Advanced Mathematics Tutorial and Problem Solutions. Volume 1 (Compatible with the 5th Edition of the Tongji Textbook) (Second Revised Edition)

Author: Peng Hui et al.
Publisher:
Publish Date: 2005-08-01
Features: This book is divided into twelve chapters, each further divided into several sections. The chapter structure and titles are consistent with those of the "Textbook." In this book, each section includes three main parts:
1. Key Knowledge Points and Exam Focuses: Using a tabular format, it systematically organizes the basic concepts, theorems, and formulas involved in each section, highlighting the key points to note when understanding and applying these concepts, theorems, and formulas. It also specifically points out the important knowledge frequently tested in various exams;
2. Classic Example Problem Analysis: Extensive research has been conducted to select representative and typical example problems for classification and analysis. During the problem-solving process, there is a "Thought Exploration" section to help readers quickly find the approach and methods to solve the problem; and a "Method Highlights" section to assist readers in identifying the key points, techniques, and patterns for solving the problem;
3. Problem Solutions: All the exercises from each section of the "Textbook" are fully solved. For some representative problems, "Thought Exploration" and "Method Highlights" are also provided during the solution process. Additionally, some problems offer multiple solutions to cultivate readers' analytical and divergent thinking abilities. Moreover, the book uses "Warning Notes" to briefly highlight key points, techniques, and common mistakes in problem-solving.
To review and reinforce the knowledge learned in each chapter, four additional sections are included after the final section of each chapter:
1. Chapter Knowledge Structure and Content Summary: The book uses a structural diagram to organically connect the key points of the chapter, forming a network structure. This helps students systematically grasp the overall knowledge system and core content of the chapter;
2. Complete Solutions to the Textbook Review Exercises: All the problems are solved, with some also including "Thought Exploration" and "Method Highlights" to help readers quickly find the approach and methods to solve the problem, as well as identify the key points, techniques, and patterns;
3. Analysis of: Typical problems from past postgraduate entrance exam papers are selected and solved in detail, with in-depth analysis provided. At the end of the book, the true questions and solutions from the 2004 and 2005 national postgraduate entrance exams are also included;
4. Synchronous Self-Assessment Questions and Solutions: Representative and high-value test questions are selected to evaluate learning outcomes and improve exam-taking skills.