An Introduction to Linear Difference Equations PDF Download
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Author: Paul Mason Batchelder
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 230
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Book Description
Author: Paul Mason Batchelder
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 230
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Book Description
Author: Samuel Goldberg
Publisher: Courier Corporation
ISBN: 0486650847
Category : Mathematics
Languages : en
Pages : 292
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Book Description
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
ISBN: 1475731108
Category : Mathematics
Languages : en
Pages : 441
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Book Description
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: Walter G. Kelley
Publisher: Academic Press
ISBN: 9780124033306
Category : Mathematics
Languages : en
Pages : 418
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Book Description
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: Paul Mason Batchelder
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 208
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Book Description
Author: R Mickens
Publisher: CRC Press
ISBN: 9780442001360
Category : Mathematics
Languages : en
Pages : 470
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Book Description
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
ISBN: 0486672603
Category : Mathematics
Languages : en
Pages : 306
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Book Description
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: Paul Mason Batchelder
Publisher:
ISBN:
Category : Difference equations
Languages : en
Pages : 209
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Book Description
Author: Saber Elaydi
Publisher: Springer Science & Business Media
ISBN: 0387230599
Category : Mathematics
Languages : en
Pages : 547
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Book Description
A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamics Contains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations. Has an extensive number of applications in a variety of fields from neural network to host-parasitoid systems. Includes chapters on continued fractions, orthogonal polynomials and asymptotics. Lucid and transparent writing style
Author: Jack K. Hale
Publisher: Springer Science & Business Media
ISBN: 1461243424
Category : Mathematics
Languages : en
Pages : 458
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Book Description
The present book builds upon an earlier work of J. Hale, "Theory of Func tional Differential Equations" published in 1977. We have tried to maintain the spirit of that book and have retained approximately one-third of the material intact. One major change was a complete new presentation of lin ear systems (Chapters 6~9) for retarded and neutral functional differential equations. The theory of dissipative systems (Chapter 4) and global at tractors was completely revamped as well as the invariant manifold theory (Chapter 10) near equilibrium points and periodic orbits. A more complete theory of neutral equations is presented (see Chapters 1, 2, 3, 9, and 10). Chapter 12 is completely new and contains a guide to active topics of re search. In the sections on supplementary remarks, we have included many references to recent literature, but, of course, not nearly all, because the subject is so extensive. Jack K. Hale Sjoerd M. Verduyn Lunel Contents Preface............................................................ v Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . . . . . . . . . . 1. Linear differential difference equations . . . . . . . . . . . . . . 11 . . . . . . 1.1 Differential and difference equations. . . . . . . . . . . . . . . . . . . . 11 . . . . . . . . 1.2 Retarded differential difference equations. . . . . . . . . . . . . . . . 13 . . . . . . . 1.3 Exponential estimates of x( ยข,f) . . . . . . . . . . . . . . . . . . . . . 15 . . . . . . . . . . 1.4 The characteristic equation . . . . . . . . . . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . 1.5 The fundamental solution. . . . . . . . . . . . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . 1.6 The variation-of-constants formula............................. 23 1. 7 Neutral differential difference equations . . . . . . . . . . . . . . . . . 25 . . . . . . . 1.8 Supplementary remarks. . . . . . . . . . . . . . . . . . . . . . . . . . . 34 . . . . . . . . . . . . . 2. Functional differential equations: Basic theory . . . . . . . . 38 . . 2.1 Definition of a retarded equation. . . . . . . . . . . . . . . . . . . . . . 38 . . . . . . . . . 2.2 Existence, uniqueness, and continuous dependence . . . . . . . . . . 39 . . . 2.3 Continuation of solutions . . . . . . . . . . . . . . . . . . . . . . . . . . 44 . . . . . . . . . . . .
