- G.3.c.ii This code in this problem uses
gradtemp[x,y], which is only defined several parts
earlier in G.3.b.i. If it's not defined, the code apparently
runs forever.
To fix, add this code to the start of the block:
temp[x_,y_] = 100/(1 + (x - 2.5)^2 + 2 (y - 3.5)^2);
gradtemp[x_,y_] = {D[temp[x,y],x],D[temp[x,y],y]};
- G.6 Lagrange's method. I found most people doing this
lesson missed the point because it only deals with the distance from a
point to the constraint path being closest when the line is
perpendicular to the constraint, which everyone finds obvious.
Solution: Assign problems from my Lagrange's
Method
Worksheet, which includes Basics and a Tutorial example.
In fairness, I must note that the worksheet itself has a bug in that
the last problem one solves "gradf = k gradg", but one side is the
zero vector, so writing "k gradf = gradg" finds less solutions.
- G.9 Linearizations and total differentials. There is a bug
that shows up if you run this lesson right after VC.02 G.4. The first
cell (which defines f and linearf) has a typo so it
does not properly clear linearf, which screws up the
graphs. The cell should read:
Clear[f,x,linearf,a]
f[x_] = Sin[1.7 x]/3 - Cos[2.1 x]/4;
linearf[x_,a_] = f'[a] (x - a) + f[a]