Calculus

Author: Liu Pu Huang
Publisher:
Publish Date: 2003-08-01
Features: The concept of limits from approximate to precise, from finite to infinite, plays a significant role in cultivating our mathematical thinking, mathematical abstraction, and mathematical application abilities. To help everyone better grasp the fundamental theories, basic knowledge, and basic methods of calculus, and to gain a more comprehensive understanding of its widespread applications in various fields, especially in the economic field, this textbook was carefully compiled based on the author's past calculus textbooks and years of adult education experience. In this book, special attention is paid to the following points: 1. Enhancing accessibility while maintaining rigor: The writing of the textbook should make teachers feel it is a good "teaching manual" and students feel it is a good "learning manual." For this textbook, we have focused on expressing difficult academic language in a more accessible way; introducing new concepts and knowledge follows a presentation style from specific to general; and the explanation of content is designed to align with everyone's thinking habits when learning new knowledge. 2. To ensure a natural connection between knowledge points and a clear focus on content, the textbook's organization has been strengthened for smoothness. One characteristic of adult education is concentrated instruction with self-study in between, and face-to-face teaching time is relatively limited. To improve classroom teaching efficiency, the arrangement of certain content in the textbook has been designed with a focus on concentrated explanations followed by examples. For example, the "Two Important Limits" in Chapter and the "Mean Value Theorem of Differentiation" in Chapter 3. This approach makes the knowledge framework clear, highlights key points, and is also convenient for post-class review or self-study. 3. Strengthening relevance based on the learning characteristics of adult education. Another feature of adult education is a greater emphasis on self-study, so we have fully considered this aspect in the textbook's writing. For example, we have strengthened geometric intuitive teaching, paid attention to a gradual progression from simple to complex, and used methods to disperse difficult points. 4. Learning is for application, so we still focus on strengthening applicability. This book can be used as a textbook for adult higher education in higher financial and economic institutions, or as a teaching and self-study book for higher vocational colleges or those taking the self-study examination for higher education.