April 2014
Beginner to intermediate
830 pages
15h 21m
Chinese
Content preview from Mathematica 錦囊妙計
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438
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第十一章
DSolve
指令的輸出結果規則式的形式，因為這是二階微分方程式，運算結果將引進兩
個常數
C[1]
及
C[2]
，提供初始條件可以消去這兩個常數。本模型常使用角頻率
ω
表示
Sqrt[k]/Sqrt[m]
。
討論說明
DSolve
指令運算的結果不會自動簡化，通常還要使用
Simplify
及
FullSimplify
指令進
行簡化，才會得到與教科書上相同的結果。以下討論一個微分方程問題，來自於 Erwin
Kreyszig 所著《
Advanced Engineering Mathematics
》（John Wiley 出版）：開放容器內的
水向外流出，水面高度如何隨時間改變。[Page-440]
由物理可得知，第一個解才是正解，因為第二個解的水面高度隨時間增加。
雖然簡化的結果精簡了些，但跟書上的解相去甚遠：
DSolve
所給的解是否正確？以上犯了一個常見的錯誤：過早將常數值代入方程式中。一
般建議解方程式時盡量使用符號表示，求得解後再將數值代入。
ch11.indd 438 2014/4/2 下午 01:03:46
11.7 極值問題求解
|
439
雖然這個解仍與書上不同，但經過簡化運算後，可以證明與書上所示相同。[Page-441]
再將
h0
與
k1
的值代入後，便可發現先前 Mathemati
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.