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Author : Samuel Goldberg
Publisher : Courier Corporation
Page : 292 pages
File Size : 49,55 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 : Saber N. Elaydi
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 39,19 MB
Release : 2013-03-14
Category : Mathematics
ISBN : 1475731108
Integrating both classical and modern treatments of difference equations, this book contains the most updated and comprehensive material on stability, Z-transform, discrete control theory, asymptotic theory, continued fractions and orthogonal polynomials. While the presentation is simple enough for use by advanced undergraduates and beginning graduates in mathematics, engineering science, and economics, it will also be a useful reference for scientists and engineers interested in discrete mathematical models. The text covers a large set of applications in a variety of disciplines, including neural networks, feedback control, Markov chains, trade models, heat transfer, propagation of plants, epidemic models and host-parasitoid systems, with each section rounded off by an extensive and highly selected set of exercises.
Author : R Mickens
Publisher : CRC Press
Page : 470 pages
File Size : 30,41 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 : Hyman Levy
Publisher : Courier Corporation
Page : 306 pages
File Size : 41,89 MB
Release : 1992-01-01
Category : Mathematics
ISBN : 0486672603
Comprehensive study focuses on use of calculus of finite differences as an approximation method for solving troublesome differential equations. Elementary difference operations; interpolation and extrapolation; modes of expansion of the solutions of nonlinear equations, applications of difference equations, difference equations associated with functions of two variables, more. Exercises with answers. 1961 edition.
Author : Walter G. Kelley
Publisher : Academic Press
Page : 418 pages
File Size : 28,3 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
Author : R.P. Agarwal
Publisher : Springer Science & Business Media
Page : 517 pages
File Size : 10,37 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 9401588996
. The theory of difference equations, the methods used in their solutions and their wide applications have advanced beyond their adolescent stage to occupy a central position in Applicable Analysis. In fact, in the last five years, the proliferation of the subject is witnessed by hundreds of research articles and several monographs, two International Conferences and numerous Special Sessions, and a new Journal as well as several special issues of existing journals, all devoted to the theme of Difference Equations. Now even those experts who believe in the universality of differential equations are discovering the sometimes striking divergence between the continuous and the discrete. There is no doubt that the theory of difference equations will continue to play an important role in mathematics as a whole. In 1992, the first author published a monograph on the subject entitled Difference Equations and Inequalities. This book was an in-depth survey of the field up to the year of publication. Since then, the subject has grown to such an extent that it is now quite impossible for a similar survey, even to cover just the results obtained in the last four years, to be written. In the present monograph, we have collected some of the results which we have obtained in the last few years, as well as some yet unpublished ones.
Author : Sui Sun Cheng
Publisher : CRC Press
Page : 284 pages
File Size : 44,46 MB
Release : 2003-02-06
Category : Mathematics
ISBN : 9780415298841
Partial Difference Equations treats this major class of functional relations. Such equations have recursive structures so that the usual concepts of increments are important. This book describes mathematical methods that help in dealing with recurrence relations that govern the behavior of variables such as population size and stock price. It is helpful for anyone who has mastered undergraduate mathematical concepts. It offers a concise introduction to the tools and techniques that have proven successful in obtaining results in partial difference equations.
Author : Glenn Fulford
Publisher : Cambridge University Press
Page : 420 pages
File Size : 34,20 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 : Ravi P. Agarwal
Publisher : CRC Press
Page : 1010 pages
File Size : 23,14 MB
Release : 2000-01-27
Category : Mathematics
ISBN : 9781420027020
A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and
Author : Paul Cull
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 44,10 MB
Release : 2008-07-01
Category : Mathematics
ISBN : 0387276459
In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology. Each chapter leads to techniques that can be applied by hand to small examples or programmed for larger problems. Along the way, the reader will use linear algebra and graph theory, develop formal power series, solve combinatorial problems, visit Perron—Frobenius theory, discuss pseudorandom number generation and integer factorization, and apply the Fast Fourier Transform to multiply polynomials quickly. The book contains many worked examples and over 250 exercises. While these exercises are accessible to students and have been class-tested, they also suggest further problems and possible research topics.