Calculus: Early Transcendentals, 5th Edition: 5th Edition

Author: Kaplan
Publisher:
Publish Date: 2004-04-01
Features: The main features of this book are:
● A chapter is dedicated to introducing ordinary differential equations;
● It involves numerical methods. Numerical methods not only have practical value but also help readers gain a deeper understanding of theoretical knowledge;
● The content is rigorous, with all definitions clearly marked, and all important results are presented as theorems in formula form;
● The end of Chapters 2, 4, and 6 provides more detailed knowledge points on real variable theory;
● A large number of exercises and solutions are provided. Some exercises are simple practice problems, while others are quite challenging to encourage readers to think more deeply. Some exercises correspond to specific knowledge points and include hints where appropriate;
● The book offers numerous references, and a further reading list is provided at the end of each chapter.
This book comprehensively introduces vectors and matrices, vector calculus, and partial differential equations. It covers both theoretical knowledge and numerical methods. The book is divided into 10 chapters. The first two chapters introduce linear algebra and partial differential equations. Chapter 3 covers divergence, curl, and some basic identities, briefly introducing rectangular coordinates, and the later sections also discuss tensors in n-dimensional space. The remaining chapters cover integration, infinite series, analytic functions, linear systems, and partial differential equations, among other topics. All definitions are clearly marked, and all important results are presented as theorems in formula form. The book provides numerous exercises with solutions. Additionally, it offers many references and a recommended reading list at the end of each chapter.
The intended readers should have a basic foundation in calculus at the lower university level. This book is suitable as a bilingual teaching material and post-class reference book for graduate students or advanced undergraduate students in courses such as advanced calculus and real analysis. It can also be used as a reference for relevant researchers.