Advanced Mathematics (Fourth Edition), Volume 1

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Features: This is the fourth edition of the book, revised under the guidance of the National Advisory Committee on the Teaching of Engineering Mathematics in Higher Education Institutions, in accordance with the spirit of the Ministry of Education's "refining textbooks that are of high quality, have a solid foundation, and are widely used." It was also updated based on the revised "Basic Requirements for the Teaching of Advanced Mathematics." The revision extensively incorporated the opinions of colleagues nationwide and was carefully refined from a teaching perspective. Some important concepts were rewritten, the exercises were adjusted, and a comprehensive exercise was added to each chapter to make the content and system more complete and facilitate teaching. The book is published in two volumes. Volume 1 covers seven chapters: Functions and Limits, Derivatives and Differentiation, Mean Value Theorems and Applications of Derivatives, Indefinite Integrals, Definite Integrals, Applications of Definite Integrals, and Space Analytic Geometry and Vector Algebra. At the end of the book, there is an introduction to 2×2 and 3×3 determinants, several commonly used curves, an integral table, and answers and hints to the exercises. The book retains the advantages of the third edition, such as a rigorous structure, clear logic, detailed explanations, accessibility, numerous examples, and ease of self-study. It also expands its applicability and flexibility while ensuring the basic teaching requirements, making it suitable for students of different disciplines in higher engineering colleges.