牛頓力學 含阻力之自由落體 帕普斯──古丁爾定理 拉格朗日力學 變分法入門 測試
Apr 3, 2022階乘函數的推廣(本文只談及n>0時的狀況) 定義 $$ \Gamma(n)=\int_{0}^{a}x^{n-1}e^{-x}dx=(n-1)! $$ (未完待續)
Mar 30, 2022Question 1 試證明$\tanh^{-1},\theta=\int_{0}^{\theta}\frac{dx}{1-x^2}$ Answer $$ \text{let},x=\tanh,t\ \Rightarrow \frac{dx}{dt}=\frac{\cosh^2,t-\sinh^2,t}{\cosh^2,t}\ =1-\tanh^2,t\ =1-x^2\ \frac{dx}{1-x^2}=dt\
Jan 9, 2022or
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