Mathematics for Dynamic Modeling

Mathematics for Dynamic Modeling

Author: Edward Beltrami

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 294

ISBN-13: 1483267865

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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.


Book Synopsis Mathematics for Dynamic Modeling by : Edward Beltrami

Download or read book Mathematics for Dynamic Modeling written by Edward Beltrami and published by Academic Press. This book was released on 2014-05-10 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematics for Dynamic Modeling

Mathematics for Dynamic Modeling

Author: Edward J. Beltrami

Publisher:

Published: 1987

Total Pages: 302

ISBN-13:

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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.


Book Synopsis Mathematics for Dynamic Modeling by : Edward J. Beltrami

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.

Mathematics for Dynamic Modeling

Mathematics for Dynamic Modeling

Author: Edward Beltrami

Publisher: Academic Press

Published: 1998

Total Pages: 248

ISBN-13: 9780120855667

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This new edition of Mathematics for Dynamic Modeling updates a widely used and highly-respected textbook. The text is appropriate for upper-level undergraduate and graduate level courses in modeling, dynamical systems, differential equations, and linear multivariable systems offered in a variety of departments including mathematics, engineering, computer science, and economics. The text features many different realistic applications from a wide variety of disciplines. The book covers important tools such as linearization, feedback concepts, the use of Liapunov functions, and optimal control. This new edition is a valuable tool for understanding and teaching a rapidly growing field. Practitioners and researchers may also find this book of interest. Contains a new chapter on stability of dynamic models Covers many realistic applications from a wide variety of fields in an accessible manner Provides a broad introduction to the full scope of dynamical systems Incorporates new developments such as new models for chemical reactions and autocatalysis Integrates MATLAB throughout the text in both examples and illustrations Includes a new introduction to nonlinear differential equations


Book Synopsis Mathematics for Dynamic Modeling by : Edward Beltrami

Download or read book Mathematics for Dynamic Modeling written by Edward Beltrami and published by Academic Press. This book was released on 1998 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition of Mathematics for Dynamic Modeling updates a widely used and highly-respected textbook. The text is appropriate for upper-level undergraduate and graduate level courses in modeling, dynamical systems, differential equations, and linear multivariable systems offered in a variety of departments including mathematics, engineering, computer science, and economics. The text features many different realistic applications from a wide variety of disciplines. The book covers important tools such as linearization, feedback concepts, the use of Liapunov functions, and optimal control. This new edition is a valuable tool for understanding and teaching a rapidly growing field. Practitioners and researchers may also find this book of interest. Contains a new chapter on stability of dynamic models Covers many realistic applications from a wide variety of fields in an accessible manner Provides a broad introduction to the full scope of dynamical systems Incorporates new developments such as new models for chemical reactions and autocatalysis Integrates MATLAB throughout the text in both examples and illustrations Includes a new introduction to nonlinear differential equations

Dynamic Models in Biology

Dynamic Models in Biology

Author: Stephen P. Ellner

Publisher: Princeton University Press

Published: 2011-09-19

Total Pages: 352

ISBN-13: 1400840961

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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.


Book Synopsis Dynamic Models in Biology by : Stephen P. Ellner

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.

Iterative Algebra and Dynamic Modeling

Iterative Algebra and Dynamic Modeling

Author: Kurt Kreith

Publisher: Springer Science & Business Media

Published: 1999-06-22

Total Pages: 350

ISBN-13: 9780387987583

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Iterative Algebra and Dynamic Modeling links together the use of technology (Excel spreadsheets, Stella modeling software) and modern mathematical techniques to explore the interaction of algebra (at the pre-calculus level) with computer and graphing calculator technology. This book was developed to teach modern applications of mathematics at an introductory level. It is based on the authors well-received teacher-training workshops using the materials.


Book Synopsis Iterative Algebra and Dynamic Modeling by : Kurt Kreith

Download or read book Iterative Algebra and Dynamic Modeling written by Kurt Kreith and published by Springer Science & Business Media. This book was released on 1999-06-22 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iterative Algebra and Dynamic Modeling links together the use of technology (Excel spreadsheets, Stella modeling software) and modern mathematical techniques to explore the interaction of algebra (at the pre-calculus level) with computer and graphing calculator technology. This book was developed to teach modern applications of mathematics at an introductory level. It is based on the authors well-received teacher-training workshops using the materials.

Mathematics for Dynamic Modeling

Mathematics for Dynamic Modeling

Author: Edward J. Beltrami

Publisher:

Published: 1987

Total Pages: 304

ISBN-13:

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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.


Book Synopsis Mathematics for Dynamic Modeling by : Edward J. Beltrami

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 304 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.

Mathematical Modeling of Earth's Dynamical Systems

Mathematical Modeling of Earth's Dynamical Systems

Author: Rudy Slingerland

Publisher: Princeton University Press

Published: 2011-03-28

Total Pages: 246

ISBN-13: 1400839114

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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


Book Synopsis Mathematical Modeling of Earth's Dynamical Systems by : Rudy Slingerland

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

The Mathematics of Marriage

The Mathematics of Marriage

Author: John M. Gottman

Publisher: MIT Press

Published: 2005-01-14

Total Pages: 423

ISBN-13: 0262572303

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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.


Book Synopsis The Mathematics of Marriage by : John M. Gottman

Download or read book The Mathematics of Marriage written by John M. Gottman and published by MIT Press. This book was released on 2005-01-14 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Mathematical Modeling

An Introduction to Mathematical Modeling

Author: Edward A. Bender

Publisher: Courier Corporation

Published: 2000-03-06

Total Pages: 274

ISBN-13: 9780486411804

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Accessible text features over 100 reality-based examples pulled from the science, engineering and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.


Book Synopsis An Introduction to Mathematical Modeling by : Edward A. Bender

Download or read book An Introduction to Mathematical Modeling written by Edward A. Bender and published by Courier Corporation. This book was released on 2000-03-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible text features over 100 reality-based examples pulled from the science, engineering and operations research fields. Prerequisites: ordinary differential equations, continuous probability. Numerous references. Includes 27 black-and-white figures. 1978 edition.

Dynamic Modeling

Dynamic Modeling

Author: R. Robert Huckfeldt

Publisher:

Published: 1982

Total Pages: 96

ISBN-13:

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Book Synopsis Dynamic Modeling by : R. Robert Huckfeldt

Download or read book Dynamic Modeling written by R. Robert Huckfeldt and published by . This book was released on 1982 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: