Hints for Assignment 3 (AMSC460, Fall 2018)
Problem 2: Use the code below to get the vectors t and conc.
Problem 2(c): Let \(C(t)\) denote the concentration.
If \(\log C(t) \approx c_1 + c_2 t\) then \(C(t) \approx e^{c_1} e^{c_2 t}\), i.e., exponential growth of the concentration. If \(\log C(t) \approx c_1 + c_2 t + c_3 t^2\) do we have growth which is faster or slower than exponential growth?
Problem 3: We consider a column which is fixed at one end and pinned at the other end. The load under which this column buckles ("Euler's critical load") is
\( \displaystyle F= \frac{\pi^2EI}{K^2L^2} \). Here \(\displaystyle K=\frac{\pi}{z_1}\).
Wikipedia gives the wrong value \(K=\sqrt{2}/2\).
Problem 4: See the example
Problem 5: Use the Newton method. DO NOT use fsolve.