Below is a extract of shot data from a seismic survey.
Time (ms) | Shot |
---|---|
0 | -0.021373 |
4 | -0.024578 |
8 | -0.023914 |
12 | -0.018227 |
16 | -0.00781 |
20 | 0.005602 |
24 | 0.019264 |
28 | 0.030235 |
32 | 0.036059 |
36 | 0.035334 |
Does matrix $C$ have an inverse? If not, then why not?
Consider the function $$f(x) = \dfrac{1}{(x − 0.3)^2 + 0.01} - \dfrac{1}{(x − 0.8)^2 + 0.04}$$.
Consider the integral: $$\int_0^{2\pi} x^2\cos(x) dx.$$
Show how the absolute error between the exact solution and the numerical solution varies with the size of the integration step for the four numerical integration methods: trapezoid rule; Simpson's rule; composite Simpson's rule; and Weddle's rule. Show your result by plotting error against integration step, $dx$.