Higher Mathematics Tutorial and Problem Solutions (Tongji 5th Edition) (Volume 2)

Author: Peng Hui et al. (Editor-in-Chief)
Publisher:
Publishing Time: Not Available
Features: Calculus is an important foundational course for science and engineering colleges and a mandatory subject for postgraduate entrance examinations. The fifth edition of "Calculus" edited by Tongji University (hereinafter referred to as "the Textbook") has become a classic textbook for this course due to its comprehensive system, rigorous structure, clear hierarchy, and accessible yet in-depth presentation. It is widely adopted by many institutions across the country. To help readers master the Textbook and calculus effectively, the authors have compiled "Calculus Companion and Problem Solutions" based on years of teaching experience. This book aims to assist and guide readers in understanding fundamental concepts, mastering basic knowledge, learning basic problem-solving methods and techniques, and improving their exam-taking skills and mathematical thinking abilities. The book is divided into twelve chapters, each further subdivided into several sections, with the chapter structure and titles aligning with the Textbook. Each section in the book includes three main parts:
1. Key Knowledge Points and Exam Focus: Using a tabular format, this section systematically organizes the basic concepts, theorems, and formulas covered in each section, highlighting important points to note when understanding and applying them, and specifically pointing out key knowledge areas frequently tested in exams.
2. Classic Example Analysis: After extensive research, representative and typical examples are selected and categorized for analysis. The problem-solving process includes:
- Thought Exploration: Helps readers quickly identify the approach and methods to solve the problem.
- Method Highlights: Assists readers in finding the key points, techniques, and patterns for solving the problem.
3. Problem Solutions: All exercises from each section of the Textbook are solved. Some representative problems also include "Thought Exploration" and "Method Highlights" during the solution process. Additionally, multiple solutions are provided for certain problems to cultivate analytical and divergent thinking. The book also includes "Cautionary Notes" in the form of brief warnings about key points, techniques, and common mistakes in problem-solving.
To review and reinforce the knowledge learned in each chapter, four additional sections are added after the final section of each chapter:
1. Chapter Knowledge Structure and 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. Comprehensive Solutions to Textbook Review Exercises: All questions are solved, with some also including "Thought Exploration" and "Method Highlights" to guide readers in quickly identifying problem-solving approaches and key techniques.
3. Analysis of Past Graduate Entrance Exam Questions: Typical questions from past national unified entrance examinations for postgraduate studies are selected and solved in detail, along with analyses.
4. Synchronized Self-Assessment Questions and Solutions: Representative and high-value test questions are selected to evaluate learning outcomes and improve exam performance.
At the end of the book, the true questions and solutions for the national postgraduate entrance examinations in 2004 and 2005 are also provided.