常微分方程：数学、工程和科学专业学生的基础教科书（修订版） Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences (Revised)

基本信息

Series:Dover Books on Mathema 1.4tics

Format:Paperback / softback 818 pages

Publisher:Dover Publications Inc.

Imprint:Dover Publications Inc.

ISBN:9780486649405

Published:28 Mar 2003

Weight:934g

Dimensions:215 x 140 x 43 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

本书是一本写得非常好、组织得非常巧妙的入门教材，对常微分方程（表达变量与其导数之间关系的方程）进行了详尽的概述。作者——康奈尔大学的莫里斯·特南鲍姆和普渡大学的哈里·波拉德——以一种简单易懂、循序渐进的方式，向数学、工程和科学专业的本科生介绍和解释了复杂且至关重要的概念，但又不牺牲数学严谨性。

本书以一节开始，该节探讨了微分方程的起源，定义了基本术语，并概述了微分方程的通解——该解实际上包含了此类方程的所有解。后续章节涉及以下主题：积分因子；稀释和累积问题；复数代数；一阶系统的线性化；拉普拉斯变换；牛顿插值公式；以及皮卡德的逐次逼近法。

本书包含两个出色的章节：一个是关于解微分方程的级数方法，另一个是关于解微分方程的数值方法。第1章讨论了勒让德微分方程、勒让德函数、勒让德多项式、贝塞尔微分方程和拉盖尔微分方程。整本书中，每个术语都定义清晰，每个定理都分析得清晰透彻，微分方程的理论和应用之间保持着令人钦佩的平衡。大量的解答和练习提高了《常微分方程》作为本科生和教学专业人员课堂教材的价值。本书最后深入探讨了各种微分方程的存在性和唯一性定理，并介绍了行列式理论和关于 Wronskians 的定理。

This unusually well-written, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations — equations which express the relationship between variables and their derivatives. In a disarmingly simple, step-by-step style that never sacrifices mathematical rigor, the authors — Morris Tenenbaum of Cornell University, and Harry Pollard of Purdue University — introduce and explain complex, critically-important concepts to undergraduate students of mathematics, engineering and the sciences.

The book begins with a section that examines the origin of differential equations, defines basic terms and outlines the general solution of a differential equation-the solution that actually contains every solution of such an equation. Subsequent sections deal with such subjects as: integrating factors; dilution and accretion problems; the algebra of complex numbers; the linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas; and Picard's Method of Successive Approximations.

The book contains two exceptional chapters: one on series methods of solving differential equations, the second on numerical methods of solving differential equations. The first includes a discussion of the Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation. Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. An abundance of solved problems and practice exercises enhances the value of Ordinary Differential Equations as a classroom text for undergraduate students and teaching professionals. The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians.

作者简介

莫里斯·塔南鲍姆 (1928 年 11 月 10 日 - 2023 年 2 月 26 日) 是一位美国物理化学家和高管，曾在贝尔实验室和 AT&T 公司工作。

Morris Tanenbaum (November 10, 1928 – February 26, 2023) was an American physical chemist and executive who worked at Bell Laboratories and AT&T Corporation.