Elementary Differential Equations, 6/e (IE-Paperback)

Description

1 .  A solid numerical emphasis ?Includes generic numerical algorithms and a limited number of illustrative graphic calculator, BASIC, and MATLAB routines.
2 .  Wide range of choices regarding breadth and depth of coverage ?The first few sections of most chapters introduce the principal ideas of each topic, with remaining sections devoted to extensions and applications.
3 .  Computer-generated figures. Includes graphics using Mathematica or MATLAB; shows students vivid pictures of direction fields, solution curves, and phase plane portraits that bring symbolic solutions of differential equations to life.
4 .  Application Modules ?Follow appropriate sections in the book; give students concrete applied emphasis and engages them in more extensive investigations than in typical exercises and problems.
5 .  Instructor''s Solutions Manual ?Provides worked-out solutions for most of the problems in the book.
6 .  Student Solutions Manual ?Contains solutions for most of the odd-numbered problems.
7 .  Proven chapter and section structure of the book is unchanged ?Instructors'' notes and syllabi will not require revision to continue teaching with the Sixth Edition.

The Sixth Edition of this widely adopted book remains the same classic differential equations text it's always been, but has been polished and sharpened to serve both instructors and students even more effectively.Edwards and Penney teach students to first solve those differential equations that have the most frequent and interesting applications. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques.

Catalog

CHAPTER1 First-Order Differential Equations 1

CHAPTER2 Linear Equations of Higher Order 100

CHAPTER3 Power Series Methods 194

CHAPTER4 Laplace Transform Methods 266

CHAPTER5 Linear Systems of Differential Equations 326

CHAPTER6 Numerical Methods 430

CHAPTER7 Nonlinear Systems and Phenomena 480

References for Further Study 555

Appendix: Existence and Uniqueness of Solutions 559

Answers to Selected Problems 573

Index I-1

描述

1 .  強調數值計算 ? 包括通用的數值算法和少量的圖形計算器、BASIC 和 MATLAB 程序。

2 .  廣泛的選擇範圍 ? 大多數章節的前幾節介紹每個主題的主要思想，其餘節點則專注於擴展和應用。

3 .  電腦生成的圖形。使用Mathematica或MATLAB進行圖形繪製，向學生展示方向場、解曲線和相平面輪廓的生動圖片，使微分方程的符號解活躍起來。

4 .  應用模塊 ? 跟隨書中相應的節點，為學生提供具體的應用重點，並讓他們進行比典型練習和問題更廣泛的調查。

5 .  教師解答手冊 ? 提供大部分問題的解答。

6 .  學生解答手冊 ? 包含大部分奇數問題的解答。

7 .  書中的章節結構保持不變 ? 教師的筆記和教學大綱不需要修改即可繼續使用第六版進行教學。

這本廣泛採用的教材的第六版仍然是一本經典的微分方程教材，但已經經過改進和提升，以更有效地服務於教師和學生。Edwards和Penney教導學生首先解決那些具有最常見和有趣應用的微分方程。精確而明確的基本存在性和唯一性定理陳述使得學生能夠理解它們在這個主題中的作用。強調數值方法的有效和可靠使用通常需要使用標準基本技巧進行初步分析。

目錄

第1章 一階微分方程 1

第2章 高階線性方程 100

第3章冪級數方法 194

第4章 Laplace變換方法 266

第5章 線性微分方程組 326

第6章 數值方法 430

第7章 非線性系統和現象 480

進一步學習的參考文獻 555

附錄：解的存在性和唯一性 559

選擇問題的答案 573

索引 I-1