方程的思考：物理科学与工程用开发数学直觉实用指南 Thinking About Equations

基本信息

Format:Paperback / softback 272 pages, Charts: 1 B&W, 0 Color; Drawings: 15 B&W, 0 Color; Graphs: 43 B&W, 0 Color

Publisher:John Wiley & Sons Inc

Imprint:John Wiley & Sons Inc

ISBN:9780470186206

Published:30 Jul 2009

Weight:467g

Dimensions:235 x 155 (mm)

信息仅供参考，具体请以实物为准

书籍简介

一本易于理解的指南，帮助您培养解决物理科学和工程学数学问题的直觉和技能

方程式在各个研究领域的问题解决中都发挥着核心作用。理解方程式的含义是形成有效解决策略的重要一步，也为更成功、更充实的工作体验奠定了基础。《思考方程式》提供了一本易于理解的指南，帮助您培养对数学方法的直观理解，同时介绍了许多实用的数学工具，可成功解决工程和物理科学中出现的问题。

方程式是几乎所有数值解的基础，作者说明了如何牢固理解问题解决，从而改进计算方法的策略。八个简洁的章节提供了全面的主题介绍，包括：

近似和估计

隔离重要变量

概括和特殊情况

量纲分析和缩放

图形方法和图形解决方案

简化方程的对称性

每章都包含一个综合讨论，结合了来自各个研究领域的已解决的问题，包括物理、工程、应用数学和物理化学。这些示例说明了解决问题时经常遇到的数学概念和技巧。为了加速学习，已解决的示例问题按它们所说明的方程相关概念分组，而不是像传统处理那样按科学和数学中的子领域分组。此外，每个问题都附有全面的解决方案、解释和评论，每章末尾的大量练习提供了测试理解的机会。

《思考方程》只需要具备基本微积分和入门物理学的应用知识，是本科高年级和研究生工程和物理科学课程的极好补充。对于在日常工作中遇到数学问题的工程、物理、化学、生物物理学和其他相关领域的各个分支的研究人员、从业者和教育工作者来说，它也是一个有价值的参考书。

An accessible guide to developing intuition and skills for solving mathematical problems in the physical sciences and engineering

Equations play a central role in problem solving across various fields of study. Understanding what an equation means is an essential step toward forming an effective strategy to solve it, and it also lays the foundation for a more successful and fulfilling work experience. Thinking About Equations provides an accessible guide to developing an intuitive understanding of mathematical methods and, at the same time, presents a number of practical mathematical tools for successfully solving problems that arise in engineering and the physical sciences.

Equations form the basis for nearly all numerical solutions, and the authors illustrate how a firm understanding of problem solving can lead to improved strategies for computational approaches. Eight succinct chapters provide thorough topical coverage, including:

Approximation and estimation

Isolating important variables

Generalization and special cases

Dimensional analysis and scaling

Pictorial methods and graphical solutions

Symmetry to simplify equations

Each chapter contains a general discussion that is integrated with worked-out problems from various fields of study, including physics, engineering, applied mathematics, and physical chemistry. These examples illustrate the mathematical concepts and techniques that are frequently encountered when solving problems. To accelerate learning, the worked example problems are grouped by the equation-related concepts that they illustrate as opposed to subfields within science and mathematics, as in conventional treatments. In addition, each problem is accompanied by a comprehensive solution, explanation, and commentary, and numerous exercises at the end of each chapter provide an opportunity to test comprehension.

Requiring only a working knowledge of basic calculus and introductory physics, Thinking About Equations is an excellent supplement for courses in engineering and the physical sciences at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers, practitioners, and educators in all branches of engineering, physics, chemistry, biophysics, and other related fields who encounter mathematical problems in their day-to-day work.

作者简介

Matt A. Bernstein 博士是梅奥诊所的放射物理学教授，在梅奥诊所的放射科和生物医学工程科任职。作为国际医学磁共振学会 (ISMRM) 会员和医学磁共振编委会成员，Bernstein 博士已发表 60 多篇期刊文章，主要在 MRI 物理学领域。

William A. Friedman 博士是威斯康星大学名誉教授和华盛顿大学附属教授。作为美国物理学会会员，Friedman 博士拥有 40 多年的学术经验，并在核物理领域撰写了 100 多篇期刊文章。

Matt A. Bernstein, PhD, is Professor of Radiologic Physics at the Mayo Clinic, where he holds appointments in the Departments of Radiology and Biomedical Engineering. A Fellow of the International Society for Magnetic Resonance in Medicine (ISMRM) and Editorial Board member of Magnetic Resonance in Medicine, Dr. Bernstein has published over sixty journal articles, mainly in the field of MRI physics.

William A. Friedman, PhD, is Emeritus Professor at the University of Wisconsin and Affiliate Professor at the University of Washington. A Fellow of the American Physical Society, Dr. Friedman has over forty years of academic experience and has authored more than one hundred journal articles in the field of nuclear physics.

部分目录，仅供参考

Preface.

Acknowledgments.

List of Worked-Out Example Problems.

1 Equations Representing Physical Quantities.

1.1 Systems of Units.

1.2 Conversion of Units.

1.3 Dimensional Checks and the Use of Symbolic Parameters.

1.4 Arguments of Transcendental Functions.

1.5 Dimensional Checks to Generalize Equations.

1.6 Other Types of Units.

1.7 Simplifying Intermediate Calculations.

Exercises.

2 A Few Pitfalls and a Few Useful Tricks.

2.1 A Few Instructive Pitfalls.

2.2 A Few Useful Tricks.

2.3 A Few “Advanced” Tricks.

Exercises.

3 Limiting and Special Cases.