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Differential & Integral Equations
Series on University Mathematics - Vol 10
Linear Algebra and its Applications
by Tzuong-TsiengMoh (Purdue University, USA) From Tzuong-Tsieng Moh, a seasoned expert in algebra, comes a new book for students to better understand linear algebra. Writing from an experienced standpoint, Moh covers the many standard aspects comprising linear algebra, such as echelon forms, matrix algebra, linear transformations, and more. Moh further includes several advanced topics and applications, as well as self-correcting codes, Heisenberg’s uncertainty principle, Maxwell’s equations in relativity form, Google’s search engine, and the theory of finitely generated modules over a PID. Readership: Graduate students and researchers interested in the basic and advanced topics of linear algebra and its applications.
316pp 978-981-3235-42-7 Nov 2020 US$98 £86
Gröbner – Shirshov Bases
Normal Forms, Combinatorial and Decision Problems in Algebra
by Leonid Bokut (Sobolev Institute of Mathematics, Russia), Yuqun Chen (South China Normal University, China), Kyriakos Kalorkoti (University of Edinburgh, United Kingdom), Pavel Kolesnikov (Sobolev Institute of Mathematics, Russia) & Viktor Lopatkin (Saint-Petersburg State University, Russia) The book is about algebras, groups, semigroups presented by generators and defining relations. One of the main problems for such presentations is the problem of normal forms of their elements. Gröbner – Shirshov bases theory is a general approach to the problem. The Shirshov paper was largely unknown outside Russia. The book covers this gap in the modern mathematical literature. Now Gröbner – Shirshov bases method has many applications both for classical algebraic structures (associative, Lie algebra, groups, semigroups) and new structures (dialgebra, pre-Lie algebra, Rota – Baxter algebra, operads). Readership: Researchers in algebra and combinatorics.
308pp 978-981-4619-48-6 Jul 2020 US$138 £120
DIFFERENTIAL & INTEGRAL EQUATIONS
Trends in Abstract and Applied Analysis - Vol 10
Impulsive and Integral Equations on Bounded and Unbounded Domains
by Feliz Manuel Minhós (Universidade de E´vora, Portugal) & Robert de Sousa (Universidade de Cabo Verde, Cape Verde) Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. Readership: Academics, researchers and graduate students on Mathematics or related fields such as Engineering who are interested in coupled systems of differential and integral equations.
Trends in Abstract and Applied Analysis - Vol 9
by Bashir Ahmad (King Abdulaziz University, Saudi Arabia), Johnny Henderson (Baylor University, USA) & Rodica Luca (“Gheorghe Asachi” Technical University of Iasi, Romania) This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann – Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors’ results, that have been obtained and highly cited in the literature in the last four years. Readership: Mathematical and scientific researchers, and graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.
468pp Mar 2021 978-981-122-445-4 US$128 £115
by Bashir Ahmad (King Abdulaziz University, Saudi Arabia) & Sotiris K Ntouyas (University of Ioannina, Greece) The main objective for writing this book is to present some recent results on single-valued and multi-valued boundary value problems, involving different kinds of fractional differential and integral operators, and several kinds of nonlocal multi-point, integral, integrodifferential boundary conditions. Much of the content of this book contains the recent research published by the authors on the topic.
Key Features
• This book provides an up-to-date development on the topic of nonlocal nonlinear boundary value problems dealing with fractional differential equations and inclusions • The material chosen for this book is significant in the sense that it covers different kinds of nonlocal fractional-order boundary value problem. Readership: Researchers working in the field of fractional calculus/ boundary value problems; graduate students with major in fractional order boundary value problems; researchers working on the theoretical aspects of fractional differential equations and inclusions.
596pp Apr 2021 978-981-123-040-0 US$188 £165
Essential Textbook An Introduction to Partial Differential Equations (with Maple)
A Concise Course
by Zhilin Li & Larry Norris (North Carolina State University, USA) The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm – Liouville eigenvalue problems and series solutions. The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. These features distinguish the book from other textbooks available in the related area. Readership: Undergraduate, beginning level mathematics/physics graduate students, students from interdisciplinary areas and engineering.
