Higher Mathematics
Tags
Summary
Editor's review
Who it's for
A good fit for
- First- or second-year students majoring in engineering or science at higher education institutions
- Learners preparing for graduate entrance examinations who need to systematically review foundational knowledge of advanced mathematics
- Working professionals in engineering and technical fields who wish to revisit or strengthen their ability to apply mathematical tools
- Enthusiasts with a strong interest in mathematics who wish to self-study the core content of advanced mathematics
Not a good fit for
- Readers who only need elementary mathematics or a general overview of mathematics for liberal arts
- Test-takers seeking quick-fix techniques or exam shortcuts without a willingness to deeply understand the theoretical system
Reading tips
- It is recommended to study in chapter order, focusing on understanding the origins and development of each definition and theorem rather than rushing ahead.
- Carefully complete the exercises after each section; this is key to testing comprehension and building computational skills.
- Abstract mathematical concepts can be understood in conjunction with specific physical or engineering models to enhance intuitive understanding.
About the publisher
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.
Contents
- 版权信息
- 内容简介
- 前言
- 第1章 函数
- 1.1 函数的概念
- 1.2 函数的几个基本性质
- 1.3 基本初等函数
- 1.4 复合函数与初等函数
- 复习题 1
- 第2章 极限与连续
- 2.1 函数的极限
- 2.2 函数极限的运算法则
- 2.3 两个重要极限
- 2.4 无穷大量与无穷小量
- 2.5 函数的连续性
- 2.6 闭区间上连续函数的性质
- 复习题 2
- 第3章 导数与微分
- 3.1 导数的概念
- 3.2 求导法则
- 3.3 求导举例
- 3.4 高阶导数
- 3.5 隐函数的导数
- 3.6 函数的微分
- 3.7 补充例题
- 复习题 3
- 第4章 中值定理与导数的应用
- 4.1 微分中值定理
- 4.2 罗必达法则
- 4.3 函数的单调性和极值
- 4.4 函数的最大值与最小值
- 复习题 4
- 第5章 不定积分
- 5.1 不定积分的概念
- 5.2 换元积分法
- 5.3 分部积分法
- 复习题 5
- 第6章 定积分
- 6.1 定积分的概念
- 6.2 定积分的性质
- 6.3 微积分学基本定理
- 6.4 定积分的换元积分法与分部积分法
- 6.5 广义积分
- 6.6 定积分的应用
- 复习题 6
- 第7章 常微分方程
- 7.1 微分方程的基本概念
- 7.2 一阶微分方程
- 7.3 线性方程解的结构
- 7.4 二阶线性常系数微分方程
- 复习题 7
- 第8章 多元函数微分学
- 8.1 多元函数及其基本概念
- 8.2 多元函数的极限与连续
- 8.3 偏导数
- 8.4 全微分
- 8.5 多元复合函数求导法则
- 8.6 隐函数求导公式
- 8.7 多元函数的极值
- 复习题 8
- 第9章 二重积分
- 9.1 二重积分的概念及其性质
- 9.2 利用直角坐标计算二重积分
- 9.3 利用极坐标计算二重积分
- 复习题 9
- 第10章 无穷级数
- 10.1 数项级数
- 10.2 正项级数
- 10.3 交错级数、绝对收敛与条件收敛
- 10.4 幂级数
- 复习题 10
- 习题参考答案
- 附录 简单积分表
- 参考文献
FAQ
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About the author
Wang Guo'an is an author with limited publicly available information; the library currently holds two of his works, Higher Mathematics and Automotive Marketing Practice. Judging from the titles, his writing spans two quite different fields: basic science and engineering coursework on the one hand, and practical marketing in the automotive industry on the other, suggesting an approach that combines theoretical teaching with vocational application. The works are commonly classified under examination preparation, indicating that they may be intended for readers studying for exams, following courses, or undergoing skills training. Higher Mathematics points to foundational mathematics teaching at the college level, while Automotive Marketing Practice focuses on hands-on knowledge in automotive sales and service. Both emphasize systematic organization of key points and practical application. Since no reliable records of his birth and death dates, nationality, education, or professional career are available, judgments about his writing style and influence can only be based on the existing titles: the language is likely to be clear and standardized in a textbook manner, with attention to orderly concepts and feasible procedures. Overall, Wang Guo'an's works reflect an interdisciplinary, practice-oriented approach to compilation and may serve as course supplements or introductory industry references.
Wang Lijing is an author about whom little public information is currently available. The library holds one work by her, Advanced Mathematics. Judging from the title and its common classification under "examinations," the book is likely intended for readers preparing for examinations in advanced mathematics, making it a test-preparation or review guide. Advanced mathematics is abstract and dense with formulas and derivations, and such guides typically organize the knowledge framework, summarize problem types, and explain solution methods, helping readers consolidate fundamentals and become familiar with common test points within limited time. Owing to limited information, Wang Lijing's educational background, affiliation, or writing experience cannot be confirmed, nor can her writing style or specific arrangement be described in detail. Readers who choose this book should use it as one reference tool within their review, in light of the examination syllabus and their actual needs, rather than as the sole basis for preparation.
Liu Yufeng, whose publicly available information is currently limited, appears in the library's records as the author of the book Advanced Mathematics. Judging from the existing information, the book is classified under examinations and serves the study and test-preparation needs of those whose exams include advanced mathematics. As the author, he undertakes the task of organizing foundational content such as limits, derivatives, and integrals into textbook-style material that is convenient for review, balancing knowledge consolidation with exam-oriented practice. Works of this kind usually emphasize clear concepts, representative worked examples, and well-matched exercises, helping readers build a knowledge framework and become familiar with common question types within a limited time. Since there are no reliable records of his life, nationality, education, or awards, this introduction does not speculate about his personal history or exaggerate his academic standing; it only describes the editorial orientation reflected in the library's copy, and his fuller profile awaits more public information.
Li Ke is an author about whom little public information is available; his nationality, dates of birth and death, and educational background are not clearly recorded, so a complete biography cannot yet be confirmed. Judging from the two works held in the collection, Advanced Mathematics and Online Store Operations, Li Ke's writing spans the two fields of exam preparation and business management, covering a fairly wide range of subjects and showing an ability to write for different groups of readers. The former is an exam-oriented textbook, typically emphasizing a well-organized body of knowledge and practical explanation of worked examples; the latter falls under management and generally deals with the processes and methods of running an online store day to day. One work leans toward basic academic training and the other toward practical operation, and both share an emphasis on readability and application rather than theoretical elaboration. Because information about the author remains limited, his writing style and influence can only be tentatively judged from the existing titles; should more material become available, his person and work could be further supplemented and explained.