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--- gibson:teaching:spring-2015:math445:lab10 [2015/04/06 11:27]
gibson
+++ gibson:teaching:spring-2015:math445:lab10 [2015/04/08 19:27] (current)
gibson [Problem 5: quiver plot]
@@ Line 57: / Line 57: @@
 shading interp
 </code>
+===== Problem 5: quiver plot =====
+The function
+\begin{eqnarray*}
+f(x,y) = 2 e^{-(x-1)^2 - (y-1)^2} + e^{-(x+1)^2 - y^2}
+\end{eqnarray*}
+is a rough scale model of a pair of small mountains named Monte Sol and Monte Luna on the outskirts of Santa Fe, New Mexico. Monte Sol, the bigger of the two mountains is about 200 meters high above the plain, so the scale is 1 = 100 meters.
+{{:gibson:teaching:spring-2015:math445:montesol.png?direct&400|}}
+**(a)** Reproduce the above surface plot in Matlab.
+**(b)** In a gentle rainstorm, water will flow down the mountains in the direction of steepest descent, i.e. along the negative of the gradient of $f$. Find the gradient of $f$ using elementary calculus, then make an $x,y$ plot with both contours of the mountain height $f$ and a quiver plot showing the direction of flow of rainwater.
 ===== Bonus =====
@@ Line 64: / Line 78: @@
 Attribution: This lab is adapted from Prof.Mark Lyon's Math 445 Advanced Graphics lab, which is adapted from Octave demos at [[http://yapso.sourceforge.net/demo/demo.html]].
-**Note:** this lab is not over, further problems will be posted by Thursday.

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