An Introduction To Difference Equations

Autor: Saber N. Elaydi
Publisher: Springer Science & Business Media
ISBN: 1475731108
File Size: 62,78 MB
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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.

Differential Equations

Autor: Clay C. Ross
Publisher: Springer Science & Business Media
ISBN: 1475739494
File Size: 27,84 MB
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The first edition (94301-3) was published in 1995 in TIMS and had 2264 regular US sales, 928 IC, and 679 bulk. This new edition updates the text to Mathematica 5.0 and offers a more extensive treatment of linear algebra. It has been thoroughly revised and corrected throughout.

Difference Equations

Autor: Paul Cull
Publisher: Springer Science & Business Media
ISBN: 0387276459
File Size: 19,86 MB
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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.

A First Course In Differential Equations

Autor: J David Logan
Publisher: Springer Science & Business Media
ISBN: 9781441975928
File Size: 64,22 MB
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This concise and up-to-date textbook is designed for the standard sophomore course in differential equations. It treats the basic ideas, models, and solution methods in a user friendly format that is accessible to engineers, scientists, economists, and mathematics majors. It emphasizes analytical, graphical, and numerical techniques, and it provides the tools needed by students to continue to the next level in applying the methods to more advanced problems. There is a strong connection to applications with motivations in mechanics and heat transfer, circuits, biology, economics, chemical reactors, and other areas. Moreover, the text contains a new, elementary chapter on systems of differential equations, both linear and nonlinear, that introduces key ideas without matrix analysis. Two subsequent chapters treat systems in a more formal way. Briefly, the topics include: First-order equations: separable, linear, autonomous, and bifurcation phenomena; Second-order linear homogeneous and non-homogeneous equations; Laplace transforms; and Linear and nonlinear systems, and phase plane properties.

Introduction To Differential Equations

Autor: Michael Eugene Taylor
Publisher: American Mathematical Soc.
ISBN: 082185271X
File Size: 62,17 MB
Format: PDF
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The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponential and trigonometric functions, which plays a central role in the subsequent development of this chapter. Chapter 2 provides a mini-course on linear algebra, giving detailed treatments of linear transformations, determinants and invertibility, eigenvalues and eigenvectors, and generalized eigenvectors. This treatment is more detailed than that in most differential equations texts, and provides a solid foundation for the next two chapters. Chapter 3 studies linear systems of differential equations. It starts with the matrix exponential, melding material from Chapters 1 and 2, and uses this exponential as a key tool in the linear theory. Chapter 4 deals with nonlinear systems of differential equations. This uses all the material developed in the first three chapters and moves it to a deeper level. The chapter includes theoretical studies, such as the fundamental existence and uniqueness theorem, but also has numerous examples, arising from Newtonian physics, mathematical biology, electrical circuits, and geometrical problems. These studies bring in variational methods, a fertile source of nonlinear systems of differential equations. The reader who works through this book will be well prepared for advanced studies in dynamical systems, mathematical physics, and partial differential equations.

Introduction To Partial Differential Equations

Autor: Peter J. Olver
Publisher: Springer Science & Business Media
ISBN: 3319020994
File Size: 56,75 MB
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This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

Finite Difference Equations

Autor: Hyman Levy
Publisher: Courier Corporation
ISBN: 0486672603
File Size: 54,46 MB
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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.

Ordinary Differential Equations

Autor: William A. Adkins
Publisher: Springer Science & Business Media
ISBN: 1461436184
File Size: 73,37 MB
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Unlike most texts in differential equations, this textbook gives an early presentation of the Laplace transform, which is then used to motivate and develop many of the remaining differential equation concepts for which it is particularly well suited. For example, the standard solution methods for constant coefficient linear differential equations are immediate and simplified, and solution methods for constant coefficient systems are streamlined. By introducing the Laplace transform early in the text, students become proficient in its use while at the same time learning the standard topics in differential equations. The text also includes proofs of several important theorems that are not usually given in introductory texts. These include a proof of the injectivity of the Laplace transform and a proof of the existence and uniqueness theorem for linear constant coefficient differential equations. Along with its unique traits, this text contains all the topics needed for a standard three- or four-hour, sophomore-level differential equations course for students majoring in science or engineering. These topics include: first order differential equations, general linear differential equations with constant coefficients, second order linear differential equations with variable coefficients, power series methods, and linear systems of differential equations. It is assumed that the reader has had the equivalent of a one-year course in college calculus.

Applied Partial Differential Equations

Autor: J David Logan
Publisher: Springer
ISBN: 3319124935
File Size: 55,94 MB
Format: PDF
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This textbook is for the standard, one-semester, junior-senior course that often goes by the title "Elementary Partial Differential Equations" or "Boundary Value Problems". The audience consists of students in mathematics, engineering, and the sciences. The topics include derivations of some of the standard models of mathematical physics and methods for solving those equations on unbounded and bounded domains, and applications of PDE's to biology. The text differs from other texts in its brevity; yet it provides coverage of the main topics usually studied in the standard course, as well as an introduction to using computer algebra packages to solve and understand partial differential equations. For the 3rd edition the section on numerical methods has been considerably expanded to reflect their central role in PDE's. A treatment of the finite element method has been included and the code for numerical calculations is now written for MATLAB. Nonetheless the brevity of the text has been maintained. To further aid the reader in mastering the material and using the book, the clarity of the exercises has been improved, more routine exercises have been included, and the entire text has been visually reformatted to improve readability.

Discrete Chaos Second Edition

Autor: Saber N. Elaydi
Publisher: CRC Press
ISBN: 1584885920
File Size: 57,48 MB
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While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determinant stability, bifurcation analysis, and the detailed analysis of the center manifold theory. This edition also covers L-systems and the periodic structure of the bulbs in the Mandelbrot set as well as new applications in biology, chemistry, and physics. The principal improvements to this book are the additions of PHASER software on an accompanying CD-ROM and the MapleTM and Mathematica® code available for download online. Incorporating numerous new topics and technology not found in similar texts, Discrete Chaos, Second Edition presents a thorough, up-to-date treatment of the theory and applications of discrete dynamical systems.