Download or read book Mathematical Modelling in One Dimension written by J. Banasiak and published by Cambridge University Press. This book was released on 2013-02-21 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uses a wide variety of applications to demonstrate the universality of mathematical techniques in describing and analysing natural phenomena.
Download or read book Mathematical Physics in One Dimension written by Elliott H. Lieb and published by Academic Press. This book was released on 2013-09-17 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Physics in One Dimension: Exactly Soluble Models of Interacting Particles covers problems of mathematical physics with one-dimensional analogs. The book discusses classical statistical mechanics and phase transitions; the disordered chain of harmonic oscillators; and electron energy bands in ordered and disordered crystals. The text also describes the many-fermion problem; the theory of the interacting boson gas; the theory of the antiferromagnetic linear chains; and the time-dependent phenomena of many-body systems (i.e., classical or quantum-mechanical dynamics). Physicists and mathematicians will find the book invaluable.
Download or read book Mathematical Modelling in One Dimension written by Jacek Banasiak and published by Cambridge University Press. This book was released on 2013-02-21 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling in One Dimension demonstrates the universality of mathematical techniques through a wide variety of applications. Learn how the same mathematical idea governs loan repayments, drug accumulation in tissues or growth of a population, or how the same argument can be used to find the trajectory of a dog pursuing a hare, the trajectory of a self-guided missile or the shape of a satellite dish. The author places equal importance on difference and differential equations, showing how they complement and intertwine in describing natural phenomena.
Download or read book Introduction to Mathematical Modeling and Computer Simulations written by Vladimir Mityushev and published by CRC Press. This book was released on 2018-02-19 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students.
Download or read book Mathematical Modelling of Zombies written by Robert Smith? and published by University of Ottawa Press. This book was released on 2014-10-14 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: You’re outnumbered, in fear for your life, surrounded by flesheating zombies. What can save you now? Mathematics, of course. Mathematical Modelling of Zombies engages the imagination to illustrate the power of mathematical modelling. Using zombies as a “hook,” you’ll learn how mathematics can predict the unpredictable. In order to be prepared for the apocalypse, you’ll need mathematical models, differential equations, statistical estimations, discretetime models, and adaptive strategies for zombie attacks—as well as baseball bats and Dire Straits records (latter two items not included). In Mathematical Modelling of Zombies, Robert Smith? brings together a highly skilled team of contributors to fend off a zombie uprising. You’ll also learn how modelling can advise government policy, how theoretical results can be communicated to a nonmathematical audience and how models can be formulated with only limited information. A forward by Andrew Cartmel—former script editor of Doctor Who, author, zombie fan and all-round famous person in science-fiction circles—even provides a genealogy of the undead. By understanding how to combat zombies, readers will be introduced to a wide variety of modelling techniques that are applicable to other real-world issues (biology, epidemiology, medicine, public health, etc.). So if the zombies turn up, reach for this book. The future of the human race may depend on it.
Download or read book An Introduction to Mathematical Modeling written by Edward A. Bender and published by Courier Corporation. This book was released on 2012-05-23 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Employing a practical, "learn by doing" approach, this first-rate text fosters the development of the skills beyond the pure mathematics needed to set up and manipulate mathematical models. The author draws on a diversity of fields — including science, engineering, and operations research — to provide over 100 reality-based examples. Students learn from the examples by applying mathematical methods to formulate, analyze, and criticize models. Extensive documentation, consisting of over 150 references, supplements the models, encouraging further research on models of particular interest. The lively and accessible text requires only minimal scientific background. Designed for senior college or beginning graduate-level students, it assumes only elementary calculus and basic probability theory for the first part, and ordinary differential equations and continuous probability for the second section. All problems require students to study and create models, encouraging their active participation rather than a mechanical approach. Beyond the classroom, this volume will prove interesting and rewarding to anyone concerned with the development of mathematical models or the application of modeling to problem solving in a wide array of applications.
Download or read book Mathematical Modeling and Simulation written by Kai Velten and published by John Wiley & Sons. This book was released on 2009-06-01 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise and clear introduction to the topic requires only basic knowledge of calculus and linear algebra - all other concepts and ideas are developed in the course of the book. Lucidly written so as to appeal to undergraduates and practitioners alike, it enables readers to set up simple mathematical models on their own and to interpret their results and those of others critically. To achieve this, many examples have been chosen from various fields, such as biology, ecology, economics, medicine, agricultural, chemical, electrical, mechanical and process engineering, which are subsequently discussed in detail. Based on the author`s modeling and simulation experience in science and engineering and as a consultant, the book answers such basic questions as: What is a mathematical model? What types of models do exist? Which model is appropriate for a particular problem? What are simulation, parameter estimation, and validation? The book relies exclusively upon open-source software which is available to everybody free of charge. The entire book software - including 3D CFD and structural mechanics simulation software - can be used based on a free CAELinux-Live-DVD that is available in the Internet (works on most machines and operating systems).
Download or read book Measuring Professional Competence for the Teaching of Mathematical Modelling written by Raphael Wess and published by Springer Nature. This book was released on 2021-07-14 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book presents a structural model and an associated test instrument designed to provide a detailed analysis of professional competences for teaching mathematical modelling. The conceptualisation is based on the COACTIV model, which describes aspects, areas and facets of professional competences of teachers. The manual provides an overview of the essential teaching skills in application-related contexts and offers the tools needed to capture these aspects. It discusses the objectives and application areas of the instrument, as well as the development of the test. In addition, it describes the implementation and evaluates the quality and results of the structural equation analysis of the model. Teaching mathematical modelling is a cognitively challenging activity for (prospective) teachers. Thus, teacher education requires a detailed analysis of professional competence for teaching mathematical modelling. Measuring this competence requires theoretical models that accurately describe requirements placed upon teachers, as well as appropriate evaluation tools that adequately capture skills and abilities in this field. This book presents an instrument that measures the professional competences in a sample of 349 prospective teachers.
