#!/usr/bin/env python
# coding: utf-8

# # 2.18 Programming for Geoscientists class test 2012. 

# ## Note: 2013 was the first time the exam was run using iPython rather than using a text editor and the command line. This iPython version was created for the 2013 class so that they would know what to expect.

# # Test instructions
# 
# * This test contains **5** questions each of which should be answered.
# * Write your program in a Python cell just under each question.
# * You can write an explanation of your solution as comments in your code.
# * In each case your solution program must fulfil all of the instructions - please check the instructions carefully and double check that your program fulfils all of the given instructions.
# * Save your work regularly.
# * At the end of the test you should email your IPython notebook document (i.e. this document) to [Gerard J. Gorman](http://www.imperial.ac.uk/people/g.gorman) at g.gorman@imperial.ac.uk

# **1.** Ignore this question from 2012 as it deals with material no longer covered.

# **2.** Write a program, that creates a *list* $t$ with 6 values, 0.1, 0.2, ..., 0.6. Compute a corresponding *list* $y$ of $y(t)$ values using the formula:
# $$y(t) = v_0t − gt^2,$$
# where $v_0=6.0$ and $g=9.8$.
# 
# * Store these two lists, t and y, in a new list t1.
# * Write out a table with a column of t and a column of y values by traversing the data in the nested t1 list.
# * You may use list or NumPy array for t and y.
# * Print out a table header with the column names ’t’ and ’y’.
# * For printing the table, iterate the nested list t1, do not access the previously computed t and y lists directly.
# * Print out the table t1 using format specifiers so that the columns are aligned.

# **3.** The factorial of n, written as n!, is defined as:
# $$n! = n(n − 1)(n − 2)...2\cdot1,$$
# with the special cases
# $$1! = 1, 0! = 1.$$
# For example, $4! = 4\cdot3\cdot2\cdot1 = 24$, and $2! = 2\cdot1 = 2$.
# 
# * Write a function fact(n) that returns $n!$. You **must** not use the *fact* function from the math module.
# * Return 1 immediately if $x$ is 1 or 0, otherwise use a loop to compute $n!$.
# * The function must be called *fact* and take a single argument called n.
# * The software should check that the supplied value is a non-negative integer. If it is not, raise a ValueError exception.

# **4.** A table of temperatures and densities, in units of degrees ($C$) and $kg/m^3$, are given in the file [data/density_air.dat](https://raw.githubusercontent.com/ggorman/Introduction-to-programming-for-geoscientists/master/notebook/data/density_air.dat)
# Write a program that reads in the data from file into a list for temperature (first column) and density (second column) and plots the variation of density against temperature.
# 
# * The input file contains blank lines and lines starting with a ’#’, which you must ignore when reading in the data.
# * You may use list or NumPy array for temperature and density.
# * Plot the variation of density against temperature.
# * Label the x axis "Temperature (Celsius)" and the y axis "Density ($kg/m^3$)".
# * Use the plot title "Density of air at different temperatures, at 1 atm pressure".
# * Display a legend with the label ’Air’.

# **5.** Based on the data in the file [data/constants.txt](https://raw.githubusercontent.com/ggorman/Introduction-to-programming-for-geoscientists/master/notebook/data/constants.txt), make a dictionary where the keys are the names of the physical constant and the values are a tuple containing the numerical value and the units.
# 
# * Use a Python dictionary to store the data.
# * All numerical values should be of type float.
# * Print out the dictionary without any formatting.

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