Calculus Tutorial (Part 1) 2nd Edition

Author: Han Yunrui
Publisher:
Publish Date: 2006-08-01
Features: This book is a carefully revised version of "Calculus Tutorial" compiled by the author based on years of teaching experience and research results, as well as references to several outstanding 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 progress in steps and stages. To facilitate teaching and self-study, the 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 solutions through theoretical, numerical, and graphical analysis. These problems are closely aligned with the fundamental requirements of calculus teaching and training, helping to cultivate students' abilities in analysis and problem-solving. The book is divided into two volumes. The first volume includes the basic concepts and properties of real numbers and functions, the theory of limits and continuous functions, calculus of single-variable functions, and series of terms and functions. The second volume covers the 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.