高等微積分 I-1 (繁體中文版)
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高等微積分 I-1 (繁體中文版)

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About the Book

高等微積分在一般的數學訓練中佔據最基本的位置,它是從基本的數字計算到高階的抽象思考的必經之路。許多學生對這門課感到焦慮與害怕。傳統的一些課本對一些學生而言,特別是還只習慣於微積分的計算的學生,產生很大的障礙與恐懼。為了能稍微化解學生的學習問題,並讓學生更愿意投入到這門課中,本書作者編寫了幾本高等微積分課本。這些書源於作者在清華大學數學系教授的幾次高等微積分的講義。因應科技的進步,學習的方式可以更多樣化,所以這些書的一個目標是使用手機於學習上,讓學生方便在手機上閱讀,而且不再只是無聲的黑白文字,書中必須包含許多顏色和圖形,有些圖形還能動。另一方面,在這些書中,所有的證明都應該盡量簡單、易於理解和邏輯完整,論證不能跨度太大,每個使用到的結果都應該能往前追溯。為了方便在手機上使用,本書的檔案不可太大,因此高等微積分一的內容根據考試分為兩本書:高等微積分I-1和高等微積分I-2,每本書包含兩次考試。書中附有考試試題和模擬考試試題,每一章節都附有練習題。基於一些基本的微積分知識,本書可以視為自完備並適合自學,能夠讓學生的高等微積分知識形成一個完整的體系。

高等微積分是一門為期兩學期的課程,每學期四學分,每週上課200分鐘,再加上每週2小時的演習課、每週的作業、每學期的四次考試,可以說,這是數學系中最繁重的課程。在現代科學和技術產業中,數學知識和抽象思維的能力變得越來越重要。數學與自動化過程、金融模型和大數據處理等密不可分,單靠微積分知識是不夠的。這也是為什麼儘管這門課程非常繁重,仍然吸引了來自電機工程、計算機科學、金融工程、管理學和醫學院等各個領域的學生來修課。

本書主要翻譯自作者的英文版高等微積分課本:Advanced calculus I-1 Second edition. 根據經驗,英文確實會拖慢部分學生吸收數學的速度。若課程內容簡單可能無所謂,但當課程內容已不好理解,授課者應儘量排除與內容無關的干擾,減少學生掌握數學內容的障礙。為了與之後課程的銜接,所有專有名詞旁都附有其英文名詞,書本最後幾頁也有中英文索引。

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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