Advanced Mathematics (Volume 1)
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Summary
Editor's review
Who it's for
A good fit for
- Undergraduates in chemical engineering, applied chemistry, bioengineering, and related majors using it alongside a higher mathematics course
- Engineering students who need a solid calculus foundation for subsequent major courses
- Teachers of engineering higher mathematics using it as a main course textbook
- Science and engineering self-learners who want to understand mathematical applications in a professional context
Not a good fit for
- Mathematics majors who need deeper theoretical analysis and proof training
- General readers who only want popular mathematics and do not plan to work through exercises systematically
- Exam candidates seeking specialized technique training for graduate entrance mathematics exams
Reading tips
- Study in chapter order: understand concepts and derivations first, then work through the basic end-of-chapter exercises.
- After each section, try restating the definitions and theorem conditions in your own words to check your understanding.
- Think about how mathematical methods are used in professional experiments or engineering examples to strengthen motivation.
- Keep an error notebook and regularly review typical mistakes in limits and integrals.
About the publisher
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.
Contents
- 版权信息
- 前言
- 内容简介
- 第一章 极限
- §1.1 数列的极限
- §1.2 函数的极限
- §1.3 无穷小与无穷大
- §1.4 极限的运算法则
- §1.5 极限存在准则·两个重要极限
- §1.6 无穷小的比较
- §1.7 函数的连续性与间断点
- §1.8 连续函数的运算与初等函数的连续性
- §1.9 闭区间上连续函数的性质
- 总练习题一
- 第二章 导数与微分
- §2.1 导数的概念
- §2.2 函数的求导法则
- §2.3 高阶导数
- §2.4 隐函数及由参数方程所表示的函数的导数·相关变化率
- §2.5 函数的微分及其应用
- 总练习题二
- 第三章 微分中值定理与导数应用
- §3.1 微分中值定理
- §3.2 洛必达法则
- §3.3 泰勒公式
- §3.4 函数的单调与极值
- §3.5 函数的最大值与最小值
- §3.6 曲线的凹凸性与拐点
- §3.7 函数图形的描绘
- §3.8 曲 率
- *§3.9 函数方程的数值解法
- 总练习题三
- 第四章 不定积分
- §4.1 不定积分的概念与性质
- §4.2 换元积分法
- §4.3 分部积分法
- §4.4 特殊类型函数的积分
- 总练习题四
- 第五章 定积分及其应用
- §5.1 定积分的概念及性质
- §5.2 微积分基本公式
- §5.3 定积分的换元积分法和分部积分法
- §5.4 广义积分
- §5.5 定积分的元素法
- §5.6 定积分的应用
- *§5.7 定积分的数值计算方法
- 总练习题五
- 第六章 常微分方程
- §6.1 常微分方程的基本概念
- §6.2 可分离变量的微分方程
- §6.3 齐次方程
- §6.4 一阶线性微分方程
- §6.5 可降阶的高阶微分方程
- §6.6 二阶线性微分方程
- §6.7 二阶常系数齐次线性微分方程
- §6.8 二阶常系数非齐次线性微分方程
- §6.9 欧拉方程
- *§ 6.10 一阶微分方程的数值解法
- § 6.11 微分方程应用举例
- 总练习题六
- 附录一 二阶和三阶行列式的计算
- 附录二 常用的参数方程与极坐标系的曲线
- 习题答案与提示
FAQ
How is this book different from a higher mathematics textbook for mathematics majors?
What does Volume One mainly cover?
Can students with a weak foundation use it directly?
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About the author
Chu Baozeng is an author mainly engaged in compiling advanced mathematics textbooks. Public information about this author is currently limited, and his nationality, dates of birth and death, and educational background cannot be confirmed. Judging from the four works included in the database, his writing focuses on basic mathematics courses for engineering students in higher education. Representative works include Advanced Mathematics (Volume 1), Advanced Mathematics (Volume 2), and Advanced Mathematics (Volume 2), a mathematics textbook for engineering colleges in the 21st century. These textbooks are intended for university engineering students and cover the core knowledge system of advanced mathematics. They are arranged in two volumes to facilitate semester-based teaching. The works are classified under examinations and popular science, indicating that their compilation takes into account both course study and exam review. Overall, Chu Baozeng's textbooks emphasize foundational and systematic content and serve the daily needs of mathematics teaching in universities, offering practical value in engineering mathematics education.
Chen Zhaodou: public information is limited. At present, it is known only that four of his works have been collected, mainly concentrated on the compilation of higher mathematics textbooks. His representative works include Higher Mathematics (Volume I), Higher Mathematics (Volume II), and Higher Mathematics (Volume II), a higher mathematics textbook for engineering students in 21st-century colleges and universities. These titles indicate that his writing is aimed at higher mathematics teaching for engineering students in colleges and universities, covering both the first and second volumes of higher mathematics. In common classifications, his works are grouped under examinations and popular science, suggesting that, in addition to classroom use, the relevant textbooks are often used by readers for exam preparation and self-study. Overall, Chen Zhaodou's compilation work centers on the basic higher mathematics curriculum and serves the mathematics learning needs of engineering students, with a style inclined toward systematic and standard textbook conventions.
