nil asked in 科學數學 · 1 decade ago

關於向量分析名詞的定義(20點)

我想請問一下大家,下面幾個名詞再向量分析中的定義是什麼

conservative,vector field,divergerce,gradient,curl,potartial function,flux

以上

拜託大加快幫幫忙喔

Update:

請回答我他的定義解釋 不是公式喔 例如divergence就是在向量分析上面表示的就是通量諸如此類的答案

1 Answer

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  • linch
    Lv 7
    1 decade ago
    Favorite Answer

    以下都是指三度空間

    A vector field F on a domain in space is a function that assigns a vector to each point in the domain.

    Like: F(x,y,z) = M(x,y,z) i + N(x,y,z) j + P(x,y,z) k

    --------------------------------------------

    F is conservative in D ==>∫F•dr (是一個線積分) is path independent in D (線積分與路徑無關)

    -----------------------------------------------------

    The gradient vector of f(x,y,z) is the vector

    ▽f(x,y,z) = f_x(x,y,z) i + f_y(x,y,z) j + f_z(x,y,z) k

    f_x(x,y,z) 表示 f 對 x 偏微

    -----------------------------------------------------

    If F is a field defined on D and F(x,y,z) = ▽f(x,y,z) for some function f on D, then f is called a potartial function for F.

    -----------------------------------------------------

    The divergence of a vector field F(x,y,z) = M(x,y,z) i + N(x,y,z) j + P(x,y,z) k is the scaler function

    div F = ▽•F = M_x(x,y,z) + N_y(x,y,z) + P_z(x,y,z)

    -----------------------------------------------------

    The flux of a vector field F across an oriented surface S in the direction of n (normal vector) is given by the formula

    Flux = ∫∫_S F•n dσ

    ∫∫_S F•ndσ 表示 F•n 在 S 上做重積分

    2009-01-11 02:26:36 補充:

    漏了一個 Curl

    F(x,y,z) = M(x,y,z) i + N(x,y,z) j + P(x,y,z) k

    Curl F = ▽╳F = (P_y(x,y,z) - N_z(x,y,z)) i + (M_z(x,y,z) - P_x(x,y,z)) j + (N_x(x,y,z) - M_y(x,y,z)) k

    2009-01-12 11:43:41 補充:

    你要的不是"定義"嗎?

    那些都是定義啊!

    怎麼又變成解釋定義了?

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