Higher Mathematics Tutorial and Problem Solutions - (Accompanying the Tongji 5th Edition Textbook) - (Volume 2) - (Second Revised Edition)

Author: Peng Hui
Publisher:
Publish Date: 2006-01-01
Features: Calculus is an important foundational course for science and engineering colleges and also a mandatory subject for postgraduate entrance exams. 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 approach. 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 divisions and titles matching those of "the Textbook." Each section in the book includes three main parts:
1. Key Knowledge Points and Exam Focuses: In a tabular format, it systematically organizes the basic concepts, theorems, and formulas covered in each section, highlighting important issues to consider when understanding and applying these concepts, theorems, and formulas. It also points out key knowledge points frequently tested in exams.
2. Classic Example Analysis: Extensive research has been conducted to select representative and typical examples for classification analysis. During the problem-solving process, there are "Thought Exploration" sections to help readers quickly find the approach and methods to solve the problem; there are also "Method Highlights" to help readers identify the key points, techniques, and patterns for solving the problem.
3. Problem Solutions: All the exercises in each section of "the Textbook" are fully solved. Some representative problems also include "Thought Exploration" and "Method Highlights" during the solution process. Additionally, some problems provide multiple solutions to cultivate analytical and divergent thinking skills. The book also uses "Cautionary Notes" to briefly highlight key points, techniques, and common mistakes in problem-solving.
To review and consolidate the knowledge learned in each chapter, four additional parts are included after the final section of each chapter:
1. Chapter Knowledge Structure and Summary: The book uses structural diagrams to organically connect the key points of the chapter, forming a network structure. This helps students systematically grasp the knowledge system and core content of the chapter as a whole.
2. Comprehensive Solutions to Textbook Review Exercises: All the questions 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 questions from papers are selected and solved in detail, along with analysis. At the end of the book, the real 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 assess learning outcomes and improve exam-taking skills.