Calculus Basics Tutorial

Author: Zhang Yinsheng
Publisher:
Publish Date: 2004-08-01
Features: This textbook is suitable for undergraduate programs with fewer credit hours and vocational and technical colleges, as well as for personal self-study as an introductory reference for advanced mathematics courses. To reflect the typicality and breadth of the content, some examples and exercises in the book are adapted from other works, and we extend our gratitude here. Advanced mathematics not only provides a high-level mathematical technique but also represents a cultural quality and literacy essential for human progress. Learning and to some extent mastering the knowledge of advanced mathematics is a fundamental requirement for contemporary college students.
However, due to the abstract nature of mathematics and its symbolic language, which are relatively distant from people's daily lives, it poses significant obstacles and difficulties in both teaching and learning advanced mathematics. As a result, there are still many unsatisfactory aspects in the teaching process of advanced mathematics: it is abstract to teach, dull to learn, and confusing to apply, making what should be a vibrant course a persistent challenge for both teachers and students in the classroom.
Looking toward the new century, with the rapid development of the socio-economy, industries in society and various disciplines in universities have all placed new and higher demands on advanced mathematics. Can we make the teaching of advanced mathematics more engaging and practical? This is a question we often consider. To address this, when compiling this textbook, we strive to achieve the following:
1. To the extent possible, base the content on practical examples, emphasizing the intuitive description and real-world context of concepts and theorems to overcome students' psychological barriers in mathematical cognition; logical reasoning is kept to a minimum.
2. To fully utilize advanced modern teaching technologies, enabling students to grasp the basic applications of computers in advanced mathematics during their learning process, making abstract concepts more concrete and simplifying complex calculations.
3. To cultivate students' awareness and ability to apply mathematics, thereby continuously enhancing their initiative and enthusiasm for learning mathematics.