@@ -302,7 +302,7 @@ A hypothetical metal has a Fermi energy $\epsilon_F = 5.2 \, \mathrm{eV}$ and a
4. Now, find this difference in energy by calculating the integral found in 1 numerically. Compare your result with 3.
??? hint
You can do numerical integration in MATLAB with [`integrate(fun,xmin,xmax)`](https://www.mathworks.com/help/matlab/ref/integral.html).
You can do numerical integration in MATLAB with [`integral(fun,xmin,xmax)`](https://www.mathworks.com/help/matlab/ref/integral.html).
5. Calculate the heat capacity for $T = 1000 \,\mathrm{K}$ in eV/K.
6. Numerically compute the heat capacity by approximating the derivative of energy difference found in 4 with respect to $T$. To this end, make use of the fact that $$\frac{dy}{dx}=\lim_{\Delta x \to 0} \frac{y(x + \Delta x) - y(x - \Delta x)}{2 \Delta x}.$$ Compare your result with 5.
