Advanced Mathematics. Volume 2

Author: Tongji University
Publisher:
Publish Date: 2001-07-01
Features: This book is primarily intended for vocational and technical college students in engineering disciplines at higher education institutions, but it can also be used by students in business and management programs. It serves as a textbook or reference book for adult education, self-study exams, "upgrading to a bachelor's degree" programs, and diploma exams. This book is part of the Ministry of Education's vocational and technical college planning textbooks. Based on the latest "Basic Requirements for Higher Mathematics Teaching in Vocational and Technical Education" issued by the Ministry of Education, as well as the "Review and Examination Syllabus for Admissions to Undergraduate Programs in Adult Higher Education Institutions (Non-teacher training category)," it was collectively compiled by four universities—Tongji University, Tianjin University, Zhejiang University, and Chongqing University—after extensive research, analysis, comparison of various similar textbooks, and incorporating feedback from peers nationwide. The book is divided into two volumes, containing a total of 11 chapters (see table of contents). Its distinctive features include "connecting theory to practice, deepening concepts, emphasizing applications, and valuing innovation," fully reflecting the principle of "aiming at application with essential and sufficient content." The content is arranged in close alignment with elementary mathematics, progressing from specific to general, and from concrete to abstract. It explains fundamental concepts and theorems through geometric, physical, and practical contexts, making it easy to teach and learn. Given the widespread use of computers and the increasing sophistication of mathematical software, the book attempts to integrate higher mathematics teaching with computer functions. Both volumes include four simple yet engaging mathematical experiments in the appendices, accompanied by demonstration disks. These experiments are part of and an extension of higher mathematics but are relatively independent, allowing for demonstrations or experiments based on actual teaching needs after the core content is covered. The book combines the textbook with supplementary materials, serving dual purposes. While maintaining the strengths of traditional textbooks—such as rigorous structure and clear logic—it includes a "Study Guide" at the end of each chapter, covering basic requirements, key points, example analysis and solutions, and comprehensive review exercises (divided into Category A and Category B). The book features abundant examples and exercises, with rolling reviews of key content to facilitate self-study. While ensuring the fulfillment of basic teaching requirements, it appropriately broadens the knowledge base, expands adaptability, and strengthens the integration of computer functions, making it conducive to flexible and elastic teaching models. It also lays a solid foundation for further studies, such as "upgrading to a bachelor's degree."