deletions | additions       diff --git a/section_Estimation_of_uncertainty_There__.tex b/section_Estimation_of_uncertainty_There__.tex  index 00abfe6..d7a58f8 100644  --- a/section_Estimation_of_uncertainty_There__.tex  +++ b/section_Estimation_of_uncertainty_There__.tex 
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First-order variance: $\sigma^2_y=\nabla_x C_x \nabla^T_x=\left(\sum_{i=1}^{2}\frac{\partial{f}}{\partial{x_i}}\sigma_i\right)^2$  The first order Taylor expansion assumes linearity over $\bar {x_i}$, {x_i}$. We used  second-order expansion corrects expansions to correct  for bias in non-linear expressions. This approach was used implemented  whenever possible to shorten computing time.