Advanced Mathematics

Author: Zhu Guangbin, Editor-in-Chief
Publisher:
Publish Date: 2006-08-01
Features: Mathematics is an ancient and mature discipline, and the acquisition of mathematical knowledge and skills undoubtedly plays a crucial role in enhancing a person's overall quality. The teaching objective of higher vocational colleges is to cultivate applied talents, and the study of mathematics is an important part of achieving this goal. In higher vocational mathematics teaching, the principle of "applying what you learn and using what is sufficient" is often emphasized. However, what does "sufficient" mean? How to grasp this "degree"? How can mathematics teaching be "closer to majors, closer to applications, and closer to students' learning realities"? In the practice of higher vocational mathematics teaching, we have explored, been puzzled, and reflected, and have also taken some detours. Through practice and reflection, this textbook was born. Its writing process is our continuous teaching practice, and it was developed under the dual guidance of higher vocational training objectives and higher vocational teaching practice. During the writing process, we paid special attention to the following points:
1. To help higher vocational students learn mathematics well, at the beginning of the textbook, we provide a relatively complete review of the mathematical foundations learned in high school that will be used in future studies.
2. When writing the textbook, we fully considered the basic requirements of higher vocational mathematics teaching and carefully selected the content, adhering to the principle of "moderation and sufficiency." We strive to differentiate it from undergraduate and junior college textbooks of the same level, as well as from junior college textbooks of the same level. In terms of text presentation, while ensuring scientific accuracy, we focus on clarity and ease of teaching and learning, avoiding an excessive pursuit of mathematical rigor.
3. During the writing process, we place more emphasis on conclusions than on processes, more emphasis on methods than on theories, and more emphasis on practicality than on comprehensiveness. Therefore, this textbook prioritizes case studies over theoretical analysis and proof. Based on a clear understanding of basic concepts, it highlights the cultivation of computational and applied skills.
4. Considering the principle of "applying what you learn," the examples in this textbook are derived from real-world production and life scenarios. After explaining many key points, there is a "Try It" section, which allows teachers to assess students' mastery of the material during in-class exercises.
5. In terms of chapter structure, in addition to teaching content, each chapter includes exercises divided into three types: multiple-choice questions, fill-in-the-blank questions, and problem-solving questions, for use in teaching. At the end of each chapter, there is a "Chapter Summary" that summarizes the essential concepts, content, and methods that must be mastered, along with self-assessment questions for students to evaluate their learning outcomes. For convenience of use, we have placed commonly used formulas and tables in the appendix at the end of the textbook. This textbook is suitable for all majors in engineering and finance-related higher vocational and junior college institutions. It can also be selected by various higher vocational and junior colleges based on disciplinary and professional needs. For a broad audience of students pursuing various junior college-level studies, reading this textbook will also be highly beneficial. This textbook is divided into two parts: Part 1 primarily introduces the basic knowledge and applications of single-variable calculus, which is a compulsory chapter for all majors. Part 2 mainly includes multivariable calculus, infinite series, Laplace transforms, linear algebra, linear programming basics, and an introduction to probability theory. Each higher vocational college can choose different topics based on disciplinary and professional needs.