高等微积分 I-1 (简体中文版)
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高等微积分 I-1 (简体中文版)

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About the Book

高等微积分在一般的数学训练中佔据最基本的位置,它是从基本的数字计算到高阶的抽象思考的必经之路。许多学生对这门课感到焦虑与害怕。传统的一些课本对一些学生而言,特别是还只习惯于微积分的计算的学生,产生很大的障碍与恐惧。为了能稍微化解学生的学习问题,并让学生更愿意投入到这门课中,本书作者编写了几本高等微积分课本。这些书源于作者在台湾清华大学数学系教授的几次高等微积分的讲义。因应科技的进步,学习的方式可以更多样化,所以这些书的一个目标是使用手机于学习上,让学生方便在手机上阅读,而且不再只是无声的黑白文字,书中必须包含许多颜色和图形,有些图形还能动。另一方面,在这些书中,所有的证明都应该尽量简单、易于理解和逻辑完整,论证不能跨度太大,每个使用到的结果都应该能往前追溯。为了方便在手机上使用,本书的档案不可太大,因此高等微积分一的内容根据考试分为两本书:高等微积分I-1和高等微积分I-2,每本书包含两次考试。书中附有考试试题和模拟考试试题,每一章节都附有练习题。基于一些基本的微积分知识,本书可以视为自完备并适合自学,能够让学生的高等微积分知识形成一个完整的体系。

高等微积分是一门为期两学期的课程,每学期四学分,每週上课200分钟,再加上每週2小时的演习课、每週的作业、每学期的四次考试,可以说,这是数学系中最繁重的课程。在现代科学和技术产业中,数学知识和抽象思维的能力变得越来越重要。数学与自动化过程、金融模型和大数据处理等密不可分,单靠微积分知识是不够的。这也是为什麽尽管这门课程非常繁重,仍然吸引了来自电机工程、计算机科学、金融工程、管理学和医学院等各个领域的学生来修课。

本书主要翻译自作者的英文版高等微积分课本:Advanced calculus I-1 Second edition. 根据经验,英文确实会拖慢部分学生吸收数学的速度。若课程内容简单可能无所谓,但当课程内容已不好理解,授课者应尽量排除与内容无关的干扰,减少学生掌握数学内容的障碍。为了与之后课程的衔接,所有专有名词旁都附有其英文名词,书本最后几页也有中英文索引。

This book is a translation into English of Advanced calculus I-1 which was originally written in English.

About the Author

Jyh Haur Teh
Jyh Haur Teh

A professor in the department of mathematics, National Tsing Hua University of Taiwan, Hsinchu, Taiwan.

Website: http://www.math.nthu.edu.tw/~jyhhaur

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