220pp Aug 2021 978-981-122-862-9 US$78 £70
Series in Applied and Computational Mathematics - Vol 4
Hyperbolicity in Delay Equations
by Luis Barreira (Universidade de Lisboa, Portugal) & Claudia Valls (Universidade de Lisboa, Portugal) This book provides a comprehensive introduction to the study of hyperbolicity in both linear and nonlinear delay equations. This includes a self-contained discussion of the foundations, main results and essential techniques, with emphasis on important parts of the theory that apply to a large class of delay equations. The central theme is always hyperbolicity and only topics that are directly related to it are included. Among these are robustness, admissibility, invariant manifolds, and spectra, which play important roles in life sciences, engineering and control theory, especially in delayed feedback mechanisms. Readership: Graduate students and researchers specializing in differential equations and dynamical systems.
240pp 978-981-123-024-0 Apr 2021 US$88 £75
Interdisciplinary Mathematical Sciences - Vol 21
An Introduction to Nonautonomous Dynamical Systems and their Attractors
by Peter E Kloeden (Universität Tübingen, Germany) & Meihua Yang (Huazhong University of Science and Technology, China) Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a “Thousand Expert” Professorship at the Huazhong University of Science and Technology in Wuhan.
Key Features
• In recent decades new concepts of nonautonomous attractors have been developed in the mathematical literature and provide a better understanding of the dynamics in nonautonomous systems • This book aims to make these new ideas accessible to modelers in other areas such as biomathematics, ecology, meteorology, physics, etc.
Readership: Upper level undergraduate, graduate students, researchers in Mathematics and in areas of applications such as biomathematics, ecology, meteorology, medicine, etc.
156pp 978-981-122-865-0 Dec 2020 US$58 £50
Essential Textbook Basic Insights in Vector Calculus
With a Supplement on Mathematical Understanding
by Terrance J Quinn (Middle Tennessee State University, USA), Zine Boudhraa (Montgomery College, Maryland, USA) & Sanjay Rai (Montgomery College, Maryland, USA) “This book offers insight and motivation into the major theorems of undergraduate single-variable and multivariable calculus. In this, the text is successful — working from physical principles and complete with many pictures, the text demystifies the ‘big theorems’ that arise in the calculus sequence. As a result, the text is a worthwhile and engaging read for both undergraduate and graduate students looking to better understand the results that appear at the end of a traditional Calculus 3 course. It would also be recommended to a professor of Calculus 3 who is looking for inquiry-based approaches or thought experiments to use in their course.” MAA Reviews The book provides an introduction to three famous theorems of vector calculus, Green’s theorem, Stokes’ theorem and the divergence theorem (also known as Gauss’s theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows. Readership: Undergraduate students and lecturers of calculus courses in mathematics major as well as engineering and other related areas.
by Harold Cohen (California State University, Los Angeles, USA) & Daniel Gallup (Pasadena City College, USA)
This book is for students in a first course in ordinary differential equations. The material is organized so that the presentations begin at a reasonably introductory level. Subsequent material is developed from this beginning. As such, readers with little experience can start at a lower level, while those with some experience can use the beginning material as a review, or skip this part to proceed to the next level.
The book contains methods of approximation to solutions of various types of differential equations with practical applications, which will serve as a guide to programming so that such differential equations can be solved numerically with the use of a computer.
Key Feature:
• The book presents methods for solving differential equations that many other text do not cover. These include Heaviside operator methods, phase plane analysis and several detailed methods for approximating solutions that cannot be obtained analytically.
Readership: Undergraduate students studying mathematics, physics, engineering, business, economics and banking who are interested in the practical applications of differential equations.
816pp 978-981-3276-65-9 Sep 2020 US$168 £150
WKB Analysis, Focal Points, Coherent States
(2nd Edition)
by Rémi Carles (CNRS, France & Universitéde Rennes 1, France)
The second edition of this book consists of three parts. The first one is dedicated to the WKB methods and the semi-classical limit before the formation of caustics. The second part treats the semi-classical limit in the presence of caustics, in the special geometric case where the caustic is reduced to a point (or to several isolated points). The third part is new in this edition, and addresses the nonlinear propagation of coherent states. The three parts are essentially independent.
Key Features
• First book on the semi-classical analysis for nonlinear Schrödinger equations • Includes tools of independent interest for the study of nonlinear Schrödinger equations
Readership: Graduate students, researchers in the fields of partial differential equations and mathematical physics.
