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Measuring Sub-23 Nanometer Real Driving Particle Number Emissions Using the Portable DownToTen Sampling System
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Establishing a link between vehicular PM sources and PM measurements in urban street canyons

Alfred D Eisner1, Jennifer Richmond-Bryant, Russell W Wiener

  • 1Alion Science and Technology, P.O. Box 12313, Research Triangle Park, NC 27709, USA. eisner.alfred@epa.gov

Journal of Environmental Monitoring : JEM
|December 22, 2009
PubMed

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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...