Higher Mathematics Comprehensive Guidance (Volume 2): Tongji · Higher Mathematics (Fifth Edition) Solutions

Author: Liu Houtan, Hou Bin, et al
Publisher:
Publishing Date: 2004-01-01
Features: This book is a guiding reference for higher mathematics learning and teaching. Its features are as follows:
(1) The content of this book is strictly controlled within the teaching syllabi of science and engineering majors (non-mathematics) at the undergraduate and graduate levels, as well as the national postgraduate entrance examination syllabus. For parts that exceed the syllabus but may still be tested, an asterisk () is used to indicate them.
(2) The book is organized in the order of textbook chapters, with each chapter consisting of five parts:
1. Key Points Overview. This includes the rationale for the chapter, the problems to be addressed, important concepts, definitions, theorems, and various problem-solving procedures. Essentially, the "Key Points Overview" serves as class notes and is the theoretical foundation for problem-solving.
2. Difficulties and Solutions. This covers the judgment of important true-or-false issues, the understanding of key concepts, definitions, and theorems, and the analysis of common mistakes in problem-solving. These are crucial for improving mathematical proficiency. As is well-known, solving problems is an important means of mastering theory and promoting application in mathematics learning. Practice makes perfect—seeing more solutions broadens one's knowledge, and doing more exercises sharpens one's skills. Based on years of experience in teaching higher mathematics, the authors have categorized problem-solving training into difficulty levels i, ii, and iii, providing progressive practice, which is further divided into the following sections.
3. Selected Problem Solutions. Difficulty level i, selected from Higher Mathematics (4th Edition) compiled by Tongji University. This book is widely used and has been in circulation for a long time, and it has been proven to be one of the excellent higher mathematics textbooks currently available. The exercises included are classic and essential for fundamental training. We have removed a few simple and repetitive exercises, leaving the rest as "Selected Problem Solutions." For students in junior and senior colleges who are just beginning to learn higher mathematics, this is a must-master basic training. For easy reference, the following coding system is used, for example, 3·2·4（2） indicates that the problem is selected from the 4th major problem of the 2nd section of the 3rd chapter (2).
4. Selected Practice Problems. Difficulty level ii, selected from typical examination papers and question banks of universities. It is recommended that readers first attempt these problems independently. If difficulties arise, they can refer to the answers provided at the end to summarize their learning experiences. This section of practice problems will broaden problem-solving perspectives and improve skills, undoubtedly being highly beneficial for students preparing for final exams.
5. Typical Examples. Difficulty level iii, including almost all unified examination questions from the national postgraduate entrance examinations from 1987 to 2001, as well as typical problems with similar difficulty levels. For readers preparing for postgraduate entrance exams, after reviewing the "Key Points Overview" and "Difficulties and Solutions," they can directly study the "Typical Examples" to grasp the trends of the exam, enhance problem-solving flexibility, and significantly improve their abilities. Among the vast sea of mathematical problems, how to select materials and topics to guide readers to use the least time to progress step-by-step and efficiently achieve good results in final exams or postgraduate entrance exams is a very worthwhile issue to explore. The authors have made some attempts in this regard, and any shortcomings are sincerely welcome to be criticized and corrected by experts and readers.
Additionally, the book includes two final examination papers and two new postgraduate entrance examination papers and solutions from 2003 for reference during revision.