Applied Calculus

Author: Zhang Yinsheng An Jianye
Publisher:
Publishing Date: 2002-07-01
Features: Calculus is the essence of rational wisdom in the history of human civilization. Its emergence not only renewed the face of mathematics but also significantly promoted the development of science, technology, and even social sciences. Currently, the theory and methods of calculus have been widely applied in various fields such as natural sciences, engineering technology, and social sciences. It provides not only an advanced mathematical technique but also a cultural quality and refinement essential for human progress. Learning and to some extent mastering the knowledge of calculus is not only a requirement for students in science and engineering but also a fundamental and essential requirement for students in economics, management, humanities, and other disciplines.
However, due to the abstract form and symbolic language of mathematics, which are relatively distant from people's direct lives, calculus teaching and learning have faced significant obstacles and difficulties. As a result, there are still many unsatisfactory aspects in the teaching of calculus in universities: it is abstract to teach, dull to learn, and confusing to apply, making what could have been a vibrant course a persistent challenge for both teachers and students.
Looking toward the 21st century, with the rapid development of the economy and society, various industries and university disciplines have placed new and higher demands on calculus, making calculus education reform even more urgent and important. Can we make the teaching of calculus more vivid and practical? This is a question we often consider. For this reason, we have written this textbook.
When compiling this book, we paid attention to the following points:
1. We tried to start from practical examples, emphasizing the intuitive description and real-world background of concepts and theorems to overcome students' psychological barriers in mathematical cognition. Logical reasoning was kept to a reasonable extent.
2. We fully utilized advanced modern educational technologies, such as computers, to make abstract concepts more tangible and simplify complex calculations. We focused on the liveliness and of the content, reducing overly difficult and tedious computational techniques to free students from.
3. We added practical examples, exercises, and mathematical models to enhance students' awareness and ability to apply mathematics, thereby continuously improving their initiative and enthusiasm for learning.
Practical Calculus is one of the outcomes of the teaching reform project "Research and Practice on the Integration of Information Technology and Economic Mathematics Courses" in ordinary universities in Tianjin in the early 21st century.
Contributors to this book include:
Text sections:
- Zhang Yinsheng (Sections 1.1 to 1.5, 2.1 to 2.3, 3.7)
- An Jianye (Chapters 4 and 5, Sections 1.6, 2.4, 3.8, 6.6)
- Li Binglin (Sections 3.1 to 3.6, 6.1 to 6.5)
- Wang Quanwen (Chapters 7 and 8)
CD-ROM sections:
- An Jianye (simulated demonstrations, calculus models, electronic teaching plans for Chapters 4 and 5, detailed solutions for exercises in Chapters 4 and 5)
- Zhang Yinsheng (course objectives, detailed solutions for exercises in Chapters 1 and 2)
- Li Binglin (detailed solutions for exercises in Chapters 3 and 6)
- Wang Quanwen (analysis of postgraduate examination questions, detailed solutions for exercises in Chapters 7 and 8)
- Li Meifeng (unit tests for Chapters 2, 3, 4, and 5, electronic teaching plans for Chapters 2, 3, and 7)
- Wang Yujin (unit tests for Chapters 1, 6, 7, and 8, electronic teaching plans for Chapters 1, 6, and 8)
- Teng Shujun (biographies of mathematicians)
Additionally, Zhao Fenxia contributed significantly to the printing work, for which we express our gratitude.
To reflect the typicality and breadth of the content, some examples and exercises in the book are adapted from other works, for which we are also grateful. Due to our limitations, there may be areas in the book that are unsatisfactory. We sincerely invite readers to point out any shortcomings.