Chapt. 1 Quantities, Units, Conversions, Measurement, Significant Figures, and Uncertainties13sufficiently small (x−x0). The smaller (x−x0) is the less important the higher order terms. Inphysics (and other fields no doubt), one is often interested in the behavior near some importantpointx0, and so truncates the Taylor’s series to find an simple approximate expression for theneighborhood ofx0. For examplef(x) =f(x0),0th order orconstant approximation;f(x0) + (x−x0)f′(x0),1st order orlinear approximation;f(x0) + (x−x0)f′(x0) +(x−x0)22f′′(x0),2nd order orquadratic approximation.The 0th order expansion, approximates the function as a constant which is the function value atx0; the 1st order expansion approximates the function by a line that is tangent to the functionatx0; the 2nd order expansion approximates the function by a quadratic that is tangent to the
This is the end of the preview.
access the rest of the document.