这种新的真实分析方法强调在应用中使用主体，展示真实分析的原理和理论如何在各种环境中应用。应用包括多项式逼近、离散动力系统、微分方程、傅里叶级数和物理学、傅里叶级数和逼近、小波、凸性和优化。每章都有许多有用的练习。
基础理论的处理包括实数、函数和微积分，同时强调赋范向量空间，尤其是Rn的作用。应用章节大多是独立的，让读者可以选择主题。本书适用于既有微积分知识又有线性代数知识的学生，他们希望仔细研究分析及其在应用中的应用。
回顾本书的前一版，真实分析与真实应用
“一本平衡得很好的书！第一门坚实的分析课程，包括证明，在任何数学课程中都是核心课程。——系；————然而，市场上畅销的新书并不总是能达到目标：理论与应用之间的平衡，技术证明与直觉想法之间的平衡，古典与现代学科之间的平衡，现实生活中的练习与钻研新概念的练习之间的平衡。”。戴维森·唐西格（Davidson Donsig）的书很出色，而且确实很中肯。”
Palle E.T.Jorgenson，亚马逊评论。通用域名格式
肯尼斯·R·戴维森是滑铁卢大学的数学教授。艾伦·P·唐西格是内布拉斯加州大学林肯分校的数学副教授。
Real Analysis and Applications: Theory in Practice
This new approach to real analysis stresses the use of the subject in applications, showing how the principles and theory of real analysis can be applied in various settings. Applications cover approximation by polynomials, discrete dynamical systems, differential equations, Fourier series and physics, Fourier series and approximation, wavelets, and convexity and optimization. Each chapter has many useful exercises.
The treatment of the basic theory covers the real numbers, functions, and calculus, while emphasizing the role of normed vector spaces, and particularly of Rn. The applied chapters are mostly independent, giving the reader a choice of topics. This book is appropriate for students with a prior knowledge of both calculus and linear algebra who want a careful development of both analysis and its use in applications.
Review of the previous version of this book, Real Analysis with Real Applications
“A well balanced book! The first solid analysis course, with proofs, is central in the offerings of any math.-dept.; –-and yet, the new books that hit the market don’t always hit the mark: the balance between theory and applications, –-between technical proofs and intuitive ideas, –-between classical and modern subjects, and between real life exercises vs. the ones that drill a new concept. The Davidson-Donsig book is outstanding, and it does hit the mark.”
Palle E. T. Jorgenson, Review from Amazon.com
Kenneth R. Davidson is University Professor of Mathematics at the University of Waterloo. Allan P. Donsig is Associate Professor of Mathematics at the University of Nebraska-Lincoln.
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