Advanced Mathematics (Volume 2) (Second Edition)

Name: Advanced Mathematics (Volume 2) (Second Edition)
ISBN: 9787568919296

蒋卫生 / 王开荣 / 张谋 / 穆春来 / 李东Chongqing University Press · ChinaJan 2021

3.6

Word count: 133K words
Chapters: 53
ISBN: 9787568919296

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Summary

This textbook focuses on cultivating students' mathematical literacy and provides a systematic exposition of calculus. Basic concepts, principles, methods, and applications unfold progressively. It emphasizes intuition and readability, strives to ensure the integrity and traceability of the overall system, and inspires students' creativity in analyzing and solving problems with what they have learned. The book is divided into two volumes. The upper volume covers limits, derivatives and differentials, the fundamental theorems of differential calculus and their applications, indefinite integrals, definite integrals, and applications of definite integrals; the lower volume covers vector algebra and analytic geometry in space, differentiation of functions of several variables and its applications, multiple integrals, line and surface integrals, infinite series, and differential equations.

Editor's review

Higher Mathematics (Vol. 2), 2nd Edition is a newly revised textbook published by Chongqing University Press, edited by Professor Jiang Weisheng, ISBN 9787568919296. As a core textbook for a foundational science and engineering course, this book continues the clear structure and rigorous style of the previous edition, with notable improvements in content organization and worked examples. This second volume covers core topics including analytic geometry in space, differential calculus of functions of several variables, multiple integrals, line and surface integrals, infinite series, and ordinary differential equations—the bridge between higher mathematics and subsequent specialized courses.

From an editor's professional perspective, the book's most prominent value lies in its 'problem-driven' narrative logic. Each chapter introduces abstract concepts from practical engineering or physics problems—for example, introducing line integrals of the second kind through gravitational field problems. This arrangement effectively alleviates beginners' fear of mathematical abstraction and helps build intuitive understanding. The worked examples and exercises are thoughtfully selected, including both classic problems to consolidate foundational knowledge and some challenging comprehensive application problems, with a clear gradation.

Compared with some textbooks that pursue 'comprehensive coverage,' this book is relatively restrained in length and focused in emphasis. Professor Jiang Weisheng has long taught engineering mathematics, and his experience is reflected in his precise grasp of engineering students' practical needs: some overly theoretical proofs are omitted, while calculation methods and application examples are strengthened, making the book particularly suitable for application-oriented engineering students. Based on frontline teaching feedback, the second edition has refined the presentation of some concepts to make them easier to understand and updated some exercises to connect more closely with contemporary technological contexts.

Overall, this is a clearly positioned and highly practical teaching book. It may not be the textbook with the deepest mathematical theory, but it is certainly a reliable guide to help most engineering students solidly master the core tools of Higher Mathematics Vol. 2 and transition smoothly to specialized coursework. For mathematics majors pursuing rigorous logical beauty, it may be somewhat insufficient, but its clear engineering application orientation is precisely its core value.

Who it's for

A good fit for

Undergraduates in engineering majors (such as mechanical, electrical, computer, and civil engineering) currently studying Higher Mathematics Vol. 2
Candidates preparing for graduate entrance examinations who need to review or consolidate knowledge of multivariable calculus, series, and related topics
Working professionals in engineering and technical fields who need to consult or refresh relevant mathematical tools
Beginners who prefer to understand mathematical concepts starting from practical problems and application scenarios

Not a good fit for

Mathematics majors or learners with extremely high requirements for the rigor and completeness of the mathematical theoretical system
Students in social sciences or economics and management who only need the most basic concepts of higher mathematics and do not require the in-depth content of Vol. 2

Reading tips

It is recommended to study in the order of the textbook chapters, focusing on the practical problems introduced at the beginning of each chapter to establish learning motivation
For difficult topics such as multiple integrals and line and surface integrals, be sure to complete a sufficient number of calculation exercises by hand; never just read without practicing
The comprehensive review problems at the end of the book are relatively integrative and can be used after completing the entire volume to test knowledge integration and application ability

