**Description: **This directory contains the MATLAB codes for Examples 7.15 and 7.16 along with an example illustrating the

accuracy of the sensitivity equation for the spring model in Example 7.15.

**Data Files: **

final_al_data.txt

**Example7_15: **This is a spring model in which the stiffness K is considered fixed and known and the damping parameter C

is the parameter considered in statistical analysis. The code Example7_15_long.m takes approximately 45 s to run.

**Codes**: Example7_15.zip or individually as Example7_15.m, Example7_15_long.m , spring_function.m

Sensitivity Equation: This example illustrates the solution to the sensitivity equation for the damping coefficient C in the spring model $$\backslash begin\{array\}\{l\}\; \backslash ddot\{z\}\; +\; C\; \backslash dot\{z\}\; +\; K\; z\; =\; 0\; \backslash \backslash \; z(0)\; =\; 0\; ,\; \backslash dot\{z\}\; =\; -C\; \backslash end\{array\}$$

of Example 7.15. Specifically, it compares the analytic sensitivity solution with the computed solution to the sensitivity equation.

**Codes:** spring_sensitivity.m, spring_rhs.m, spring_sens_rhs.m

Example 7.16: This is the steady state heat example for data collected from an aluminum rod as detailed in Example 3.5. This

requires the data final_al_data.txt.

**Codes:** Example7_16.zip or individually as Example7_16.m, heat_fun_al.m