The mathematical modelling of free and moving boundary problems are an important topic in engineering, industry, technology and theoretical sciences. These models allow us to make calculations involved in phase change transitions of materials due to heat transfer. Boundary layer applications are widespread in research and industry. Boundary Element Methods for Heat Transfer with Phase Change Problems: Theory and Application equips the reader with information about heat transfer problems occurring during phase changes. The book covers several boundary element methods, including methods for phase changes, fixed and moving domains and new approaches. The contents are rounded off with chapters on numerical results and industrial applications. Key features: - Simple, didactic presentation of boundary layer problems for heat transfer problems - Covers a wide range of boundary element methods - Includes methods for fixed and moving domains - Explains industrial applications of the methods - Includes solutions to numerical problems The book serves as a textbook for students of advanced mathematics and engineering. It is also a handbook for researchers working on numerical analysis, who require a focused volume on boundary element methods for heat transfer applications.

Vector calculus is an essential mathematical tool for performing mathematical analysis of physical and natural phenomena. It is employed in advanced applications in the field of engineering and computer simulations. <p></p> This textbook covers the fundamental requirements of vector calculus in curricula for college students in mathematics and engineering programs. Chapters start from the basics of vector algebra, real valued functions, different forms of integrals, geometric algebra and the various theorems relevant to vector calculus and differential forms. <p></p> Readers will find a concise and clear study of vector calculus, along with several examples, exercises, and a case study in each chapter. The solutions to the exercises are also included at the end of the book. <p></p> This is an ideal book for students with a basic background in mathematics who wish to learn about advanced calculus as part of their college curriculum and equip themselves with the knowledge to apply theoretical concepts in practical situations.

High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible. Mathematical models can be used to predict answers to many important questions about the environment. This application comes with several complex theoretical and practical obstacles which need to be resolved. A successfully applicable mathematical model needs to enable researchers to • Mathematically describe all important physical and chemical processes. • Apply fast and sufficiently accurate numerical methods. • Ensure that the model runs efficiently on modern high speed computers. • Use high quality input data, both meteorological data and emission inventories, in the runs. • Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model. • Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters. • Visualize and animate the output results in order to make them easily understandable even to non-specialists. This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.

Sobolev spaces were firstly defined by the Russian mathematician, Sergei L. Sobolev (1908-1989) in the 1930s. Several properties of these spaces have been studied by mathematicians until today. Functions that account for existence and uniqueness, asymptotic behavior, blow up, stability and instability of the solution of many differential equations that occur in applied and in engineering sciences are carried out with the help of Sobolev spaces and embedding theorems in these spaces. An Introduction to Sobolev Spaces provides a brief introduction to Sobolev spaces at a simple level with illustrated examples. Readers will learn about the properties of these types of vector spaces and gain an understanding of advanced differential calculus and partial difference equations that are related to this topic. The contents of the book are suitable for undergraduate and graduate students, mathematicians, and engineers who have an interest in getting a quick, but carefully presented, mathematically sound, basic knowledge about Sobolev Spaces.

This book represents a novel approach for the trigonometry and an original scientific work in this field, by using the ensemble structure composed of the real analysis and the axiomatic fundaments of geometry. Throughout this e &ndash; book one presents, in a proper manner, definitions, properties, formulae and applications more specific of the subject title and its immediate connections. The book is recommended not only as a pertinent introduction for the high school students, being also very useful for the university students, mathematics teachers and anyone who is interested in the major elements regarding the essence of real mathematics.

All developments in mathematics and computer science facilitate development of industrial applications. This e-book approaches the subject in a profoundly interdisciplinary manner. The spectrum of subjects covered in this e-book includes mathematics, computer science, materials science and industrial applications. Specifically, the e-book elaborates on mathematical models of phase-field transitions. Nonlinear parabolic systems represent the core of this book. Mathematically speaking, it presents methods related to existence, uniqueness and regularity of solution, fractional steps, analysis of some boundary optimal control problems governed by phase-field transition system, conceptual algorithms to compute the approximate solution and boundary control.

Understanding Calculus as a Logical Extension of Arithmetic re-examines the calculus paradigm by expanding the set of &lsquo;indeterminate forms&rsquo; espoused by l&rsquo;H&ocirc;pital 320 years ago. Starting from the 54 possible binary combinations of the foundational numbers (zero, one and infinity), a replacement for the function theory formulated earlier by Newton and Leibniz, is presented. A logical extension of the three concepts of differentiation, integration and the Naperian base number e follows this introduction, which is interpreted as &lsquo;zero divided by zero&rsquo;, &lsquo;infinity times zero&rsquo; and &lsquo;one raised to the infinite power&rsquo;, respectively. The concept that a number postulated as representing &lsquo;nothing&rsquo; is reinforced a useful connection to calculus theory. This treatise proposes a &lsquo;similar&rsquo; number to denote and quantify &lsquo;all&rsquo;, in order to understand the concept of infinity. Other topics covered in this text include analytical geometry, infinite sequences and infinite series. Understanding Calculus as a Logical Extension of Arithmetic is a useful reference on advanced calculus theory for mathematics students and researchers.

Complex Analysis for Science and Technology is a textbook for undergraduate and postgraduate students undertaking science, technology, engineering and mathematics (STEM) courses. The book begins with an introduction to basic complex numbers, followed by chapters covering complex functions, integrals, transformations and conformal mapping. Topics such as complex series and residue theory are also covered. Key features of this textbook include: -simple, easy-to-understand explanations of relevant concepts -a wide range of simple and complex examples -several figures where appropriate

Convergence Theorems for Lattice Group-valued Measures explains limit and boundedness theorems for measures taking values in abstract structures. The book begins with a historical survey about these topics since the beginning of the last century, moving on to basic notions and preliminaries on filters/ideals, lattice groups, measures and tools which are featured in the rest of this text. Readers will also find a survey on recent classical results about limit, boundedness and extension theorems for lattice group-valued measures followed by information about recent developments on these kinds of theorems and several results in the setting of filter/ideal convergence. In addition, each chapter has a general description of the topics and an appendix on random variables, concepts and lattices is also provided. Thus readers will benefit from this book through an easy-to-read historical survey about all the problems on convergence and boundedness theorems, and the techniques and tools which are used to prove the main results. The book serves as a primer for undergraduate, postgraduate and Ph. D. students on mathematical lattice and topological groups and filters, and a treatise for expert researchers who aim to extend their knowledge base.

&lt;p&gt;&lt;/p&gt; Differential and Integral Calculus - Theory and Cases is a complete textbook designed to cover basic calculus at introductory college and undergraduate levels. Chapters provide information about calculus fundamentals and concepts including real numbers, series, functions, limits, continuity, differentiation, antidifferentiation (integration) and sequences. Readers will find a concise and clear study of calculus topics, giving them a solid foundation of mathematical analysis using calculus. The knowledge and concepts presented in this book will equip students with the knowledge to immediately practice the learned calculus theory in practical situations encountered at advanced levels. &lt;p&gt;&lt;/p&gt; Key Features: &lt;p&gt;&lt;/p&gt; - Complete coverage of basic calculus, including differentiation and integration &lt;p&gt;&lt;/p&gt; - Easy to read presentation suitable for students &lt;p&gt;&lt;/p&gt; - Information about functions and maps &lt;p&gt;&lt;/p&gt; - Case studies and exercises for practical learning, with solutions &lt;p&gt;&lt;/p&gt; - Case studies and exercises for practical learning, with solutions &lt;p&gt;&lt;/p&gt; - References for further reading &lt;p&gt;&lt;/p&gt;