英文名称:Mathematical Analysis 课程编号:

适用专业:数学与应用数学专业(Mathematics and Applied Mathematics)

          信息与计算科学专业(Information and Computing Science)

学时:270 学分:15 实验学时: 课内上机学时:

一、预修课程

    初等数学

二、中文内容提要

    《数学分析》是数学与应用数学、信息与计算科学专业的一门重要基础理论课。本课程既是进一步学习复变函数、微分方程、微分几何、概率论、实变函数与泛函分析等后继课程的阶梯,又与中学数学中的实数系、函数、方程、不等式、极值、面积、体积、弧长等内容有密切联系。理解和掌握《数学分析》的概念、理论和方法,对于学生加深理解数学的基本思想和方法,培养抽象思维能力和逻辑思维能力,提高数学素养具有重要的意义。主要内容包括:实数集和函数,数列极限,函数极限,连续性,导数和微分,微分中值定理及其应用,实数完备性,积分、级数(包括幂级数、Fourier级数)、多元微分学、重积分、含参变量积分、曲线积分、曲面积分等。

三、英文内容提要

    “Mathematical Analysis” is an important basic theoretical course in the major of Math & Applied Mathematics and Information & Computational Science. To comprehend and master the concept, theory and method of “Mathematical Analysis” makes great sense in helping students to make deeper understanding of the basic idea and method of Math, bring up their ability of abstract thinking and logical thinking, and improve their myth background. This course mainly contents real number muster and function, limit of number sequence, limit of function, continuity, derived number and differential, differential mean value theorem and its application, completeness of real number, integral, series(including positive series and Fourier series), multiple- differential, double integral, integral with parameter, curve integral, camber integral and so on.

四、教 材:《数学分析》,作者:刘玉链、傅沛仁,出版社:高等教育出版社2003年7月

五、教材类别:(校外编)