發表回覆

主題 通關密語 訪客發文, 請參考 這裡 輸入通關密語.

顯示表情符號

站內上傳圖檔     Upload.cc免費圖片上傳

數學塗鴉工具     常用數學符號表    

用Latex打數學方程式

 


 

+ / -檢視主題

發表 yll 於 星期三 二月 14, 2007 5:24 pm

#ed_op#DIV#ed_cl#我上課前一定自己準備筆記#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#學生邊抄比筆記邊和我討論內容#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#再出練習題請同學上台#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#上課過程中從不翻課本#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#原因是課本不是我編的#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#我無法按照它的內容去講解#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#也常有我覺得很不洽當的解題或說明方式#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#唯有用自己整理的教材才能對學生做最好的表達#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#課本一直只是個參考#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#告訴我要教的內容有哪些#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#一點意見#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#給你參考#ed_op#IMG src="/phpBB2/richedit/smileys/yy02.gif"#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl#

發表 亞斯 於 星期三 二月 14, 2007 12:01 pm

我很想聽聽大家的意見
下學期就要教了
極限的概念和應用
在混亂的高三下學期
我沒有把握可以讓學生很輕鬆地瞭解與應用
問同事如何教
他們總是覺得我在假裝
天知道我真的不知如何教好!
而且現在的教材好像比以前少了一些
不知除了課本內容外
該補充哪些東西

[閒聊]從龍騰版數甲下的夾擠原理說起

發表 亞斯 於 星期二 二月 06, 2007 8:39 pm

#ed_op#DIV#ed_cl#不知道該擺在哪兒#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#就落腳在此#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#放錯請勿怪#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#找極限時用夾擠是常有的事#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#這東西其實很直觀#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#跟高一的學生講時大都能接受(不見得會應用)#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#怎麼證我也會#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#只是要用到解析性定義#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#DIV#ed_cl#課本裡要把證明列出我也不反對#ed_op#/DIV#ed_cl#反正不可能考高中生#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#只是......#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#且看龍騰課本的證明#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#[夾擠原理]#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#設{a#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#},{b#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}與{c#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}是三數列,k為一非負整數,而且對任意大於k的正整數n,恆有#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#a#ed_op#SUB#ed_cl#n≤#ed_op#/SUB#ed_cl#b#ed_op#SUB#ed_cl#n≤#ed_op#/SUB#ed_cl#c#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl# . 若{a#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}與{c#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}皆收斂且極限值同為L,則數列{b#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#}亦收斂,而且#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#lim(n-->∞)} b#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#=L#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#[證明]#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#當n>k時, a#ed_op#SUB#ed_cl#n≤#ed_op#/SUB#ed_cl#b#ed_op#SUB#ed_cl#n≤#ed_op#/SUB#ed_cl#c#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl# ,故有0#ed_op#SUB#ed_cl#≤#ed_op#/SUB#ed_cl#b#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#-a#ed_op#SUB#ed_cl#n≤#ed_op#/SUB#ed_cl#c#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#-a#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#lim(n-->∞)}(c#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#-a#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl# )=0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#亦即c#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#-a#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#隨著n越來越大而趨近於0,因此b#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#-a#ed_op#SUB#ed_cl#n#ed_op#/SUB#ed_cl#亦隨著n越來越大而趨近於0#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#................#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#看出問題了吧#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#這根本是循環論證#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#難道以前沒人發現嗎?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#真不知該如何教#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl##ed_op#FONT color=#ff0000#ed_cl#感謝yll魔王#ed_op#/FONT#ed_cl##ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#發現更可怕的事#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#徐式的參考書也是這樣寫#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#不知其他版本是如何?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#難道是從75學年開始的統編版高三理科數學就是如此嗎?#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#這麼直觀的一個定理#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#不能證就不要證嗎#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#何必畫蛇添足(對不起用了成語)弄了個邏輯有問題的證明#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#寫出來的人恐怕還沾沾自喜#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#自Weierstrass提出"epsilon-delta"的解析性定義之後#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#評價不一#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#但總是解決"消逝的幽靈"的問題#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#而且現在數學系學生都要接觸#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#當然不是數學系的不必鑽研#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#但是這是否意味在高中階段#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#我只要教會學生如何去算就好了#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl# #ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#記得在第一次大一修微積分時#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#陳金次教授語重心長地表示#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#如果不懂微積分基本定理而只會計算#ed_op#/DIV#ed_cl##ed_op#DIV#ed_cl#怎麼叫做會微積分?#ed_op#/DIV#ed_cl#