Practical Mathematics for Higher Vocational Education
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Summary
This book covers the applied portion of advanced mathematics for higher vocational colleges. It is divided into seven chapters: Chapter 1 Functions; Chapter 2 Limits and Continuity; Chapter 2 Limits and Continuity; Chapter 3 Derivatives and Differentials; Chapter 4 Applications of Derivatives; Chapter 5 Indefinite Integrals; Chapter 6 Definite Integrals and Their Applications; Chapter 7 Ordinary Differential Equations. The book can be used for basic mathematics courses in higher vocational and technical colleges. It is written for the learning characteristics and talent-training objectives of architecture-focused vocational colleges, with the following features: 1. Designed around the class hours of basic courses in architecture vocational schools; 2. Content is primarily foundational, with knowledge coverage centered on practical application.
Editor's review
Written for students at architectural vocational colleges, this book combines the fundamentals of higher mathematics with practical needs. Its chapters progress from functions, limits and continuity, and derivatives and differentials to indefinite integrals, definite integrals and their applications, and ordinary differential equations, forming a complete and clearly structured sequence. Its distinctive feature is that the depth of content is controlled according to the class hours allocated to basic courses in vocational colleges, with emphasis on foundational knowledge and practical application rather than excessive theorizing, so that students can grasp core concepts and calculation methods within limited class hours. The order of topics follows the general pattern of mathematics learning: first establishing a foundation in functions and limits, then moving on to derivatives and integrals, and finally encountering ordinary differential equations, making the book suitable for use as a classroom textbook. For vocational students who need to fill gaps in their mathematical foundation while also understanding how mathematics works in engineering and architectural contexts, this book provides a practical learning framework. When reading, attention should be paid to worked examples and end-of-chapter exercises, combining conceptual understanding with calculation practice; when encountering abstract definitions, readers may first grasp them through figures and examples before returning to the rigorous formulation.
Who it's for
A good fit for
- Students at architectural vocational colleges who need to study the fundamentals of higher mathematics according to course progress
- Readers with a relatively weak mathematics foundation who wish to fill gaps in functions and calculus with an application-oriented approach
- Vocational mathematics teachers looking for a basic textbook that fits the class-hour arrangements of architecture-related majors
- Students preparing for review or retakes of vocational mathematics courses who need to systematically organize the chapter framework
Not a good fit for
- Students preparing for postgraduate entrance examinations or needing rigorous mathematical analysis training; the depth of this book is limited
- Mathematics majors seeking a systematic study of all theoretical proofs in higher mathematics
- Engineering technicians who only need to consult handbooks for building structure calculations; this book is not a professional reference work
Reading tips
- First read through the functions and limits chapters in order, and practice the basic concepts and operations until proficient before moving on to derivatives and integrals.
- After finishing each chapter, close the book and restate the core definitions and formulas of the chapter, then independently complete the basic end-of-chapter exercises to test mastery.
- When encountering abstract concepts, understand them with the help of figures and simple examples; there is no need to struggle with rigorous proofs from the start—learn to use them first, then deepen understanding.
- Read the chapters on applications of derivatives and applications of definite integrals alongside practical problems from professional courses to appreciate the usefulness of mathematical tools.
Contents
- 版权信息
- 1
- 2
- 3
- 4
- 5
FAQ
Is this book suitable for self-study by vocational students with a weak mathematics foundation?
Fairly suitable. This book is written for architectural vocational students, with content focused on fundamentals and a relatively compact class-hour arrangement; the explanations emphasize basic concepts and practical applications. When self-studying, readers can first study the worked examples and then do the exercises, slow down when encountering difficult points such as limits and integrals, and use the book together with class notes for better results. If completely starting from zero, it is advisable to also consult teachers on key definitions.
What main chapters does the book contain?
The book has 7 chapters in total, in order: functions; limits and continuity; derivatives and differentials; applications of derivatives; indefinite integrals; definite integrals and their applications; and ordinary differential equations. The content covers the foundational knowledge of the applied portion of higher mathematics in vocational colleges, and the chapter order follows the idea of fundamentals first and applications later, making it convenient to arrange study according to the semester teaching schedule.
What is the difference between this book and undergraduate higher mathematics textbooks?
This book is aimed at architectural vocational colleges and is designed according to the class hours of basic vocational courses. Its content focuses on fundamentals and practical applications, with relatively concise theoretical derivations and proofs, and it does not pursue the complete theoretical system of undergraduate textbooks. It is more suitable for learners with limited class hours whose goal is to master calculation methods and applications, rather than for students who need in-depth training in mathematical theory.
After finishing this book, can students handle subsequent courses in architecture-related majors?
This book provides foundational knowledge of functions, limits, derivatives, integrals, and ordinary differential equations, which can lay a mathematical foundation for the calculation content involved in subsequent architecture-related courses. However, subsequent professional courses will also use specific engineering methods and standards, which need to be studied in conjunction with professional textbooks. It is recommended to treat this book as a foundational tool and actively review the relevant mathematical methods in professional courses.
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About the author
李晓娜
Author
Li Xiaona — public information about this author is limited. At present, only two works of quite different kinds are known under this name: The Fables of La Fontaine and Practical Mathematics for Higher Vocational Colleges. The former belongs to foreign literature and is usually presented in the form of fables, with concise narration and clear morals, through which readers reflect on human affairs and moral lessons; the latter falls into the category of examinations and vocational education, emphasizing practicality and teaching support for higher vocational students' mathematics learning. Since the two works belong to literature and supplementary teaching materials respectively, they span a considerable range and reflect involvement in editing content across different fields. As no reliable records of birth and death dates, nationality, or life experience have been found, this entry makes no speculation and records only objective information based on the works in the database for readers' reference.