Download or read book Principles of Mathematical Modelling written by Alexander A. Samarskii and published by CRC Press. This book was released on 2001-12-20 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling is becoming increasingly versatile and multi-disciplinary. This text demonstrates the broadness of this field as the authors consider the principles of model construction and use common approaches to build models from a range of subject areas. The book reflects the interests and experiences of the authors, but it explores mathematical modeling across a wide range of applications, from mechanics to social science. A general approach is adopted, where ideas and examples are favored over rigorous mathematical procedures. This insightful book will be of interest to specialists, teachers, and students across a wide range of disciplines..
Download or read book Applied Mathematical Models in Human Physiology written by Johnny T. Ottesen and published by SIAM. This book was released on 2004-01-01 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces mathematicians to real applications from physiology. Using mathematics to analyze physiological systems, the authors focus on models reflecting current research in cardiovascular and pulmonary physiology. In particular, they present models describing blood flow in the heart and the cardiovascular system, as well as the transport of oxygen and carbon dioxide through the respiratory system and a model for baroreceptor regulation.
Download or read book Dynamic Models in Biology written by Stephen P. Ellner and published by Princeton University Press. This book was released on 2011-09-19 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.
Download or read book Mathematical Modeling in Economics Ecology and the Environment written by N.V. Hritonenko and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems of interrelation between human economics and natural environment include scientific, technical, economic, demographic, social, political and other aspects that are studied by scientists of many specialities. One of the important aspects in scientific study of environmental and ecological problems is the development of mathematical and computer tools for rational management of economics and environment. This book introduces a wide range of mathematical models in economics, ecology and environmental sciences to a general mathematical audience with no in-depth experience in this specific area. Areas covered are: controlled economic growth and technological development, world dynamics, environmental impact, resource extraction, air and water pollution propagation, ecological population dynamics and exploitation. A variety of known models are considered, from classical ones (Cobb Douglass production function, Leontief input-output analysis, Solow models of economic dynamics, Verhulst-Pearl and Lotka-Volterra models of population dynamics, and others) to the models of world dynamics and the models of water contamination propagation used after Chemobyl nuclear catastrophe. Special attention is given to modelling of hierarchical regional economic-ecological interaction and technological change in the context of environmental impact. Xlll XIV Construction of Mathematical Models ...
Download or read book Computational and Mathematical Modeling in the Social Sciences written by Scott de Marchi and published by Cambridge University Press. This book was released on 2005-08-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an overview of mathematical modeling concentrating on game theory, statistics and computational modeling.
Download or read book Linear Mathematical Models In Chemical Engineering written by Martin Aksel Hjortso and published by World Scientific Publishing Company. This book was released on 2010-01-15 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Latest Edition: Linear Mathematical Models in Chemical Engineering (2nd Edition)Understanding the mathematical modeling of chemical processes is fundamental to the successful career of a researcher in chemical engineering. This book reviews, introduces, and develops the mathematics that is most frequently encountered in sophisticated chemical engineering models.The result of a collaboration between a chemical engineer and a mathematician, both of whom have taught classes on modeling and applied mathematics, the book provides a rigorous and in-depth coverage of chemical engineering model formulation and analysis as well as a text which can serve as an excellent introduction to linear mathematics for engineering students. There is a clear focus in the choice of material, worked examples, and exercises that make it unusually accessible to the target audience. The book places a heavy emphasis on applications to motivate the theory, but simultaneously maintains a high standard of rigor to add mathematical depth and understanding.
Download or read book Teaching and Learning Mathematical Modelling written by Gilbert Greefrath and published by Springer. This book was released on 2016-08-20 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This survey provides an overview of the German discussion on modelling and applications in schools. It considers the development from the beginning of the 20th century to the present, and discusses the term “mathematical model” as well as different representations of the modelling process as modelling cycles. Different trends in the historical and current debate on applications and modelling can be differentiated as perspectives of modelling. Modelling is now one of the six general mathematical competencies defined in the educational standards for mathematics introduced in Germany in 2003, and there have been several initiatives to implement modelling in schools, as well as a whole range of empirical research projects focusing on teachers or students in modelling processes. As a special kind for implementing modelling into school, modelling weeks and days carried out by various German universities have been established.
Download or read book Model Emergent Dynamics in Complex Systems written by A. J. Roberts and published by SIAM. This book was released on 2014-12-18 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author?s objectives are to use sound theory to explore algebraic techniques, develop interesting applications, and discover general modeling principles. Model Emergent Dynamics in Complex Systems unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between such multiscale models and clarifying difficulties and apparent paradoxes and addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty. The basis for the author?s methodology is the theory and the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems; in particular, center and slow manifolds are heavily used. The wonderful aspect of this approach is the range of geometric interpretations of the modeling process that it produces?simple geometric pictures inspire sound methods of analysis and construction. Further, pictures drawn of state spaces also provide a route to better assess a model?s limitations and strengths. Geometry and algebra form a powerful partnership and coordinate transforms and manifolds provide a powerfully enhanced and unified view of a swathe of other complex system modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, two timing, and WKB theory.
Download or read book Partial Differential Equations Modeling Analysis and Numerical Approximation written by Hervé Le Dret and published by Birkhäuser. This book was released on 2016-02-11 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.
