Containing the proceedings from the 41st conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM), this book is a collection of high quality papers that report on advances in techniques that reduce or eliminate the type of meshes associated with such methods as finite elements or finite differences. As design, analysis and manufacture become more integrated the chances are that the users will be less aware of the capabilities of the analytical techniques that are at the core of the process. This reinforces the need to retain expertise in certain specialised areas of numerical methods, such as BEM/MRM, to ensure that all new tools perform satisfactorily in the integrated process. The maturity of BEM since 1978 has resulted in a substantial number of industrial applications that demonstrate the accuracy, robustness and easy use of the technique. Their range still needs to be widened, taking into account the potentialities of the Mesh Reduction techniques in general. The papers in this volume help to expand the range of applications as well as the type of materials in response to industrial and professional requirements.

Fractal calculus is the simple, constructive, and algorithmic approach to natural processes modeling, which is impossible using smooth differentiable structures and the usual modeling tools such as differential equations. It is the calculus of the future and will have many applications.This book is the first to introduce fractal calculus and provides a basis for the research and development of this framework. It is suitable for undergraduate and graduate students in mathematics and physics who have mastered general mathematics, quantum physics, and statistical mechanics, as well as researchers dealing with fractal structures in various disciplines.

This monograph aims to provide for the first time a unified and homogenous presentation of the recent works on the theory of Bloch periodic functions, their generalizations, and their applications to evolution equations. It is useful for graduate students and beginning researchers as seminar topics, graduate courses and reference text in pure and applied mathematics, physics, and engineering.

Elementary Number Theory, 6th Edition, blends classical theory with modern applications and is notable for its outstanding exercise sets. A full range of exercises, from basic to challenging, helps students explore key concepts and push their understanding to new heights. Computational exercises and computer projects are also available. Reflecting many years of professor feedback, this edition offers new examples, exercises, and applications, while incorporating advancements and discoveries in number theory made in the past few years.

Precise approach with definitions, theorems, proofs, examples and exercises. Topics include partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Numerous graded exercises with selected answers.

For a two-semester or three-semester course in Calculus for Life Sciences. Calculus for Biology and Medicine, Third Edition, addresses the needs of students in the biological sciences by showing them how to use calculus to analyze natural phenomena-without compromising the rigorous presentation of the mathematics. While the table of contents aligns well with a traditional calculus text, all the concepts are presented through biological and medical applications. The text provides students with the knowledge and skills necessary to analyze and interpret mathematical models of a diverse array of phenomena in the living world. Since this text is written for college freshmen, the examples were chosen so that no formal training in biology is needed.

This is the best seller in this market. It provides a comprehensive introduction to complex variable theory and its applications to current engineering problems. It is designed to make the fundamentals of the subject more easily accessible to students who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books-both in level of exposition and layout-it incorporates physical applications throughout the presentation, so that the mathematical methodology appears less sterile to engineering students.

A substantial number of problems in physics, chemical physics, and biology, are modeled through reaction-diffusion equations to describe temperature distribution or chemical substance concentration. For problems arising from ecology, sociology, or population dynamics, they describe the density of some populations or species. In this book the state variable is a concentration, or a density according to the cases. The reaction function may be complex and include time delays terms that model various situations involving maturation periods, resource regeneration times, or incubation periods. The dynamics may occur in heterogeneous media and may depend upon a small or large parameter, as well as the reaction term. From a purely formal perspective, these parameters are indexed by n. Therefore, reaction-diffusion equations give rise to sequences of Cauchy problems.The first part of the book is devoted to the convergence of these sequences in a sense made precise in the book. The second part is dedicated to the specific case when the reaction-diffusion problems depend on a small parameter intended to tend towards 0. This parameter accounts for the size of small spatial and randomly distributed heterogeneities. The convergence results obtained in the first part, with additionally some probabilistic tools, are applied to this specific situation. The limit problems are illustrated through biological invasion, food-limited or prey-predator models where the interplay between environment heterogeneities in the individual evolution of propagation species plays an essential role. They provide a description in terms of deterministic and homogeneous reaction-diffusion equations, for which numerical schemes are possible.

For courses in Differential Equations and Linear Algebra. The right balance between concepts, visualisation, applications, and skills Differential Equations and Linear Algebra provides the conceptual development and geometric visualisation of a modern differential equations and linear algebra course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena - a comprehensive approach that makes accessible a wider range of more realistic applications. The book combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout.

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. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Caratheodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.

This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.

