APPENDIX G
Taylor Series Expansions
Consider a function z=F(x). When a small change Δ x is made to x, there is a corresponding small change Δ z in z. A first approximation to the relationship between Δ z and Δ x is
This relationship is exact if z is a linear function of x and approximate in other situations. A more accurate approximation is
This relationship is exact if z is a quadratic function of x and approximate in other situations. By adding more terms in the series, we can increase accuracy. The full expansion is
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