Test 1 - Python Edition

Transcription

1 'XNH8QLYHUVLW\ (GPXQG73UDWW-U6FKRRORI(QJLQHHULQJ EGR 103L Spring 2018 Test 1 - Python Edition Shaundra B. Daily & Michael R. Gustafson II NetID (please print): In keeping with the Community Standard, I have neither provided nor received any assistance on this test. I understand if it is later determined that I gave or received assistance, I will be brought before the Undergraduate Conduct Board and, if found responsible for academic dishonesty or academic contempt, fail the class. I also understand that I am not allowed to speak to anyone except the instructor about any aspect of this test until the instructor announces it is allowed. I understand if it is later determined that I did speak to another person about the test before the instructor said it was allowed, I will be brought before the Undergraduate Conduct Board and, if found responsible for academic dishonesty or academic contempt, fail the class. Signature: Notes You will be turning in each problem in a separate pile. Most of these problems will require working on additional pieces of paper - Make sure that you do not put work for more than any one problem on any one piece of paper. For this test, you will be turning in four different sets of work. Again, Please do not work on multiple problems on the same sheet of paper. Also - please do not put work for one problem on the back of another problem. Be sure your name and NetID show up on every page of the test. If you are including work on extra sheets of paper, put your name and NetID on each and be sure to staple them to the appropriate problem. Problems without names will incur at least a 25% penalty for the problem. Work must be down in dark ink and on only one side of the page. This first page should have your name, NetID, and signature on it. It should be stapled on top of and turned in with your submission for Problem I. Every other pile should have your test page on top followed by any previously blank paper used for that problem. You will not need and can not use a calculator on this test. You will be asked to write several lines of code on this test. Make sure what you write is Python code and not mathematics. Be very careful with any symbols you use. You do not need to put the honor code statement in your codes. The honor code statement on this page and your NetID on each problem stands in for that. You may assume that the following have been run for any code you write: import math as m import numpy as np import matplotlib. pyplot as plt If you specifically want to import things in a different way, you need to show that explicitly on each code.

2 Problem I: [25 pts.] The Basics - NOT IN PYTHON YET!!! See CS 101 tests, specifically first problems, for similar code.

3 Problem II: [25 pts.] Roll of the Dice Yahtzee is a popular game by Milton Bradley which involves rolling five six-sided dice, each with integers 1 through 6 represented, in the hopes of getting various combinations. In the actual game, you get up to three chances to make the best hand out of your five dice. This problem involves performing a statistical analysis of just the first roll of the dice and of the possibility of getting five of the same value in that first roll of the dice. You are going to write a script called count_fives that will start by asking the user how many total rolls to analyze. You must make sure the user gives you a single positive integer; in cases where the user gives an invalid input, you should have the program tell the user there was a problem and ask as many times as needed to get a valid input. You do not have to specify which rule(s) they broke. Once your program has a single valid positive integer, it will then proceed to simulate rolling five six-sided dice as many times as specified. The program must keep track separately of how many times the dice showed 5 1 s, how many times 5 2 s, etc., and then once all the rolls are complete, print that information in an aligned table. The table will also include a line with the total number of times a five of a kind was rolled and will print out the percentage of rolls for that. Here is an example run with the spaces clearly shown: Single positive integer, please: -1 Incorrect - a single positive integer, please: 2.3 Incorrect - a single positive integer, please: [1, 4] Incorrect - a single positive integer, please: Five of a kind count: 1: 15 2: 17 3: 13 4: 13 5: 12 6: 11 all: 81 (0.0810%) You can assume that the counts will never be above 999. As an aside, the probability of getting a five of a kind in one roll with five six-sided dice is or %. You should carefully think about the different steps needed for this program, come up with an efficient way to check for five of a kind, plan out how you are going to keep track of things, and perhaps even draw a picture or map of how your program will work before you start writing code. If you are unsure of how to do one part, skip it and write the next part of the code assuming the previous part works.