Larson/Edwards' student-oriented CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 8th INTERNATIONAL METRIC Edition with WebAssign digital resources and online tutorials clearly introduces the concepts and rules behind calculus. Updated content is designed to remove barriers to learning to include all students in the learning experience. New features, such as "Big Ideas of Calculus," and updated exercises work with annotated examples and online tutorials at CalcView.com, CalcChat.com and LarsonCalculus.com to help students master key concepts. New automatically-graded Proof Problems, Expanded Problems and interactive learning modules also strengthen conceptual understanding. You can customize WebAssign online resources to deliver content that's best for your course needs.

Using the familiar software Microsoft ® Excel, this book examines the applications of complex variables. Implementation of the included problems in Excel eliminates the “black box” nature of more advanced computer software and programming languages and therefore the reader has the chance to become more familiar with the underlying mathematics of the complex variable problems. This book consists of two parts. In Part I, several topics are covered that one would expect to find in an introductory text on complex variables. These topics include an overview of complex numbers, functions of a complex variable, and the Cauchy integral formula. In particular, attention is given to the study of analytic complex variable functions. This attention is warranted because of the property that the real and imaginary parts of an analytic complex variable function can be used to solve the Laplace partial differential equation (PDE). Laplace's equation is ubiquitous throughout science and engineering as it can be used to model the steady-state conditions of several important transport processes including heat transfer, soil-water flow, electrostatics, and ideal fluid flow, among others. In Part II, a specialty application of complex variables known as the Complex Variable Boundary Element Method (CVBEM) is examined. CVBEM is a numerical method used for solving boundary value problems governed by Laplace's equation. This part contains a detailed description of the CVBEM and a guide through each step of constructing two CVBEM programs in Excel. The writing of these programs is the culminating event of the book. Students of complex variables and anyone with interest in a novel method for approximating potential functions using the principles of complex variables are the intended audience for this book. The Microsoft Excel applications (including simple programs as well as the CVBEM program) covered will also be of interest in the industry, as these programs are accessible to anybody with Microsoft Office.

Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green's function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.

SINGLE VARIABLE CALCULUS, Metric, 9th Edition, provides you with the strongest foundation for a STEM future. James Stewart's Calculus series is the top-seller in the world because of its problem-solving focus, mathematical precision and accuracy, and outstanding examples and problem sets. Selected and mentored by Stewart, Daniel Clegg and Saleem Watson continue his legacy and their careful refinements retain Stewart's clarity of exposition and make the 9th edition an even more usable learning tool. The accompanying WebAssign includes helpful learning support and new resources like Explore It interactive learning modules. Showing that Calculus is both practical and beautiful, the Stewart approach and WebAssign resources enhance understanding and build confidence for millions of students worldwide.

This book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. Starting from first principles, it takes the reader to the frontier of current research. This second edition has been completely rewritten, offering substantial improvements to the exposition and simplified proofs, as well as new results. The book starts with a thorough account of the generic chaining, a remarkably simple and powerful method to bound a stochastic process that should belong to every probabilist's toolkit. The effectiveness of the scheme is demonstrated by the characterization of sample boundedness of Gaussian processes. Much of the book is devoted to exploring the wealth of ideas and results generated by thirty years of efforts to extend this result to more general classes of processes, culminating in the recent solution of several key conjectures. A large part of this unique book is devoted to the author's influential work. While many of the results presented are rather advanced, others bear on the very foundations of probability theory. In addition to providing an invaluable reference for researchers, the book should therefore also be of interest to a wide range of readers.

This unique book gathers various scientific and mathematical approaches to and descriptions of the natural and physical world stemming from a broad range of mathematical areas - from model systems, differential equations, statistics, and probability - all of which scientifically and mathematically reveal the inherent beauty of natural and physical phenomena. Topics include Archimedean and Non-Archimedean approaches to mathematical modeling; thermography model with application to tungiasis inflammation of the skin; modeling of a tick-Killing Robot; various aspects of the mathematics for Covid-19, from simulation of social distancing scenarios to the evolution dynamics of the coronavirus in some given tropical country to the spatiotemporal modeling of the progression of the pandemic. Given its scope and approach, the book will benefit researchers and students of mathematics, the sciences and engineering, and everyone else with an appreciation for the beauty of nature. The outcome is a mathematical enrichment of nature's beauty in its various manifestations. This volume honors Dr. John Adam, a Professor at Old Dominion University, USA, for his lifetime achievements in the fields of mathematical modeling and applied mathematics. Dr. Adam has published over 110 papers and authored several books.