mathematics for dynamic modeling

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Mathematics For Dynamic Modeling

Author : Edward Beltrami
ISBN : 9781483267869
Genre : Science
File Size : 41. 72 MB
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Mathematics for Dynamic Modeling provides an introduction to the mathematics of dynamical systems. This book presents the mathematical formulations in terms of linear and nonlinear differential equations. Organized into two parts encompassing nine chapters, this book begins with an overview of the notions of equilibrium and stability in differential equation modeling that occur in the guise of simple models in the plane. This text then focuses on nonlinear models in which the limiting behavior of orbits can be more complicated. Other chapters consider the problems that illustrate the concepts of equilibrium and stability, limit cycles, chaos, and bifurcation. This book discusses as well a variety of topics, including cusp catastrophes, strange attractors, and reaction–diffusion and shock phenomena. The final chapter deals with models that are based on the notion of optimization. This book is intended to be suitable for students in upper undergraduate and first-year graduate course in mathematical modeling.

Iterative Algebra And Dynamic Modeling

Author : Kurt Kreith
ISBN : 0387987584
Genre : Computers
File Size : 28. 67 MB
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Iterative Algebra and Dynamic Modeling links together the use of technology (Excel, Stella) and modern mathematical techniques to explore the interaction of algebra (at the precalculus level) with computer and graphing calculator technology. The book will find use in a variety of college courses, and also in enrichment courses at the high school level.

Dynamic Modeling Of Environmental Systems

Author : Michael Deaton
ISBN : 9781461213000
Genre : Mathematics
File Size : 40. 64 MB
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A primer on modeling concepts and applications that is specifically geared toward the environmental field. Sections on modeling terminology, the uses of models, the model-building process, and the interpretation of output provide the foundation for detailed applications. After an introduction to the basics of dynamic modeling, the book leads students through an analysis of several environmental problems, including surface-water pollution, matter-cycling disruptions, and global warming. The scientific and technical context is provided for each problem, and the methods for analyzing and designing appropriate modeling approaches is provided. While the mathematical content does not exceed the level of a first-semester calculus course, the book gives students all of the background, examples, and practice exercises needed both to use and understand environmental modeling. It is suitable for upper-level undergraduate and beginning-graduate level environmental professionals seeking an introduction to modeling in their field.

Dynamic Models In Biology

Author : Stephen P. Ellner
ISBN : 9781400840960
Genre : Science
File Size : 60. 55 MB
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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.

The Mathematics Of Marriage

Author : John Mordechai Gottman
ISBN : 0262250454
Genre : Psychology
File Size : 76. 35 MB
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Divorce rates are at an all-time high. But without a theoretical understanding of the processes related to marital stability and dissolution, it is difficult to design and evaluate new marriage interventions. The Mathematics of Marriage provides the foundation for a scientific theory of marital relations. The book does not rely on metaphors, but develops and applies a mathematical model using difference equations. The work is the fulfillment of the goal to build a mathematical framework for the general system theory of families first suggested by Ludwig Von Bertalanffy in the 1960s.The book also presents a complete introduction to the mathematics involved in theory building and testing, and details the development of experiments and models. In one "marriage experiment," for example, the authors explored the effects of lowering or raising a couple's heart rates. Armed with their mathematical model, they were able to do real experiments to determine which processes were affected by their interventions.Applying ideas such as phase space, null clines, influence functions, inertia, and uninfluenced and influenced stable steady states (attractors), the authors show how other researchers can use the methods to weigh their own data with positive and negative weights. While the focus is on modeling marriage, the techniques can be applied to other types of psychological phenomena as well.

Handbook Of Dynamic System Modeling

Author : Paul A. Fishwick
ISBN : 1420010859
Genre : Mathematics
File Size : 68. 59 MB
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The topic of dynamic models tends to be splintered across various disciplines, making it difficult to uniformly study the subject. Moreover, the models have a variety of representations, from traditional mathematical notations to diagrammatic and immersive depictions. Collecting all of these expressions of dynamic models, the Handbook of Dynamic System Modeling explores a panoply of different types of modeling methods available for dynamical systems. Featuring an interdisciplinary, balanced approach, the handbook focuses on both generalized dynamic knowledge and specific models. It first introduces the general concepts, representations, and philosophy of dynamic models, followed by a section on modeling methodologies that explains how to portray designed models on a computer. After addressing scale, heterogeneity, and composition issues, the book covers specific model types that are often characterized by specific visual- or text-based grammars. It concludes with case studies that employ two well-known commercial packages to construct, simulate, and analyze dynamic models. A complete guide to the fundamentals, types, and applications of dynamic models, this handbook shows how systems function and are represented over time and space and illustrates how to select a particular model based on a specific area of interest.