4 Problem III: [20 pts.] Voltage An engineer built an electric circuit by connecting a 9 V battery, through a switch, to a resistor and a capacitor. The engineer closed the switch (turned it on, so the battery was connected to the rest of the circuit) for a very long time and then starting taking measurements of the voltage across the capacitor. The engineer opened the switch (turned it off, so the battery was no longer connected) and waited for the capacitor voltage to drop to 5 V. At that point the engineer closed the switch again. Now the engineer wants to compare the measured values with the theoretical values for the capacitor voltage. The measured values are in a file called CapVoltage.dat that has two columns of information. The first column has the time at which a voltage was measured (relative to when the switch was opened - that is, time 0 was after the switch had been closed for a very long time). The second column has the capacitor voltage. Here is the start of the file: e e e e e e e e e e e e e e e e e e e e e+00 The analytical model for the voltage is given by: t < 0 9 v C (t) = 0 t < e t t e (t 0.58) Write code that will load the data and then make a single plot with two data sets - the original data plotted as black points and the analytical model plotted as a solid black line. The analytical model should have the same domain as the data and should use 1000 points to create the line. Give the graph labels, a grid, a title, and a legend as shown below and write the code to save it in a file called cap_plot.eps. Capacitor Voltage 9 8 Voltage, V Data Model Time, s Note: I have made the font sizes larger for clarity; you are not required to do that.

5 Problem IV: [15 pts.] The Kitchen Sink (1) Write a function called Re that takes three lists called (u, L, and ν, where ν is the Greek letter nu) and returns a list with the Reynolds number: Re = ul ν Note: Your function should work if the inputs are all lists that are the same length and should return a list of the same size. You may assume that the user calls the function correctly; for example: In [1]: Re([1], [2], [3]) Out[1]: [ ] In [2]: Re([1, 2, 3], [4, 5, 6], [7, 8, 9]) Out[2]: [ , 1.25, 2.0] (2) How many times will the following loop run, and what are the values of J, K, L, and M when it is finished? K=0; L=[]; M=1 for J in [[2,3], [1,4], [6,5]]: K += J[0] L = L+J M *= min(j) (3) Write a function called cone which can take up to two inputs and yields two outputs. The help file for it is: cone(r, h=none) cone Calculate the volume and surface area of a right circular cone (vol, sa) = cone(r, h) input: r = radius of the base of the cone (required) h = height of the cone (default = same as r) output: vol: volume of the cone sa: surface area of the cone The formulas are: vol = πr2 h 3 sa = πr 2 + πr r 2 + h 2 You may assume the inputs are valid. Once your function is written, also show the code you could use on the command line to calculate the volume and surface area of a cone of radius 3 and height 4 and store them in variables called the_volume and the_sa, respectively.

6 Problem V: [15 pts.] The Complete Surprise! The Maclaurin series calculation for the hyperbolic sin is given as: f(x) = sinh(x) = n=0 x 2n+1 (2n + 1)! Complete the following code segment for so_fun.m (modified from Chapra, Figure 4.2) so that your function satisfies all the requirements given in the comment at the top of the function, including handling the default cases: def so_fun(x, es=0.0001, maxit=50): ³³³ Maclaurin series of hyperbolic sin function so_fun(x,es,maxit) input: x = value at which series evaluated es = stopping criterion (default = ) maxit = maximum iterations (default = 50) output: fx = estimated value ea = approximate relative error (%) iter = number of iterations Based on IterMeth.m from Figure 4.2 on p. 105 of Applied Numerical Methods with MATLAB for Scientists and Engineers Steven C. Chapra, 4th Edition ³³³ You do not need to re-write the comments in your code!. Your program may assume that the user correctly enters a single value for x and that if the user also enters values for es and/or maxit that they are 1x1 as well. Note that this formula will generally converge for all values of x. Note: The first (n = 0) term is x. The first iteration solution is thus x when n = 0, while the second iteration would be the solution once the n = 1 term in the series is added (in this case, x + x 3 /3!). MATLAB has a built-in factorial command you may use.