Study Guide for Advanced Mathematics (Second Edition)

Author: Hubei Provincial Department of Education Group
Publisher: Wuhan University Press
Brief Introduction:
Textbook construction, the development of "dual-qualification" teacher teams, and the construction of practical teaching bases are the three fundamental tasks in vocational and technical education teaching work. They serve as an important guarantee for achieving the training objectives of vocational and technical education, and are one of the most urgent tasks in establishing and promoting the distinctive features of higher vocational education. In recent years, vocational and technical education has been developing rapidly. Compared to this, textbook construction still lags behind the needs of vocational and technical education development, and there are still many issues, such as insufficient recognition of the importance of textbook construction in vocational and technical education; lack of in-depth research on the writing form, system, and style of vocational and technical education textbooks, resulting in a severe shortage of textbooks with distinctive features of vocational and technical education. The textbooks selected by vocational and technical colleges do not fully reflect the characteristics of vocational and technical education. Textbook construction lacks the guidance of industry experts and lacks scientific theoretical support, failing to meet the requirements of the knowledge economy and the development of modern high technologies. Moreover, the construction of practical and training textbooks配套 to professional textbooks is severely lagging, and so on. The problems existing in the textbook construction of vocational and technical education seriously affect the quality of higher vocational education and the cultivation of talents. With the rapid development of higher vocational education and the continuous deepening of educational and teaching reform, to establish the distinctive features of vocational and technical education and improve the quality of talent cultivation, vocational and technical colleges must strengthen their own textbook construction system.
This textbook emphasizes a focus on the industry, enhancing its relevance and practicality, reflecting the requirements of adaptability, usability, and conciseness, and paying attention to the cultivation of students' practical abilities. At the same time, the textbook construction not only focuses on the reform of content and system, innovating the system structure and writing form, but also pays attention to the reform of methods and means, keeping pace with the times to meet the actual needs of talents at all levels in the development of science and technology and economic construction.
Table of Contents:
Chapter 1: Functions, Limits, and Continuity
1.1 Summary of Content
1.2 Analysis of Difficulties
1.3 Case Studies and Reviews
1.4 Selected Solutions to Exercises
1.5 Comprehensive Exercises
Chapter 2: Derivatives and Differentiation
2.1 Summary of Content
2.2 Analysis of Difficulties
2.3 Case Studies and Reviews
2.4 Selected Solutions to Exercises
2.5 Comprehensive Exercises
Chapter 3: Applications of Derivatives
3.1 Summary of Content
3.2 Analysis of Difficulties
3.3 Case Studies and Reviews
3.4 Selected Solutions to Exercises
3.5 Comprehensive Exercises
Chapter 4: Indefinite Integrals
4.1 Summary of Content
4.2 Analysis of Difficulties
4.3 Case Studies and Reviews
4.4 Selected Solutions to Exercises
4.5 Comprehensive Exercises
Chapter 5: Definite Integrals and Models
5.1 Summary of Content
5.2 Analysis of Difficulties
5.3 Case Studies and Reviews
5.4 Selected Solutions to Exercises
5.5 Comprehensive Exercises
Chapter 6: Differential Equations
6.1 Summary of Content
6.2 Analysis of Difficulties
6.3 Case Studies and Reviews
6.4 Selected Solutions to Exercises
6.5 Comprehensive Exercises
Chapter 7: Vector Algebra and Space Analytic Geometry
7.1 Summary of Content
7.2 Analysis of Difficulties
7.3 Case Studies and Reviews
7.4 Selected Solutions to Exercises
7.5 Comprehensive Exercises
Chapter 8: Multivariable Calculus
8.1 Summary of Content
8.2 Analysis of Difficulties
8.3 Case Studies and Reviews
8.4 Selected Solutions to Exercises
8.5 Comprehensive Exercises
Chapter 9: Multivariable Calculus
9.1 Summary of Content
9.2 Analysis of Difficulties
9.3 Case Studies and Reviews
9.4 Selected Solutions to Exercises
9.5 Comprehensive Exercises
Chapter 10: Infinite Series
10.1 Summary of Content
10.2 Analysis of Difficulties
10.3 Case Studies and Reviews
10.4 Selected Solutions to Exercises
10.5 Comprehensive Exercises
Appendix: Comprehensive Test (I)
Comprehensive Test (II)
Comprehensive Test (III)