高等微積分是被公認為所有數學系課程中最重要的學科,在這個人人都看重的學科當中,不論是老師或學生,似乎又被「最重要」這三個字綁住而喘不過氣。 每個人都想要學好高等微積分,但在學習過程中頻頻遇到困難又該如何解,這個 Podcast 是希望用聲音搭配李國瑋老師自編的講義【第零章 - 高等微積分簡介】,傳達給剛入門數學分析的同學。 透過聽廣播的節奏,漸漸的了解數學分析課的樣貌。 建議您搭配這一個 PDF 檔案一同聆聽: bit.ly/3b30jUQ 這個 Podcast 不只是針對準備修高微的同學,對於正在學習數學的同學,也能透過這個 Podcast 試圖幫助你重新看待數學、甚至思考如何改變自己學習數學的方法。 Powered by Firstory Hosting
Publishes | Daily | Episodes | 29 | Founded | 5 years ago |
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Language | Categories | How ToEducation |
例題 2 與例題 3 介紹了兩個有理數集的切割;這兩個切割在大空間是有理數集的情況下,「最小上界」一個存在另一個不存在。這個錄音檔是給予證明。下一個錄音檔就要開始說明這件事情和實數之間的關聯。
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這個錄音檔先證明的是,若集合 E 包含於有序集 S 的最小上界存在,則唯一。特別注意的是
:這個定理是接受最小上界存在,才證唯一性。至於一個集合的最小上界存在與否,這個定理並沒有說明,我們要用別的方法證明。
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認識實數的完備性,第一步是先定義「切割」;第二步是定義集合 E 在有序集 S 的「最小上界」。到時候要用這個概念區分例題 2 與例題 3 切割的最大差異,進而了解實數的意義。
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例題 3 再用一個例子示範何謂有理數集的切割。這個例子除了要細細體會怎麼去造 r" 以完成切割的第三個條件外,到時候我們要花時間比較例題 2 與例題 3 的切割之最大差異,這就會關係到實數的意義。
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把高微艱深的內容用大量的口語化表達出來,雖然資訊量很大,但對於學習很有幫助,在念高微的時候會知道需要注意哪些地方,很感謝瑋哥的用心
如題
How this podcast ranks in the Apple Podcasts, Spotify and YouTube charts.
Apple Podcasts | #114 | |
Apple Podcasts | #177 |
Listeners, social reach, demographics and more for this podcast.
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瑋哥聊高微 launched 5 years ago and published 29 episodes to date. You can find more information about this podcast including rankings, audience demographics and engagement in our podcast database.
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