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Author : Glenn Fulford
Publisher : Cambridge University Press
Page : 420 pages
File Size : 29,31 MB
Release : 1997-06-12
Category : Mathematics
ISBN : 9780521446181
Any student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject.
Author : Glenn Fulford
Publisher : Cambridge University Press
Page : 416 pages
File Size : 48,27 MB
Release : 1997-06-12
Category : Mathematics
ISBN : 9780521440691
The theme of this book is modeling the real world using mathematics. The authors concentrate on the techniques used to set up mathematical models and describe many systems in full detail, covering both differential and difference equations in depth. Among the broad spectrum of topics studied in this book are: mechanics, genetics, thermal physics, economics and population studies.
Author : Ronald E. Mickens
Publisher : World Scientific
Page : 264 pages
File Size : 23,29 MB
Release : 1994
Category : Mathematics
ISBN : 9810214588
This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of ?exact? and ?best? finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation.
Author : R Mickens
Publisher : CRC Press
Page : 470 pages
File Size : 50,76 MB
Release : 1991-01-01
Category : Mathematics
ISBN : 9780442001360
In recent years, the study of difference equations has acquired a new significance, due in large part to their use in the formulation and analysis of discrete-time systems, the numerical integration of differential equations by finite-difference schemes, and the study of deterministic chaos. The second edition of Difference Equations: Theory and Applications provides a thorough listing of all major theorems along with proofs. The text treats the case of first-order difference equations in detail, using both analytical and geometrical methods. Both ordinary and partial difference equations are considered, along with a variety of special nonlinear forms for which exact solutions can be determined. Numerous worked examples and problems allow readers to fully understand the material in the text. They also give possible generalization of the theorems and application models. The text's expanded coverage of application helps readers appreciate the benefits of using difference equations in the modeling and analysis of "realistic" problems from a broad range of fields. The second edition presents, analyzes, and discusses a large number of applications from the mathematical, biological, physical, and social sciences. Discussions on perturbation methods and difference equation models of differential equation models of differential equations represent contributions by the author to the research literature. Reference to original literature show how the elementary models of the book can be extended to more realistic situations. Difference Equations, Second Edition gives readers a background in discrete mathematics that many workers in science-oriented industries need as part of their general scientific knowledge. With its minimal mathematical background requirements of general algebra and calculus, this unique volume will be used extensively by students and professional in science and technology, in areas such as applied mathematics, control theory, population science, economics, and electronic circuits, especially discrete signal processing.
Author : Frank R. Giordano
Publisher : Cengage Learning
Page : 640 pages
File Size : 32,82 MB
Release : 2008-07-03
Category : Mathematics
ISBN : 9780495011590
Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, giving students hands-on experience developing and sharpening their skills in the modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem-solving process to enhance students' problem-solving capabilities -- whatever their level. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible -- beginning with short projects -- the book facilitates their progressive development and confidence in mathematics and modeling. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Author : Bellman
Publisher : Academic Press
Page : 484 pages
File Size : 38,89 MB
Release : 1963-01-01
Category : Mathematics
ISBN : 0080955142
Differential-Difference Equations
Author : P. Forrester
Publisher :
Page : pages
File Size : 16,75 MB
Release : 1996
Category :
ISBN :
Author : Ioannis Dassios
Publisher : MDPI
Page : 160 pages
File Size : 49,26 MB
Release : 2020-06-23
Category : Technology & Engineering
ISBN : 3039288253
This Special Issue collects the latest results on differential/difference equations, the mathematics of networks, and their applications to engineering and physical phenomena. It features nine high-quality papers that were published with original research results. The Special Issue brings together mathematicians with physicists, engineers, as well as other scientists.
Author : T.P. Dreyer
Publisher : Routledge
Page : 304 pages
File Size : 21,9 MB
Release : 2017-09-06
Category : Mathematics
ISBN : 135143070X
Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.
Author : T.P. Dreyer
Publisher : Routledge
Page : 302 pages
File Size : 15,84 MB
Release : 2017-09-06
Category : Mathematics
ISBN : 1351430696
Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.