Chapra Text:

Chapter $23$:

$23\mathrm{.}1$

$23\mathrm{.}1$ Compute forward and backward difference approximations of $O(h)$ and $O(h^2),$ and central difference approximations of $O(h^2)$ and $O(h^4)$ for the first derivative of $y=cosx$ at $x=\frac{}{4}$ using a value of $h=\frac{}{12}.$ Estimate the true percent relative error ${}_l$ for each approximation.

$23\mathrm{.}27$

$23\mathrm{.}27$ Chemical reactions often follow the model:

$\frac{dc}{dt}=-k{c}^n$

where $c=$ concentration, $t=$ time, $k=$ reaction rate, and $n=$ reaction order. Given values of $c$ and $d\frac{c}{d}t,k$ and $n$ can be evaluated by a linear regression of the logarithm of this equation:

$log(-\frac{dc}{dt})=logk+nlogc$

Use this approach along with the following data to estimate $k$ and $n$ :

$\backslash$table$[[t,10,20,30,40,50,60],[c,3\mathrm{.}52,2\mathrm{.}48,1\mathrm{.}75,1\mathrm{.}23,0\mathrm{.}87,0\mathrm{.}61]]$