About the publisher

Chongqing University Press China · Founded in 1985

Chongqing University Press is a comprehensive university press whose publishing areas span social and cultural studies, industrial technology, finance and economics, medicine, social psychology, and theory. Judging from its catalog, the press publishes both academic works and popular science titles. Representative books include E. H. Gombrich's Shadows: The Depiction of Cast Shadows in Western Art, Magnesium-Based Hydrogen Storage Materials by Pan Fusheng et al., Research on China's Regional Spatial Development Models by Sun Jiuwen, and titles from the Gynecologic Oncology Committee of the Chinese Anti-Cancer Association, such as the Guidelines for Diagnosis and Treatment of Common Gynecologic Malignancies in China (2019) and Bipolar Disorder: What You and Your Family Need to Know. Its authors work in art history, materials science, regional economics, clinical medicine, and social research methods. Public information is limited, but its publishing profile combines academic translation, industrial technology, and practical medical guides.

版权信息
第7章向量代数与空间解析几何
7.1 空间直角坐标系与向量
7.2 向量的乘法运算
7.3 平面与直线
7.4 空间曲面与曲线
7.5 二次曲面
习题7
第8章多元函数微分法及其应用
8.1 多元函数的基本概念
8.2 偏导数
8.3 全微分
8.4 多元复合函数的求导法则
8.5 隐函数的微分法
8.6 多元函数微分学在几何上的应用
8.7 方向导数与梯度
8.8 多元函数的泰勒公式与极值
习题8
第9章重积分
9.1 二重积分的概念和性质
9.2 二重积分的计算法
9.3 三重积分
9.4 重积分的应用
∗9.5 含参变量的积分
习题9
第10章曲线积分与曲面积分
10.1 对弧长的曲线积分
10.2 对坐标的曲线积分
10.3 格林公式及其应用
10.4 对面积的曲面积分
10.5 对坐标的曲面积分
10.6 高斯公式、通量与散度
10.7 斯托克斯公式、环流量与旋度
习题10
第11章无穷级数
11.1 常数项无穷级数
11.2 常数项无穷级数的审敛法
11.3 幂级数
11.4 函数展开成幂级数
11.5 傅里叶级数
习题11
第12章微分方程
12.1 微分方程的基本概念
12.2 变量可分离的微分方程
12.3 一阶线性微分方程
12.4 全微分方程
12.5 可降阶的高阶微分方程
12.6 二阶变系数线性微分方程
12.7 二阶常系数线性微分方程
12.8 微分方程的幂级数解法
习题12
习题答案
参考文献

FAQ

What are the characteristics of this book compared with Tongji University's Higher Mathematics?

This book is more oriented toward engineering applications, with concepts often introduced through engineering examples, relatively concise theoretical derivations, and examples and exercises that are more closely aligned with engineering students' professional backgrounds. The Tongji edition has a more complete and classic theoretical system and a broader scope of application. Readers can choose according to their own professional needs and learning style.

Is this book suitable for self-study?

Yes. The book's explanations are relatively detailed, the steps in worked examples are clear, and it includes answers or hints to exercises (please confirm the version you have), making it suitable for readers with a certain high school mathematics foundation to study on their own. It is recommended to combine it with open course videos and other resources for better results.

What are the main changes in the 2nd edition compared with the 1st edition?

The 2nd edition mainly optimizes the presentation of some concepts based on teaching feedback to make them clearer and easier to understand; updates and supplements some examples and exercises to make them more contemporary and representative; and may have made minor adjustments to the order of some chapters to make the teaching logic smoother. For specific changes, please refer to the book's preface.

