

In [1]:

    
import fit_pendulum_data as p1
import midpoint_vec as p2
import Lagrange_poly1 as p3
import Lagrange_poly2 as p4
import Lagrange_poly2b as p5
import sympy as sp
import numpy as np
import matplotlib.pyplot as plt

Exercise 5.18

Plots L vs T from a source file and fits polynomials of varying degrees to it



In [2]:

    
p1.part_a()









    Out[2]:





([0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0],
 [0.6, 0.9, 1.1, 1.3, 1.4, 1.6, 1.7, 1.8, 1.9, 2.0])

Below are the polynomials being fit to the data



In [3]:

    
p1.part_b()

Exercise 5.22

Computes the midpoint rule in different forms



In [4]:

    
p2.midpointint(p2.function, 1, 3, 50)[0]









    Out[4]:





12.231183999999999



In [5]:

    
p2.sum_vectorized(p2.function, 1, 3, 50)









    Out[5]:





12.231183999999999



In [6]:

    
p2.sum_numpy(p2.function, 1, 3, 50)









    Out[6]:





12.231183999999999

Exercise 5.23, 5.24, 5.25 (3 part)

Lagrange Interpolation



In [7]:

    
p4.graph(p4.sin, 20, 0, 10, [0,10,-2,2])



In [8]:

    
p5.problem_5_25()



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