Write C programs for the following:
1.
(a) Derive the formula similar to Equation (17) in the
03/19 lecture note
but at x = b (last point).
(b)
The altitude (ft)
from the sea level and the corresponding time (sec) for a fictitious rocket were measured as follows:
| Time | 0 | 20 | 40 | 60 | 80 | 100 | 120 | 140 | 160 | 180 | 200 |
| Altitude | 370 | 9170 | 23835 | 45624 | 62065 | 87368 | 97355 | 103422 | 127892 | 149626 | 160095 |
Numerically compute the velocity from the table above for t = 0 ∼ 200 keeping the same accuracy as the central difference scheme.
At t=0, use Equation (17) in the
03/19 lecture note and
at t=200, use the formula you derived in (a).
2.
(a) Evaluate analytically
(b) Write a C program to numerically integrate the above using the Simpson rule.
Note that the graph of x ln x looks like
Note also that ln x → − ∞ as x → 0. So the challenge is how to handle the seemingly singular point of x = 0.
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On 24 Mar 2025, 09:55.