Numerically calculate the same integral using ƒ and package scipy.integrate. Compare to the analytical integral, and comment.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

 

Q1.1) (10 pts) Consider the function f(x) = (sin x) ecos. Determine its analytical integral between points a and b, and code the analytical integral in python. Calculate the value for a = 0 and b = π.

The integral is sin ecos dx = cosa - ecosb

Q1.2) (15 pts) Numerically calculate the same integral using ƒ and package scipy.integrate. Compare to the analytical integral, and comment.

Q2.1) (10 pts) Load time-series data in file Data_Assgt03_2022W.txt. Plot with errorbars.

Q2.2) (20 pts) Use a model y = a sint with parameter a to build a x2 function, and minimize it, using scipy.optimize. Estimate parameter a. Overlay fit on data.

Q2.3) (15 pts) Display value of x2, degrees of freedom and p-value of this model. Is this a good fit?

Q2.4) (15 pts) Plot x2(a).

Q2.5) (15 pts) Determine the 68% confidence interval for a using ▲x2 = 1 and library optimize.root_scalar.

 

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