Download or read book Mathematical Modeling of Earth s Dynamical Systems written by Rudy Slingerland and published by Princeton University Press. This book was released on 2011-03-28 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise guide to representing complex Earth systems using simple dynamic models Mathematical Modeling of Earth's Dynamical Systems gives earth scientists the essential skills for translating chemical and physical systems into mathematical and computational models that provide enhanced insight into Earth's processes. Using a step-by-step method, the book identifies the important geological variables of physical-chemical geoscience problems and describes the mechanisms that control these variables. This book is directed toward upper-level undergraduate students, graduate students, researchers, and professionals who want to learn how to abstract complex systems into sets of dynamic equations. It shows students how to recognize domains of interest and key factors, and how to explain assumptions in formal terms. The book reveals what data best tests ideas of how nature works, and cautions against inadequate transport laws, unconstrained coefficients, and unfalsifiable models. Various examples of processes and systems, and ample illustrations, are provided. Students using this text should be familiar with the principles of physics, chemistry, and geology, and have taken a year of differential and integral calculus. Mathematical Modeling of Earth's Dynamical Systems helps earth scientists develop a philosophical framework and strong foundations for conceptualizing complex geologic systems. Step-by-step lessons for representing complex Earth systems as dynamical models Explains geologic processes in terms of fundamental laws of physics and chemistry Numerical solutions to differential equations through the finite difference technique A philosophical approach to quantitative problem-solving Various examples of processes and systems, including the evolution of sandy coastlines, the global carbon cycle, and much more Professors: A supplementary Instructor's Manual is available for this book. It is restricted to teachers using the text in courses. For information on how to obtain a copy, refer to: http://press.princeton.edu/class_use/solutions.html

Download or read book Data Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Download or read book Mathematics for Dynamic Modeling written by Edward J. Beltrami and published by . This book was released on 1987 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Mathematics for Dynamic covers tools such as linearization, feedback concepts, the use of Liapunov functions, and optimal control. Each chapter includes exercises, many of which expand on the material in the text.

Download or read book Mathematical Models written by Richard Haberman and published by SIAM. This book was released on 1998-12-01 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author uses mathematical techniques to give an in-depth look at models for mechanical vibrations, population dynamics, and traffic flow.

Download or read book Modeling Life written by Alan Garfinkel and published by Springer. This book was released on 2017-09-06 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions. Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking. Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

Download or read book Science at the Frontier written by National Academy of Sciences and published by National Academies Press. This book was released on 1992-02-01 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Science at the Frontier takes you on a journey through the minds of some of the nation's leading young scientists as they explore the most exciting areas of discovery today. Based on the second Frontiers of Science symposium sponsored by the National Academy of Sciences, this book describes recent accomplishments and new directions in ten basic fields, represented by outstanding scientists convening to discuss their research. It captures the excitement and personal quality of these exchanges, sometimes pointing to surprising connections spanning the boundaries of traditional disciplines, while providing a context for the reader that explains the basic scientific framework for the fields under discussion. The volume explores: New modifications to scientific theory as geologists probe deep inside the earth and astrophysicists reach to the limits of the observable universe for answers to some of nature's most fundamental and vexing questions. The influence of research in smog formation on the public debate about how to effectively control air pollution. The increasing use of computer modeling in science, from describing the evolution of cellular automata to revealing the workings of the human brain via neural networks. The rise of dynamical systems (the study of chaotic behavior in nature) to a full-fledged science. The search to understand the regulation of gene activity and the many biological problems-such as the onset of cancer-to which it applies. Recent progress in the quest to transform what we know about photosynthesis into functional, efficient systems to tap the sun's energy. Current developments in magnetic resonance imaging and its promise for new breakthroughs in medical diagnosis. Throughout this work the reader is witness to scientific discovery and debate centered on such common concerns as the dramatic and transforming effect of computers on scientists' thinking and research; the development of more cross-disciplinary perspectives; and the very nature of the scientific enterprise itself-what it is to be part of it, and its significance for society. Science at the Frontier is must reading for informed lay readers, scientists interested in fields other than their own, and science students considering a future specialization.

Download or read book Modeling Analysis And Control Of Dynamical Systems With Friction And Impacts written by Pawel Olejnik and published by #N/A. This book was released on 2017-07-07 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is aimed primarily towards physicists and mechanical engineers specializing in modeling, analysis, and control of discontinuous systems with friction and impacts. It fills a gap in the existing literature by offering an original contribution to the field of discontinuous mechanical systems based on mathematical and numerical modeling as well as the control of such systems. Each chapter provides the reader with both the theoretical background and results of verified and useful computations, including solutions of the problems of modeling and application of friction laws in numerical computations, results from finding and analyzing impact solutions, the analysis and control of dynamical systems with discontinuities, etc. The contents offer a smooth correspondence between science and engineering and will allow the reader to discover new ideas. Also emphasized is the unity of diverse branches of physics and mathematics towards understanding complex piecewise-smooth dynamical systems. Mathematical models presented will be important in numerical experiments, experimental measurements, and optimization problems found in applied mechanics.

