problem0():
  Find least squares solution to A*x=b

  Matrix A:
[[0.   0.   1.  ]
 [0.04 0.2  1.  ]
 [0.16 0.4  1.  ]
 [0.36 0.6  1.  ]
 [0.64 0.8  1.  ]
 [1.   1.   1.  ]]
  Right hand side b:
[150.697 179.323 203.212 226.505 249.633 281.422]
  Least squares solution x:
[  5.70133929 121.13408929 152.47446429]
  L2 norm of residual is  5.221927734494775

problem1
  Surface area =  166.85562602840403
  Approximation:  157.2888076299005

problem2
  Integral of sinc(x) from 0 to 8 is  0.48737422505781997
  Error estimate is  1.0414821262350049e-10

problem3
  Use dblquad() to estimate a double integral.
  Integral of y * x**2  over 1<=y<=4 0<=x<=2,   42.00000000000001
  Error estimate is  4.662936703425658e-13

problem4():
  Use p_roots to get Newton-Cotes quadrature rule
  Estimate integral of sinc(x) from 0 to 8.
  estimated integral is  0.20462476111604286

problem5():
  Use p_roots to get Gauss-Legendre quadrature rule
  Estimate integral of sinc(x) from 0 to 8.
  estimated integral is  0.48737212487804343

problem6():
  Use interp1d() to interpolate sinc(x) from -8 to 8.
  Graphics saved as "problem6.png"

problem7():
  Seek maximum value of sinc(x) in interval  1.0  <= x <=  4.0
  Sampling estimates maximum at sinc( 2.45 ) =  0.12832284215505932
  minimize_scalar() estimates maximum at sinc( 2.45902352927921 ) =  0.12837455352573843
  mimimize_scalar() returns success flag  True

problem8
  Use brentq() to find root of jumper function.

  brentq() estimates root as  0.33186603357456285
  with f(x) =  -7.577272143066693e-14

problem9
  Use minimize() to find minimizer of madsen function.

  Starting point x0:
[3. 1.]
  with f(x0) = 
13.011988373742163

  minimize() estimates minimizing values as:
[-0.15543735  0.6945639 ]
  with f(x) = 
0.8793173809796767