Numerical Methods for Engineers (7th Edition) by steven chapra. I need a sloutio

Question

Numerical Methods for Engineers (7th Edition) by steven chapra. I need a sloution for problem exercie 4.10 and 4.12 using python

Using series.py while solving the questions using python

Python Code for series.py is given below

Code starts from here:

import math

def taylor(dfdx, n, xi, h, start=0):
"computes the nth order taylor series of f(xi+h)"
#n: order
#xi: reference point
#h: step-size (h = x(i+1) - xi)
#dfdx(i,xi): ith derivative of f(xi) for i=0,1,..,n" [dfdx(0,xi) is f(xi)]
sum = .0
for i in range(start, n+1): #loop from i=start to n
sum += dfdx(i, xi) * h**i / math.factorial(i)
return sum
#end taylor()

4.9 The Stefan-Boltzmann law can be employed to estimate the rate of radiation of energy H from a surface, as in where His in watts, A the surface area (m e the emissivity that characterizes the emitting properties of the surface (dimension- less), or a universal constant called the Stefan-Boltzmann con stant 5.67 x 10 W m 2 K 4), and T absolute temperature (K). Determine the error of H for a steel plate with A 0.15 m e 0.90, and T 650 t 20. Compare your results with the exact error. Repeat the computation but with T 650 t 40. Interpret your results. 4.10 Repeat Prob. 4.9 but for a copper sphere with radius 0.15 t 0.01 m, e 0.90 0.05, and T 550 t 20 4.11 Recall that the velocity of the falling parachutist can be com- puted by [Eq. (1.10), gm v(t) Use a first-order error analysis to estimate the error of v at t 6, if 9.81 and m 50 but c 12.5 1.5 4.12 Repeat Prob. 4.11 with g 9.81, t 6, c 12.5 t 1.5, and m 50 2

Explanation / Answer

import math

def taylor(dfdx, n, xi, h, start=0):
"computes the nth order taylor series of f(xi+h)"
#n: order
#xi: reference point
#h: step-size (h = x(i+1) - xi)
#dfdx(i,xi): ith derivative of f(xi) for i=0,1,..,n" [dfdx(0,xi) is f(xi)]
sum = .0
for i in range(start, n+1): #loop from i=start to n
sum += dfdx(i, xi) * h**i / math.factorial(i)
return sum
#end taylor()

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