Advanced Mathematics. Volume 1

Author: Yang Zesen
Publisher:
Publish Date: 2005-07-01
Features: This book is based on the Ministry of Education's teaching reform project "Research and Practice on Integrating Mathematical Modeling Ideas and Methods into Mainstream University Mathematics Courses," led by Academician Li Daqian of Fudan University, as well as the requirements of Tianjin University's "Eleventh Five-Year Plan" key textbook reform project. It is also written with the experience and insights gained from Tianjin University's long-term reforms in mathematics education. The book retains the fundamental content of calculus while also addressing the new context of technological advancements and the widespread application of computers. It includes "Mathematical Experiments" in each chapter and introduces the ideas and applications of mathematical modeling in relevant sections. Additionally, some practical application problems have been added to the exercises. The book is published in two volumes. The first volume includes six chapters: Functions and Limits, Derivatives and Differentials, Applications of Derivatives, Indefinite Integrals, Definite Integrals, and Space Analytic Geometry and Vector Algebra. The second volume includes five chapters: Multivariable Calculus, Multiple Integrals, Line Integrals and Surface Integrals, Series, and Differential Equations. Each chapter is followed by a sufficient number of exercises, and the book includes reference answers to the exercises at the end.