Elementary Calculus: A Comprehensive Guide

Author: Zhou Guozhen
Publisher:
Publish Date: 2002-01-01
Features: This book concisely introduces the fundamental knowledge of calculus, avoiding rigorous theoretical arguments and completeness, focusing on applications. A large number of examples are also an important part of the writing. Starting from the introduction of limits, it successively introduces concepts such as derivatives, differentials, definite integrals, and indefinite integrals, emphasizing their connections, i.e., the Fundamental Theorem of Calculus. It systematically introduces methods for finding derivatives and various techniques for calculating integrals, and provides detailed examples of the applications of definite integrals in geometry and physics, as well as the role of derivatives in studying the properties of functions. Additionally, it outlines the theory of infinite series, including tests for convergence and the expansion of functions into power series. The last chapter introduces the basic knowledge of differential equations and the solutions to five special forms of equations, illustrating their applications in solving various physical and engineering problems. This book is aimed at high school students and readers with high school-level mathematics knowledge. From it, readers can not only learn the fundamental knowledge of calculus but also understand how to apply calculus to solve practical problems.