This book falls within the category of what has been labeled “advanced mathematics for scientists and engineers” and is written for first-year graduate students of engineering and physical science. It is assumed that the reader has gone through the standard undergraduate courses in calculus, linear algebra, ordinary differential equations, and partial differential equations. Unlike other popular texts [1], [2], this book is written at a more advanced level and avoids repetition of several topics that have been covered at the undergraduate level (for example, ordinary differential equations, Laplace transforms, vector calculus, basic linear algebra, Fourier analysis, and elementary boundary value problems). It is clear that the authors have gone to great lengths in selecting which topics to include, and the pedagogical presentation is excellent. The example problems and end-of-chapter exercises are well chosen and help motivate the formal mathematical framework. A unique feature of the text is revisiting topics from different viewpoints, which fosters the beauty and power of the mathematical theory. For example, the Fredholm alternative is first considered in the context of linear algebra and then later in the context of ordinary differential equations. In the preface, the authors grapple with the problem of how the ubiquitous use of computers and software impacts the presentation of topics in advanced mathematics courses. This is an extremely critical issue, and I cannot agree more with their statement: “Although computers have altered the way we do our mathematics, and how we construct solutions, and how we consider the parts of a given problem in relation to the whole, it was a change in form, not content.” The text is divided into three parts: Linear Algebra, Complex Variables, and Ordinary and Partial Differential Equations. The authors dispel the notion that these three topics are isolated from one another by showing mutual connections in both theory and applications.

中文翻译：

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工程师和科学家的基础数学[书架]


本书属于“科学家和工程师的高等数学”范畴，是为工程和物理科学一年级研究生编写的。假设读者已经学完微积分、线性代数、常微分方程和偏微分方程的标准本科课程。与其他流行文本 [1]、[2] 不同，本书是在更高级的水平上编写的，避免了重复本科阶段已涵盖的几个主题（例如，常微分方程、拉普拉斯变换、向量微积分、基础数学）线性代数、傅里叶分析和基本边值问题）。显然，作者在选择要包含的主题方面花费了很大的精力，而且教学演示也非常出色。示例问题和章末练习都经过精心挑选，有助于激发正式的数学框架。本书的一个独特之处是从不同的角度重新审视主题，这增强了数学理论的美感和力量。例如，首先在线性代数的背景下考虑 Fredholm 替代方案，然后在常微分方程的背景下考虑。在序言中，作者解决了计算机和软件的普遍使用如何影响高等数学课程中主题的呈现的问题。这是一个极其关键的问题，我非常同意他们的说法：“尽管计算机改变了我们做数学的方式，改变了我们构建解决方案的方式，以及我们如何考虑给定问题的各个部分与整体的关系，这是形式的变化，而不是内容的变化。正文分为三个部分：线性代数、复变量、常微分方程和偏微分方程。作者通过展示理论和应用方面的相互联系，消除了这三个主题彼此孤立的观念。