nil asked in 科學數學 · 1 decade ago



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




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

  • linch
    Lv 7
    1 decade ago
    Favorite Answer


    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:




    • Login to reply the answers
Still have questions? Get your answers by asking now.