Dynamical Models In Biology

Author : Miklós Farkas
ISBN : 0080530605
Genre : Mathematics
File Size : 44. 50 MB
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Dynamic Models in Biology offers an introduction to modern mathematical biology. This book provides a short introduction to modern mathematical methods in modeling dynamical phenomena and treats the broad topics of population dynamics, epidemiology, evolution, immunology, morphogenesis, and pattern formation. Primarily employing differential equations, the author presents accessible descriptions of difficult mathematical models. Recent mathematical results are included, but the author's presentation gives intuitive meaning to all the main formulae. Besides mathematicians who want to get acquainted with this relatively new field of applications, this book is useful for physicians, biologists, agricultural engineers, and environmentalists. Key Topics Include: Chaotic dynamics of populations The spread of sexually transmitted diseases Problems of the origin of life Models of immunology Formation of animal hide patterns The intuitive meaning of mathematical formulae explained with many figures Applying new mathematical results in modeling biological phenomena Miklos Farkas is a professor at Budapest University of Technology where he has researched and instructed mathematics for over thirty years. He has taught at universities in the former Soviet Union, Canada, Australia, Venezuela, Nigeria, India, and Columbia. Prof. Farkas received the 1999 Bolyai Award of the Hungarian Academy of Science and the 2001 Albert Szentgyorgyi Award of the Hungarian Ministry of Education. A 'down-to-earth' introduction to the growing field of modern mathematical biology Also includes appendices which provide background material that goes beyond advanced calculus and linear algebra

Dynamic Modeling In The Health Sciences

Author : James L. Hargrove
ISBN : 9781461216445
Genre : Medical
File Size : 42. 7 MB
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This book and CD-ROM package integrates the use of STELLA software into the teaching of health, nutrition and physiology, and may be used on its own in nutrition and physiology courses, or can serve as a supplement to introduce the role that simulation modelling can play. The author presents key subjects ranging from the theory of metabolic control, through weight regulation to bone metabolism, and gives readers the tools to simulate these using the STELLA software. Topics include methods for simulation of gene expression, a multi-stage model of tumour development, theories of ageing, circadian rhythms and physiological time, as well as a model for managing weight loss and preventing obesity.

Bayesian Forecasting And Dynamic Models

Author : Mike West
ISBN : 9780387227771
Genre : Mathematics
File Size : 38. 74 MB
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This text is concerned with Bayesian learning, inference and forecasting in dynamic environments. We describe the structure and theory of classes of dynamic models and their uses in forecasting and time series analysis. The principles, models and methods of Bayesian forecasting and time - ries analysis have been developed extensively during the last thirty years. Thisdevelopmenthasinvolvedthoroughinvestigationofmathematicaland statistical aspects of forecasting models and related techniques. With this has come experience with applications in a variety of areas in commercial, industrial, scienti?c, and socio-economic ?elds. Much of the technical - velopment has been driven by the needs of forecasting practitioners and applied researchers. As a result, there now exists a relatively complete statistical and mathematical framework, presented and illustrated here. In writing and revising this book, our primary goals have been to present a reasonably comprehensive view of Bayesian ideas and methods in m- elling and forecasting, particularly to provide a solid reference source for advanced university students and research workers.

Elementary Mathematical Modeling

Author : James T. Sandefur
ISBN : 053437803X
Genre : Mathematics
File Size : 37. 12 MB
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ELEMENTARY MATHEMATICAL MODELING uses mathematics to study problems arising in areas such as Genetics, Finance, Medicine, and Economics. Throughout the course of the book, students learn how to model a real situation, such as testing levels of lead in children or environmental cleanup. They then learn how to analyze that model in relationship to the real world, such as making recommendations for minimum treatment time for children exposed to lead paint or determining the minimum time required to adequately clean up a polluted lake. Often the results will be counterintuitive, such as finding that an increase in the rate of wild-life harvesting may actually decrease the long-term harvest, or that a lottery prize that is paid out over a number of years is worth far less than its advertised value. This use of mathematics illustrates and models real-world issues and questions, bringing the value of mathematics to life for students, enabling them to see, perhaps for the first time, the utility of mathematics.

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