8 minute read
Numerical Analysis & Approximation
Bestseller Infinite-Dimensional Analysis
Operators in Hilbert Space; Stochastic Calculus via Representations, and Duality Theory
by Palle Jorgensen (The University of Iowa, USA) & James Tian (American Mathematics Society, USA) We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4 – 6. This further connects to key areas in quantum physics. Readership: Undergraduate and graduate students and professionals who want to learn about exciting connections to applied problems in analysis, stochastic processes, dynamical system, representation theory, and mathematical physics.
252pp Feb 2021 978-981-122-577-2 US$88 £75
Series on Analysis, Applications and Computation - Vol 8 The Linearised Dam-Break Problem
by D J Needham, S McGovern & J A Leach (University of Birmingham, UK) The monograph addresses a canonical problem in linear water wave theory, through the development-detailed, asymptotic analysis of contour integrals in the complex plane. It is anticipated that the methodology developed in the monograph will have applications to many associated linear wave evolution problems, to which the reader may adapt the approach developed in the monograph. The approach adopted in the monograph is novel, and there are no existing publications for comparison. Readership: Graduate students and researchers.
164pp 978-981-3223-87-5 Feb 2021 US$68 £60
Bestseller
Advanced Textbooks in Physics
A Guide to Mathematical Methods for Physicists
Advanced Topics and Applications
by Michela Petrini (Sorbonne Université, Paris, France), Gianfranco Pradisi (University of Rome Tor Vergata, Italy) & Alberto Zaffaroni (University of Milano-Bicocca, Italy) This book provides a self-contained and rigorous presentation of the main mathematical tools needed to approach many courses at the last year of undergraduate in Physics and MSc programs, from Electromagnetism to Quantum Mechanics. It complements A Guide to Mathematical Methods for Physicists with advanced topics and physical applications. The different arguments are organised in three main sections: Complex Analysis, Differential Equations and Hilbert Spaces, covering most of the standard mathematical method tools in modern physics. One of the purposes of the book is to show how seemingly different mathematical tools like, for instance, Fourier transforms, eigenvalue problems, special functions and so on, are all deeply interconnected. It contains a large number of examples, problems and detailed solutions, emphasising the main purpose of relating concrete physical examples with more formal mathematical aspects. Readership: Students and professionals in the field.
NUMERICAL ANALYSIS & APPROXIMATION
Essential Textbook Explorations in Numerical Analysis
Python Edition
by James V Lambers (The University of Southern Mississippi, USA), Amber Sumner Mooney (William Carey University, USA) & Vivian A Montiforte (The University of Southern Mississippi, USA) This textbook is intended to introduce advanced undergraduate and early-career graduate students to the field of numerical analysis. This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations. Readership: Advanced undergraduate or beginning graduate students.
692pp Jan 2021 978-981-122-934-3(pbk) US$68 £60 978-981-122-793-6 US$148 £130
Practical Numerical Mathematics with MATLAB
Workbook and Solutions
by Myron M Sussman (University of Pittsburgh, USA) This workbook and solutions manual is intended for advanced undergraduate or beginning graduate students as a supplement to a traditional course in numerical mathematics and as preparation for independent research involving numerical mathematics. The solutions manual provides complete MATLAB code and numerical results for each of the exercises in the workbook and will be especially useful for those students without previous MATLAB programming experience. Upon completion of this material, students will have a working knowledge of MATLAB programming, they will have themselves programmed algorithms encountered in classwork and textbooks. Readership: Senior undergraduate and first year graduate students.
770pp Sep 2021 978-981-124-518-3(Set)(pbk) US$98 £85 978-981-124-600-5(Set) US$198 £175 Vol. 1 450pp 978-981-124-519-0(pbk) US$68 £60 978-981-124-035-5 US$128 £115 Vol. 2 320pp 978-981-124-520-6(pbk) US$58 £50 978-981-124-069-0 US$118 £105
Series on Advances in Mathematics for Applied Sciences
Advanced Mathematical and Computational Tools in Metrology and Testing XII
edited by Franco Pavese (IMEKO TC21, Italy), Alistair B Forbes (National Physical Laboratory, UK), Nien-Fan Zhang (National Institute of Standards and Technology, USA) & Anna Chunovkina (Institute for Metrology “D I Mendeleyev”, Russia) Written by researchers active in institutions developing world-leading measurement capabilities. Provides a multi-disciplinary approach to addressing measurement challenges in a wide range of application domains Readership: Researchers, graduate students, academics and quality engineers working in metrology and its applications to manufacturing, environment, health and life sciences.
