typo corrections

doc/src/week39/week39.do.txt

@@ -723,15 +723,15 @@ import matplotlib.pyplot as pt
 from mpl_toolkits.mplot3d import axes3d
 
 def f(x):
-    return 0.5*x[0]**2 + 2.5*x[1]**2
+    return x[0]**2 + 3.0*x[1]**2
 
 def df(x):
-    return np.array([x[0], 5*x[1]])
+    return np.array([2*x[0], 6*x[1]])
 
 fig = pt.figure()
 ax = fig.gca(projection="3d")
 
-xmesh, ymesh = np.mgrid[-2:2:50j,-2:2:50j]
+xmesh, ymesh = np.mgrid[-3:3:50j,-3:3:50j]
 fmesh = f(np.array([xmesh, ymesh]))
 ax.plot_surface(xmesh, ymesh, fmesh)
 !ec
@@ -764,6 +764,8 @@ it_array = np.array(guesses)
 pt.plot(it_array.T[0], it_array.T[1], "x-")
 !ec
 
+Note that we did only one iteration here. We can easily add more using our previous guesses.
+
 !split
 ===== Conjugate gradient method ===== 
 !bblock
@@ -1081,7 +1083,7 @@ X = np.c_[np.ones((n,1)), x]
 H = (2.0/n)* X.T @ X
 # Get the eigenvalues
 EigValues, EigVectors = np.linalg.eig(H)
-print(EigValues)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
 
 beta_linreg = np.linalg.inv(X.T @ X) @ X.T @ y
 print(beta_linreg)