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Nutrient load estimation in nonpoint source pollution of Hong Kong region

H E Li1, J H W Lee, A Koenig

  • 1Environmental Science Institute, Xi'an University of Technology, Xi'an 710048, Shaanxi Province, PR China. Lhuaien@mail.xaut.edu.cn

Water Science and Technology : a Journal of the International Association on Water Pollution Research
|April 27, 2005
PubMed

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Linear Approximations01:23

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For a differentiable function of two variables, linear approximation estimates values near a known point by replacing the curved surface with its tangent plane. Consider the function\begin{equation*}f(x,y)=x^2+3y^2\end{equation*}near the point (2, 1). The exact value at this point is f(2, 1) = 22 + 3(1)2 = 4 + 3 = 7.The linear approximation of f(x, y)) near (a, b) is\begin{equation*}L(x,y)=f(a,b)+f_x(a,b)(x-a)+f_y(a,b)(y-b)\end{equation*}First, compute the partial derivatives: fx(x, y) = 2x and...