550pp 978-981-124-237-3
by William Layton & Myron Sussman (University of Pittsburgh, USA) Many students come to numerical linear algebra from science and engineering seeking modern tools and an understanding of how the tools work and their limitations. Often their backgrounds and experience are extensive in applications of numerical methods but limited in abstract mathematics and matrix theory. Often enough it is limited to multivariable calculus, basic differential equations and methods of applied mathematics. This book introduces modern tools of numerical linear algebra based on this background, heavy in applied analysis but light in matrix canonical forms and their algebraic properties. Readership: Senior undergraduate and first year graduate in areas related to numerical analysis.
276pp Jul 2020 978-981-122-484-3(pbk) US$49 £45 978-981-122-389-1 US$79 £70
Nonstandard Finite Difference Schemes
Methodology and Applications
by Ronald E Mickens (Clark Atlanta Univ., USA)
Review of the First Edition:
“This book contains a clear presentation of nonstandard finite difference schemes for the numerical integration of differential equations. A set of rules for constructing nonstandard finite difference schemes is also presented. An important feature of the book is the illustration of the various discrete modeling principles, by their application to a large number of both ordinary and partial differential equations" Mathematical Reviews This second edition of Nonstandard Finite Difference Models of Differential Equations provides an update on the progress made in both the theory and application of the NSFD methodology during the past two and a half decades. In addition to discussing details related to the determination of the denominator functions and the nonlocal discrete representations of functions of dependent variables, we include many examples illustrating just how this should be done.
Key Feature
• No other book currently exists on the most recent advances and applications of the NSFD methodology Readership: This book is critical reading for anyone interested in the numerical integration of differential equations by use of finite differences. It is for both advanced undergraduate and graduate students, as well as researchers and practitioners in the field of numercial analysis.
332pp 978-981-122-253-5 Nov 2020 US$118 £105
A New Method of Constructing Brakke’s Motion
by Kazuhiro Horihata (Tohoku University, Japan) The paper entitled “Convergence of the Allen-Cahn equation to Brakke’s motion by mean curvature” by T Ilmanen constructs Brakke’s motion from Allen-Cahn equation, which is one of the measure theoretic approaches to motion by mean curvature. This book first proposes a new idea that involves a new equation of the Allen-Cahn type to construct Brakke’s motion; secondly explaining how to construct it through Ilmanen’s approach as easily as possible.
Key Feature
• New idea for constructing Brakke’s motion Readership: Researchers in calculus of variations and optimal control, partial differential equations, ordinary differential equations, integral equations, differential geometry.
Advanced Textbooks in Mathematics
Classical and Modern Optimization
by Guillaume Carlier (Université Paris Dauphine, France) The quest for the optimal is ubiquitous in nature and human behavior. The field of mathematical optimization has a long history and remains active today, particularly in the development of machine learning. Classical and Modern Optimization presents a self-contained overview of classical and modern ideas and methods in approaching optimization problems. The approach is rich and flexible enough to address smooth and non-smooth, convex and non-convex, finite or infinite-dimensional, static or dynamic situations. The first chapters of the book are devoted to the classical toolbox: topology and functional analysis, differential calculus, convex analysis and necessary conditions for differentiable constrained optimization. The remaining chapters are dedicated to more specialized topics and applications. Readership: Thought-leaders, research scientists, graduate students, advanced undergraduate students, policy-makers, research funding agencies, private research institutions, in the areas of computer science, quantum computing, information theory, neuroscience, and physics.
358pp Nov 2021 978-1-80061-086-6(pbk) US$58 £50 978-1-80061-065-1 US$128 £115
Fractals and Dynamics in Mathematics, Science, and the Arts: Theory and Applications - Vol 7
Equidistribution of Dynamical Systems
Time-Quantitative Second Law
by Jozsef Beck (Rutgers University, USA) “This is definitely an original approach to the Second Law. The main users of the book will be mathematicians with a strong background in Fourier analysis and combinatorics. However, it is also readable for physicists in particular for those who are interested in a rigorous approach to the Second Law. The book is very suitable for advanced student seminars. The writing style of the author is precise and convincing. I enjoyed reading very much
Professor Robert Tichy, Graz University of Technology, Austria
Readership: Any mathematician working in this field including the PhD students and post-docs in this huge field. Moreover, any physicist who is interested in the mathematical foundation of Statistical Mechanics.
448pp Oct 2020 978-981-122-555-0 US$148 £130
Series on Optimization and its Applications - Vol 4
The Moment-SOS Hierarchy
Lectures in Probability, Statistics, Computational Geometry, Control and Nonlinear PDEs
by Didier Henrion (LAAS-CNRS, France & University of Toulouse, France & Czech Technical University in Prague, Czech Republic), MilanKorda (LAAS-CNRS, France & University of Toulouse, France & Czech Technical University in Prague, Czech Republic) & Jean Bernard Lasserre (LAAS-CNRS, France & Institute of Mathematics, University of Toulouse, France) The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Readership: Graduate students, academics and researchers.
