Calculus Tutorial - (Upper) (2nd Edition)

Author: Han Yunrui, Hu Zhiming, Zhang Guangyuan
Publisher:
Publish Date: 2006-08-01
Features: This book is a carefully revised version of "Calculus Tutorial" compiled by the authors based on years of teaching experience and research achievements, as well as references to several excellent domestic and international textbooks. The presentation of concepts and principles in this book is scientific, accurate, clear, and accessible, with fluent language. The examples and exercises emphasize fundamental training, are rich in variety, and gradually increase in difficulty and scope. To facilitate teaching and self-study, answers to exercises and hints for supplementary problems are provided in the appendix, along with an index of calculus concepts and terminology. Additionally, in Appendix A, readers are guided to use the mathematical software Mathematica as an auxiliary tool, following the "discovery—guessing—verification—proof" model, to explore problem-solving through theoretical, numerical, and graphical analyses. These problems are closely aligned with the fundamental requirements of calculus teaching and training, helping to cultivate students' analytical and problem-solving skills. The book is divided into two volumes. The first volume includes the basic concepts and properties of real numbers and functions, theories of limits and continuous functions, calculus of single-variable functions, and series of terms and functions. The second volume covers differential calculus of multivariable functions and its applications, multiple integrals, line and surface integrals, an introduction to vector fields, and an introduction to ordinary differential equations. This book can be used as a textbook for calculus (advanced mathematics) courses in non-mathematics majors of science and engineering disciplines in universities.