Calculus Tutorial (Part 1) (2nd Edition)

Author: Han Yunrui, Hu Zhiming, Zhang Guangyuan (editors)
Publisher:
Publish Date: 2006-08-01
Features: This book is a carefully revised version of "Calculus Tutorial" based on the editors' years of teaching experience and research achievements, as well as references to several outstanding domestic and international textbooks. The presentation of concepts and principles is scientific, accurate, clear, and accessible, with fluent language. The examples and exercises emphasize fundamental training, are rich in variety, and progress in steps and stages. 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, following the "discovery—guessing—verification—proof" model, readers are guided to use the mathematical software Mathematica as an auxiliary tool to explore solutions 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 serve as a textbook for calculus (advanced mathematics) courses for non-mathematics majors in science and engineering disciplines at universities.