Boyce`s Elementary Differential Equations and Boundary Value Problems (12版)

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書名：Boyce`s Elementary Differential Equations and Boundary Value Problems 12/e 作者：Boyce 裝訂：平裝 出版社：John Wiley 出版日期：2022/08/00 ISBN：9781119820512 目錄 TABLE OF CONTENTS  1 Introduction      2 First-Order Differential Equations      3 Second-Order Linear Differential Equations      4 Higher-Order Linear Differential Equations      5 Series Solutions of First-Order and Second-Order Linear Equations      6 Systems of First-Order Linear Equations      7 The Laplace Transform      8 Numerical Methods of Solving First Order Equations  9 Nonlinear Differential Equations and Stability      10 Partial Differential Equations and Fourier Series      11 Boundary Value Problems and Sturm-Liouville Theory      Web Appendix  Special Functions: On Legendre Polynomials and Functions     ANSWERS TO PROBLEMS   INDEX 

DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS

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This book is written for students and researchers who are fond of mathematics and the natural sciences. It consists of two parts. Part I presents the theory of analysis in which the mathematical theory is described not as an accomplished palace, but as a building under construction. It uncovers how a theory has been or is being constructed. In Part II, the theory of differential equations is applied to interesting practical problems, such as pursuit-line and tractrix, attack on an object from an airplane, an insect crawling along a stretching rubber rod, the SIR model of a virus infection, string vibration, circular membrane vibration, as well as the wind ripple, sand dune and wave phenomena on a highway. Furthermore, the problems of a one-dimensional lattice vibration, the keyboard percussion vibration and the eigenvalue problems in quantum mechanics, such as the Aharonov–Bohm effect, are also investigated in detail. Request Inspection Copy Sample Chapter(s) Preface Chapter 1: Introduction to the Theory of Analysis Contents: Theories: Introduction to the Theory of Analysis Differential Equations Differential Operators Applications: Ordinary Differential Equations Partial Differential Equations Problems Involving Bessel Functions Potential Problems in Quantum Mechanics Readership: Undergraduate students, postgraduate students and researchers interested in the theory and applications of differential equations in mathematics and the natural sciences.

Instructor's Solution Manual to accompany Elementary Differential Equations and Elementary Differential Equations w/ Boundary Value Problems (9版)

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【簡介】 Written from the perspective of the applied mathematician, the latest edition of this bestselling book focuses on the theory and practical applications of Differential Equations to engineering and the sciences. Emphasis is placed on the methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace the development of the discipline and identify outstanding individual contributions. This book builds the foundation for anyone who needs to learn differential equations and then progress to more advanced studies. 【目錄】

Fundamentals of Differential Equations and Boundary Value Problems (6版)

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【簡介】 Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software. Fundamentals of Differential Equations, Eighth Edition is suitable for a one-semester sophomore- or junior-level course. Fundamentals of Differential Equations with Boundary Value Problems,¿Sixth Edition, contains enough material for a two-semester course that covers and builds on boundary value problems. The Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory). 【目錄】 1. Introduction 2. First-Order Differential Equations 3. Mathematical Models and Numerical Methods Involving First Order Equations 4. Linear Second-Order Equations 5. Introduction to Systems and Phase Plane Analysis 6. Theory of Higher-Order Linear Differential Equations 7. Laplace Transforms 8. Series Solutions of Differential Equations 9. Matrix Methods for Linear Systems 10. Partial Differential Equations 11. Eigenvalue Problems and Sturm-Liouville Equations 12. Stability of Autonomous Systems 13. Existence and Uniqueness Theory