Download or read book Mathematics of Complexity and Dynamical Systems written by Robert A. Meyers and published by Springer Science & Business Media. This book was released on 2011-10-05 with total page 1885 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Download or read book Dynamical System Models In The Life Sciences And Their Underlying Scientific Issues written by Frederic Y M Wan and published by World Scientific Publishing Company. This book was released on 2017-08-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Broadly speaking, there are two general approaches to teaching mathematical modeling: 1) the case study approach, and 2) the method based approach (that teaches mathematical techniques with applications to relevant mathematical models). This text emphasizes instead the scientific issues for modeling different phenomena. For the natural or harvested growth of a fish population, we may be interested in the evolution of the population, whether it reaches a steady state (equilibrium or cycle), stable or unstable with respect to a small perturbation from equilibrium, or whether a small change in the environment would cause a catastrophic change, etc. Each scientific issue requires an appropriate model and a different set of mathematical tools to extract information from the model. Models examined are chosen to help explain or justify empirical observations such as cocktail drug treatments are more effective and regenerations after injuries or illness are fast-tracked (compared to original developments).Volume I of this three-volume set limits its scope to phenomena and scientific issues that are modeled by ordinary differential equations (ODE). Scientific issues such as signal and wave propagation, diffusion, and shock formation involving spatial dynamics to be modeled by partial differential equations (PDE) will be treated in Vol. II. Scientific issues involving randomness and uncertainty are examined in Vol. III.

Download or read book Differential Equations and Dynamical Systems written by Lawrence Perko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence bf interest in the modern as well as the clas sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mat!!ematics (TAM). The development of new courses is a natural consequence of a high level of excitement oil the research frontier as newer techniques, such as numerical and symbolic cotnputer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Math ematical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface to the Second Edition This book covers those topics necessary for a clear understanding of the qualitative theory of ordinary differential equations and the concept of a dynamical system. It is written for advanced undergraduates and for beginning graduate students. It begins with a study of linear systems of ordinary differential equations, a topic already familiar to the student who has completed a first course in differential equations.

Download or read book Dynamical Systems in Neuroscience written by Eugene M. Izhikevich and published by MIT Press. This book was released on 2010-01-22 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.

Download or read book Introduction to the Modern Theory of Dynamical Systems written by Anatole Katok and published by Cambridge University Press. This book was released on 1995 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.

Download or read book Modelling and Control of Dynamic Systems Using Gaussian Process Models written by Juš Kocijan and published by Springer. This book was released on 2015-11-21 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph opens up new horizons for engineers and researchers in academia and in industry dealing with or interested in new developments in the field of system identification and control. It emphasizes guidelines for working solutions and practical advice for their implementation rather than the theoretical background of Gaussian process (GP) models. The book demonstrates the potential of this recent development in probabilistic machine-learning methods and gives the reader an intuitive understanding of the topic. The current state of the art is treated along with possible future directions for research. Systems control design relies on mathematical models and these may be developed from measurement data. This process of system identification, when based on GP models, can play an integral part of control design in data-based control and its description as such is an essential aspect of the text. The background of GP regression is introduced first with system identification and incorporation of prior knowledge then leading into full-blown control. The book is illustrated by extensive use of examples, line drawings, and graphical presentation of computer-simulation results and plant measurements. The research results presented are applied in real-life case studies drawn from successful applications including: a gas–liquid separator control; urban-traffic signal modelling and reconstruction; and prediction of atmospheric ozone concentration. A MATLAB® toolbox, for identification and simulation of dynamic GP models is provided for download.

Download or read book Dynamic Systems for Everyone written by Asish Ghosh and published by Springer. This book was released on 2015-04-06 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a study of the interactions between different types of systems, their environment, and their subsystems. The author explains how basic systems principles are applied in engineered (mechanical, electromechanical, etc.) systems and then guides the reader to understand how the same principles can be applied to social, political, economic systems, as well as in everyday life. Readers from a variety of disciplines will benefit from the understanding of system behaviors and will be able to apply those principles in various contexts. The book includes many examples covering various types of systems. The treatment of the subject is non-mathematical, and the book considers some of the latest concepts in the systems discipline, such as agent-based systems, optimization, and discrete events and procedures.

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 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 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.