Author : Glenn Fulford
Publisher : Cambridge University Press
Page : 420 pages
File Size : 17,74 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 : Ronald E. Mickens
Publisher : World Scientific
Page : 264 pages
File Size : 49,6 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 : Bellman
Publisher : Academic Press
Page : 484 pages
File Size : 35,48 MB
Release : 1963-01-01
Category : Mathematics
ISBN : 0080955142
Differential-Difference Equations
Author : T.P. Dreyer
Publisher : Routledge
Page : 304 pages
File Size : 10,45 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 : Frank R. Giordano
Publisher : Cengage Learning
Page : 640 pages
File Size : 34,16 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 : R Mickens
Publisher : CRC Press
Page : 470 pages
File Size : 14,56 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 : Sandra Pinelas
Publisher : Springer Science & Business Media
Page : 639 pages
File Size : 48,6 MB
Release : 2013-09-21
Category : Mathematics
ISBN : 1461473330
The volume contains carefully selected papers presented at the International Conference on Differential & Difference Equations and Applications held in Ponta Delgada – Azores, from July 4-8, 2011 in honor of Professor Ravi P. Agarwal. The objective of the gathering was to bring together researchers in the fields of differential & difference equations and to promote the exchange of ideas and research. The papers cover all areas of differential and difference equations with a special emphasis on applications.
Author : Samuel Goldberg
Publisher : Courier Corporation
Page : 292 pages
File Size : 20,5 MB
Release : 1986-01-01
Category : Mathematics
ISBN : 0486650847
Exceptionally clear exposition of an important mathematical discipline and its applications to sociology, economics, and psychology. Topics include calculus of finite differences, difference equations, matrix methods, and more. 1958 edition.
Author : J. Banasiak
Publisher : Cambridge University Press
Page : 121 pages
File Size : 18,8 MB
Release : 2013-02-21
Category : Mathematics
ISBN : 1107654688
Uses a wide variety of applications to demonstrate the universality of mathematical techniques in describing and analysing natural phenomena.
Author : Walter G. Kelley
Publisher : Academic Press
Page : 418 pages
File Size : 17,97 MB
Release : 2001
Category : Mathematics
ISBN : 9780124033306
Difference Equations, Second Edition, presents a practical introduction to this important field of solutions for engineering and the physical sciences. Topic coverage includes numerical analysis, numerical methods, differential equations, combinatorics and discrete modeling. A hallmark of this revision is the diverse application to many subfields of mathematics. Phase plane analysis for systems of two linear equations Use of equations of variation to approximate solutions Fundamental matrices and Floquet theory for periodic systems LaSalle invariance theorem Additional applications: secant line method, Bison problem, juvenile-adult population model, probability theory Appendix on the use of Mathematica for analyzing difference equaitons Exponential generating functions Many new examples and exercises
