Resit Exam (20232)
Contents
Resit Exam (20232)¶
FIZ228 - Numerical Analysis
Dr. Emre S. Tasci, Hacettepe University
28/06/2024
import numpy as np
import scipy.optimize as opt
import pandas as pd
import matplotlib.pyplot as plt
Pick and solve any 3 of the following questions
(No bonus will be given for a 4th one!)
1¶
a. Construct a pandas dataframe with 5 (imaginary) students’ information containing their:
1. Name,
2. Surname,
3. ID #,
4. FIZ227 - Programming Letter Grade
5. FIZ228 - (Prospective) Final Exam Grade
6. Overall Grade Average
b. Add your information as the 6th entry
c. Calculate the average of the “FIZ228 - (Prospective) Final Exam Grade” column and round it
d. Have the pandas return the information of the student with the highest “Overall Grade Average”
2¶
On a 1D wire, some measurements have been made and the following data have been obtained:
x |
y |
|---|---|
-1 |
0 |
2 |
-24 |
4 |
0 |
6 |
0 |
In the table above, \(x\) denotes the distance from a point marked on the wire while \(y\) corresponds to the magnitude of the property measured.
Given that the measured property is a continous quantity, estimate:
a) The value at the x = 5 position.
b) The position where the measured property’s value is equal to -75 (within a precision of the order 10-4).
(For the sake of simplicity, units have been ignored.)
3¶
Suppose that we have two kinds of particles: A and B (you can think of them as golf balls and tennis balls). When they are put in a system, the system’s energy is given by the following formula:
where \(n_{\{A,B\}}\) indicates the number of A and B particles in the system.
Due to the system’s capacity, and the fact that B particles being bigger than A particles, we have the following restriction:
Find the optimal number of A and B particles to be put into the system such that they satisfy the above restriction while yielding the maximum energy.
4¶
Solve the following ODE for the given conditions:
Plot your result.