Brief Calculus (Third Edition)

Author: Gong Sheng
Publisher:
Publish Date: 2005-08-18
Features: In Chapter, it first introduces the concepts of definite integrals and differentiation, then reveals how they become a unity of opposites through the Fundamental Theorem of Calculus. In Chapter 2, when discussing operations, it emphasizes the manifestation of this main contradiction in the process, pointing out the close relationship between differentiation and integration. In Chapter 3, it focuses on applications, training students to use calculus as a tool to solve practical problems, paying special attention to coordination with physics courses, so that students can grasp this main contradiction more firmly and flexibly through application. Chapter 4 covers ordinary differential equations, viewing it as a further development and application of the contradiction between differentiation and integration. In the second volume, when teaching multivariable calculus, it uses exterior differential forms to clearly explain how differentiation and integration become a pair of contradictions. In the third volume of this book, ε-δ language and Fourier analysis will be introduced, emphasizing the relationship between continuity and discreteness, so that students can gain a deeper understanding of the contradiction in calculus based on their previous learning.