Quod Erat Demonstrandum

2011/04/13

解微分方程

Filed under: Additional / Applied Mathematics,HKALE — johnmayhk @ 8:50 上午

[Hardsell 廣告腔] 解微分方程?用

http://www.wolframalpha.com/

啦!

y"+y=sin(x)

課程有的,同學懂的;但只要如實輸入

y"+y=sin(x)

一按 Enter,不出一秒,得出答案。

y"‘+y=sin(x)

已超越課程範圍了,同學應該不懂的;但只要如實輸入

y"‘+y=sin(x)

一按 Enter,不出一秒,得出答案。

中學的應數(applied mathematics)已進入壽終正寢的倒數階段,中學生不再學習如何解微分方程之類,但這樣不「可惜」,中學學的數學(應該說:算術運算)已有免費網上軟件代勞。不知是否已有人研發有關解決算數(counting)和概率(probability)問題的免費網上軟件。想像把題目輸入,一按 Enter,立即出答案和 steps,那時,我們還要教甚麼?我們還要「浪費」時間嗎?

4 則迴響 »

  1. 最近睇番我在大學讀過的科目,微分方程原來係大學入面接觸過最多的範疇的數學。
    有ODE,PDE和SDE。慶幸以前有讀app math…入左大學接觸這些東西都唔會太辛苦。

    迴響 由 Justin — 2011/04/13 @ 2:35 下午 | 回覆

    • Stochastic Differential Equation(SDE)完全無接觸過。

      學者認為,中學數學教的課題愈少愈好,留待大學才學,免得中學授課員教壞學生。

      我也漸漸贊成「教的課題愈少愈好」,除了生怕我教錯學生成為千古罪人外,現在似乎比以前較難提升學生學習數學的興趣。遲些再談。

      迴響 由 johnmayhk — 2011/04/13 @ 3:57 下午 | 回覆

  2. I have tried the followings on Alpha.Amazing!

    (a) probability of 1 head 5 tails

    (b) probability of 1 head 1999 tails

    Indeed, there is an open-source program called “Sage". It works like the Matlab and Mathematica.

    迴響 由 Matt — 2011/04/13 @ 3:02 下午 | 回覆

    • Thank you Matt!

      It is good to know that we can find probabilities by Wolfram. May be I need to explore to see if it can solve more complicated problems. For “Sage", I should have to explore it earlier, but I am too lazy now.

      迴響 由 johnmayhk — 2011/04/13 @ 4:00 下午 | 回覆


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