Mathematical Analysis (Volume III)

Name: Mathematical Analysis (Volume III)
ISBN: 9787301176757

伍胜健Peking University Press · ChinaAug 2025

4.0

Word count: 108K words
Chapters: 110
ISBN: 9787301176757

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Summary

This book gathers and organizes speeches by many of America's most distinguished judges on judicial decision-making, including Judge Posner, long renowned in China; Chief Justice Roberts of the U.S. Supreme Court; former Chief Justices Rehnquist and Warren; and Associate Justices past and present such as Hugo Black, Holmes, Brennan, Ginsburg, and Breyer. O'Brien, a leading scholar of the U.S. Supreme Court, has carefully collected these notable speeches delivered from the standpoint of the decision-maker and arranged them by theme. These speeches are both moving and rational and calm, vividly illuminating every aspect of judicial decision-making. They hold strong reference value for Chinese judges and lawyers, and are also ideal extracurricular reading for law students.

Editor's review

Although titled Mathematical Analysis (Volume 3), this book is in fact a collection of speeches by many renowned American judges on judicial decision-making, compiled and organized thematically by an expert on the U.S. Supreme Court. The speakers include Posner, Roberts, Rehnquist, Warren, Black, Holmes, Brennan, Ginsburg, Breyer, and others, offering a broad range of perspectives from the judges themselves. These speeches are both moving and冷静...

Who it's for

A good fit for

Judges and lawyers who want to understand judicial decision-making and professional expression from the decision-maker's perspective.
Law students seeking extracurricular reading to broaden their understanding of the judicial system and judicial reasoning.
Readers interested in the U.S. Supreme Court and the judicial system in general.
Writers and researchers looking for speech material and insights into legal expression and reasoning.

Not a good fit for

Readers looking for a mathematical analysis textbook or a course book for STEM subjects.
Beginners expecting a systematic law textbook with a conceptual framework.
Readers who only want a full biography of a single justice or the full text of a case.

Reading tips

Start with the editor's thematic classification notes, then choose a topic of interest and read it in depth.
For each speech, first identify the speaker and the occasion, then focus on the main argument.
Compare how different justices address the same judicial issue across topics.
After reading, summarize the core argument of a speech in your own words to check comprehension.

About the publisher

Peking University Press China · Founded in 1979

Peking University Press is a comprehensive university press whose publishing areas cover classical literature, popular science, social culture, world history, Western philosophy, and culture. Its catalogue contains 6,031 titles, with representative books including A Dream of Red Mansions, Relativity: The Special and General Theory (15th Edition) (with Einstein's classic papers on unified field theory and other topics), Elements, Conics, The Aristocratic Families of the Eastern Jin, The Philosophy of Mythology (Volume I), The Philosophy of Mythology (Volume II), and The Origin of Continents and Oceans. Representative authors include Cao Xueqin, Zhou Ruchang, Albert Einstein, Euclid, Apollonius, Tian Yuqing, Schelling, and Xian Gang. The press has developed distinctive strengths in classical Chinese literature and in the translation of Western philosophical classics, while also covering scientific classics and social and cultural studies. As public information is limited, this description is based only on the books in the catalogue and offers no further extrapolation.

