# 大學數學問題

- First order differential equations

- Second order differential equations

### 3 個解答

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要學differential equations當然要有一點Calculus既底子啦,不過我覺得其實直接既關係唔算真係好大,因為處理唔同類型既differential equations手法都同傳統既integration / differentiation有幾大既分別,因為differential equations既特點係個primitive function同佢既derivatives係mix埋一齊,所以你要齋integrate佢出答案又唔係,唔integrate佢又好似無乜方法咁,所以傳統方法在這個不大行得通,同埋事實上我們可以analytically解到既differential equations其實都唔多,一定要個form有返咁上下靚(例如可以寫到好似一條polynomial咁之類)先解到.所以如果你要睇書既話,可以由淺入深,睇下D書有講邊幾種type我地可以處理到同用乜野方法去處理,然後先睇背後既theory啦.

手頭上有兩三本書都可以介紹俾你:

最淺: 唔駛諗,睇返中六七既Applied Mathematics書講differential equations果本啦.是但邊套都無乜所謂.重點講first order同second order有邊D我地做得同點做,仲有applications,點樣set條differential equation出黎etc.

一般難度: Elementary Differential Equations and Boundary Value Problems, 6th ed., by Boyce, William E. & DiPrima, Richard C. John Wiley & Son出既,我讀書果個年代既中大用書,印刷精美,難度適中.如果你淨係要first order DE同second order DE既話,睇頭三個chapters已經夠.不過其實想知多D既話Chapter 4既Higher Order Linear Equations, Chapter 5既Series Solutions for 2nd Order DE, Chapter 6既Laplace Transform同Chapter 7既Systems of 1st Order DE都幾好睇.Chapter 8打後果D都幾深下,可以睇下讀完呢D野之後仲有無興趣想識多D啦.

高難度之選: Ordinary Differential Equations and Stability Theory: an Introduction, by Sanchez, David A. W.H. Freeman and Company出版,本書又細又簿,好似好快可以睇得完咁,但係都幾深下.建議你開呢本書睇之前一定要將上一本成本煲到爛晒先開.呢本書已經唔係講點solve ODE,而係講D theory,同埋D solutions既analytic studies.如果你唔係數學major就唔駛掂呢本書,但如果你係數學major而對ODE有興趣既話,睇下都無妨.

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• no, you should study Applied Mathematics - Differential Equations.

It is easier than Differentiation in Calculus.

Just some kind of quadratic equation.

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• 照你所講,你而家係U都應該Major唔係Science Subject.

應該所教的Differential equations 唔會太複雜,之前沒有讀過A.maths係會比較吃力少少. 本人認為Differential equations 呢個Topics,你首先最主要係熟讀d formula,

因為實在太多Formula要記,對Formula有一定既認識後,就可以開始集中係應用方面(因為後期既Differential equations有好多時都係要你用d技巧去做),而並非只記Formula就可以做到.Integration其實同 Differentiation 差唔多(其實基本上係Differentiation 掉番轉咁做),我本人認為Integration仲比較容易.

My Opinion:

1st Step: Differentiation's Formula

2nd Step: How to apply the Formula in the Questions

3rd Step: After u know the sleight, can start to concentrate in 1st order Differentiation

and then, 2nd order Differentiation ...(can concernrate in Integration in the same time)

希望可以幫到你^o^

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