Mathematical Analysis (Volume 1)

Author: Edited by the Department of Mathematics, Central China Normal University
Publisher:
Publish Date: 2000-08-28
Features: This book was compiled based on the teaching experience and insights of the Department of Mathematics at Central China Normal University over the years, in response to the reform of the teaching and curriculum systems for science and engineering mathematics in higher education institutions. In recent years, with changes in societal demand for talent, universities have adopted a philosophy of cultivating broad-spectrum, solidly grounded, and high-quality mathematics professionals who emphasize both knowledge-based and ability-based training. As a result, the number of elective courses in mathematics programs has surged, and traditional foundational courses have faced challenges in both teaching hours and instructional methods. Given this context, we have compiled this series of textbooks. The book is divided into two volumes and adopts a modularized writing approach, dividing the main content of mathematical analysis into three major sections: "Calculus of Univariate Functions," "Calculus of Multivariate Functions," and "Infinite Series and Limit Theory," making the textbook content more organized. The first volume covers "Calculus of Univariate Functions," consisting of four chapters: "Functions," "Limits and Continuity," "Differential Calculus of Univariate Functions," and "Integral Calculus of Univariate Functions." The second volume contains ten chapters, including six chapters on "Calculus of Multivariate Functions," which cover "Limits and Continuity of Multivariate Functions," "Differential Calculus of Multivariate Functions," "The Existence Theorem of Implicit Functions and Its Applications," "Multiple Integrals," "Line Integrals and Surface Integrals," and "Integrals with Parameters." The section on "Infinite Series and Limit Theory" includes four chapters: "Series of Terms," "Series of Functions," "Fourier Series," and "Limit Theory." The book concludes with appendices.
This textbook is designed for approximately 280–300 teaching hours (including problem-solving sessions) over three semesters. The weekly teaching hours for the three semesters can be roughly arranged as 6, 6, and 3, respectively.
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