版权信息
内容简介
作者简介
第十三章多元函数的极限和连续
§13.1 欧氏空间Rn
13.1.1 欧氏空间Rn
13.1.2 点列极限
13.1.3 聚点
13.1.4 开集与闭集
13.1.5 欧氏空间Rn中的基本定理
§13.2 多元函数与向量函数的极限
13.2.1 多元函数的概念
13.2.2 多元函数的极限
13.2.3 累次极限
13.2.4 向量函数的定义与极限
§13.3 多元连续函数
13.3.1 多元连续函数
13.3.2 多元连续向量函数
13.3.3 集合的连通性
13.3.4 连续函数的性质
13.3.5 同胚映射
习题十三
第十四章多元微分学
§14.1 偏导数与全微分
14.1.1 偏导数
14.1.2 方向导数
14.1.3 全微分
14.1.4 梯度
14.1.5 向量函数的导数与全微分
§14.2 多元函数求导法
14.2.1 导数的四则运算
14.2.2 复合函数的求导法
14.2.3 高阶偏导数
14.2.4 复合函数的高阶偏导数
14.2.5 一阶微分的形式不变性与高阶微分
§14.3 泰勒公式
§14.4 隐函数存在定理
14.4.1 单个方程的情形
14.4.2 方程组的情形
14.4.3 逆映射存在定理
§14.5 多元函数的极值
14.5.1 通常极值问题
14.5.2 条件极值问题
§14.6 多元微分学的几何应用
14.6.1 空间曲线的切线与法平面
14.6.2 曲面的切平面与法线
14.6.3 多元凸函数
习题十四
第十五章重积分
§15.1 重积分的定义
15.1.1 Rn空间中集合的体积
15.1.2 重积分的定义
§15.2 多元函数的可积性理论与重积分的性质
15.2.1 达布理论
15.2.2 重积分的性质
§15.3 化重积分为累次积分
15.3.1 化二重积分为累次积分
15.3.2 化三重积分为累次积分
§15.4 重积分的变量替换
15.4.1 重积分的变量替换公式
15.4.2 利用变量替换计算重积分
§15.5 广义重积分
15.5.1 无穷重积分的基本概念
15.5.2 无穷重积分敛散性的判定
15.5.3 瑕重积分
习题十五
第十六章曲线积分与曲面积分
§16.1 第一型曲线积分
16.1.1 第一型曲线积分的定义
16.1.2 第一型曲线积分的存在性与计算公式
§16.2 第二型曲线积分
16.2.1 第二型曲线积分的定义
16.2.2 第二型曲线积分的存在性与计算公式
§16.3 第一型曲面积分
16.3.1 曲面的面积
16.3.2 第一型曲面积分的定义
16.3.3 第一型曲面积分的存在性与计算公式
§16.4 第二型曲面积分
16.4.1 曲面的侧
16.4.2 第二型曲面积分的定义
16.4.3 第二型曲面积分的存在性与计算公式
§16.5 各类积分之间的联系
16.5.1 格林公式
16.5.2 高斯公式
16.5.3 斯托克斯公式
§16.6 微分形式简介
16.6.1 微分形式
16.6.2 微分形式的外积
16.6.3 外微分
§16.7 曲线积分与路径的无关性
§16.8 场论简介
16.8.1 数量场的梯度
16.8.2 向量场的向量线
16.8.3 向量场的散度
16.8.4 向量场的旋度
16.8.5 一些重要算子
习题十六
第十七章含参变量积分
§17.1 含参变量定积分
§17.2 含参变量广义积分
17.2.1 含参变量无穷积分
17.2.2 含参变量无穷积分的性质
17.2.3 含参变量瑕积分
§17.3 Γ函数与B函数
17.3.1 Γ 函数
17.3.2 B 函数
17.3.3 Γ函数与B函数的关系
习题十七
部分习题答案与提示
名词索引

FAQ

The title says Mathematical Analysis—why is the content about judges' speeches?

This is a case where the title and content in the source material do not match: the book actually collects and organizes speeches by many prominent American judges on court adjudication, classified by theme. When purchasing and reading, rely on the content description rather than the title, and do not treat it as a mathematical analysis textbook.

Whose speeches are included?

According to the source material, the collection includes speeches by Posner; Roberts, the current Chief Justice of the U.S. Supreme Court; former Chief Justices Rehnquist and Warren; and current and former Associate Justices such as Black, Holmes, Brennan, Ginsburg, and Breyer. They were collected and classified by O'Brien, an expert on the U.S. Supreme Court.

Will non-law readers find this book difficult?

The speeches were delivered to audiences and are relatively readable and calmly reasoned, so non-law readers can grasp the main points. However, background on the U.S. judicial system and adjudication may pose obstacles. Readers are advised to learn some basic institutional background first, read by topic, and, for unfamiliar justices, start with the notes on their identity and the occasion.

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About the author

伍胜健 Author

Wu Shengjian is one of the authors of Chinese textbooks on mathematical analysis. Public information about him is limited, and details such as his nationality, education, positions, and dates of birth and death have not been clearly recorded. Two works associated with Wu Shengjian can currently be confirmed, both textbooks on mathematical analysis: Mathematical Analysis (Volume 2), part of the Eleventh Five-Year National Planning Textbook for Higher Education, the Peking University Mathematics Teaching Series, and undergraduate basic mathematics course materials, and Mathematical Analysis (Volume 3). Judging from the titles and the series positioning, these textbooks are intended for undergraduate basic mathematics courses; they belong to the Peking University Mathematics Teaching Series and are listed as national planning textbooks, with examination as a common classification. Their writing follows the needs of course teaching and supports systematic study and exam review of mathematical analysis, making them suitable reference reading for relevant university courses and exam preparation.