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About the author

蒋卫生 Author

Jiang Weisheng is an author about whom limited public information is currently available. The known work compiled by this author is Higher Mathematics (Volume II) (2nd Edition). Judging from the title, the book belongs to exam-oriented materials and covers the core content of the second volume of higher mathematics, typically including multivariable calculus, series, and differential equations. It is mainly intended for science and engineering students or learners preparing for related examinations. Given the limited background information, Jiang Weisheng's role is best understood as that of a textbook compiler whose writing and organization serve course teaching and exam preparation. Because verifiable details about the author are scarce, no further information on education, affiliation, or research focus can be provided. Readers may regard Jiang Weisheng as one of the compilers of higher mathematics textbooks and gain a sense of the author's approach through the use of Higher Mathematics (Volume II) (2nd Edition).

王开荣 Author

Wang Kairong: publicly available information is limited, and at present only one work by this author is known in the database, namely Advanced Mathematics (Volume 2), 2nd Edition. The book belongs to the examination-preparation category, intended for readers who need to review or prepare systematically for advanced mathematics. Judging from the title and category, its content centers on the core knowledge of the second volume of advanced mathematics, with exercises and explanations that help readers organize key points and consolidate fundamentals. As a textbook-type publication, its writing style emphasizes clarity and practical guidance, combining conceptual understanding with problem-solving practice. Although the author's biography, academic background, and professional positions are not publicly documented, this work offers readers an optional study resource in the field of advanced mathematics exam preparation, suitable for use alongside classroom teaching or for self-study, and it reflects the author's experience in compiling materials for mathematics teaching and examination coaching.

张谋 Author · China

Publicly available information about Zhang Mou is currently limited, and no clear records of his life, education, or professional positions have been found. Judging from the work held in the catalog, Zhang Mou is associated with the writing of higher mathematics textbooks; his representative work is Higher Mathematics (Vol. 2), 2nd Edition, which is classified on the site under exam preparation and is aimed mainly at students who need to review higher mathematics systematically and prepare for related examinations. In terms of subject matter, such textbooks generally focus on organizing basic concepts, theorems, and problem-solving methods, emphasizing a complete knowledge system along with worked examples and exercises, so that readers can study step by step and fill in gaps. Because the author's name is given only briefly and verifiable details are scarce, his writing style and academic background cannot be described in depth; the positioning of the work, however, suggests a practical, exam-oriented approach serving the needs of university coursework and examination review.

穆春来 Author

Publicly available information about Mu Chunlai is currently limited. The only known work under this name in the bibliographic database is Advanced Mathematics (Vol. 2), 2nd Edition. Judging from the title and the common category of "examinations," this is a textbook-oriented book intended for university mathematics courses and exam review. Its content centers on the topics covered in the second volume of advanced mathematics and is aimed mainly at students who need to organize key course points systematically and prepare for course assessments or further examinations. Given this focus on textbook instruction and exam preparation, Mu Chunlai's writing is likely to emphasize a complete presentation of the knowledge system, the integration of concepts with worked examples, and a layout convenient for review and reference. Beyond this single work, no reliable information is available about the author's personal background, education, or research field, so no speculation is offered here. Readers interested in studying or preparing for advanced mathematics may use this work as a reference for understanding the author's writing direction.

李东 Author

Li Dong is an author with a notably broad range of subjects. Public information about him is limited, and his nationality and dates of birth and death are not clearly recorded; eight of his works are currently available. His writing spans several fields. In business and management, he focuses on the practical difficulties of corporate growth and business models, discussing how mature companies can sustain growth and how to analyze the fate of an enterprise. In history, he uses the Han-Xiongnu struggle as a thread to trace centuries of division and integration in the Western Regions. He has also written or contributed to textbooks and software-learning materials in science and engineering, including advanced mathematics and power supply technology for rail transit auxiliary systems, as well as a practical work on interpersonal communication aimed at personal growth. The novel The Extinction of Earthlings reveals a further side of his writing in science fiction. Overall, Li Dong's work combines knowledge popularization with practical analysis, covers a wide range of topics, and is marked by clear organization and close attention to real-world problems.