBN 13

9780471769880

Book's by David S. Lim

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