College Mathematics: Calculus

Author: Du Zhongfu
Publisher:
Publish Date: 2004-08-01
Features: This book is a research achievement of the National Planning Project of the Ministry of Education's "15th Five-Year Plan" in educational science. It is the "College Mathematics - Advanced Mathematics" volume of the applied series textbooks edited by Du Zhongfu of Beihua University (this series includes "College Mathematics - Advanced Mathematics," "College Mathematics - Linear Algebra," and "College Mathematics - Probability and Statistics"). The book consists of ten chapters, covering main topics such as: functions and limits, derivatives and differentials, matrices, mean value theorems and applications of derivatives, integral calculus of single-variable functions, ordinary differential equations, infinite series, spatial analytical geometry, differential calculus of multivariable functions, integral calculus of multivariable functions, and an introduction to field theory. The main feature of this book is the organic integration of mathematical experiments with theoretical teaching, fully utilizing modern educational technologies. Some abstract and difficult-to-teach-and-learn content that students must understand is processed through experiments or demonstrations. For complex computational problems, students are not required to do extensive practice but should grasp the content and methods. Large amounts of calculations can be completed using computers (software), freeing students from heavy computations. The experimental content plays a connecting role in the entire textbook system, with coherence between theory and experiments. Another feature of the book is its emphasis on the combination of mathematics and practical application problems, adding training in mathematical modeling to help students understand the role of mathematics and improve their modeling skills, as well as mastering the preliminary application of mathematics. The book focuses on mathematical thinking methods, using experimental means to address some important but difficult-to-extend topics in teaching, and handling computational problems through experiments. Some content with strong conceptual and methodological aspects is appropriately expanded to broaden students' perspectives. Additionally, by using this book for teaching, teachers can balance theory and experiments effectively, reducing teaching hours while achieving better results. This book is suitable for non-mathematics majors in applied institutions.