"""
Lecture 2 : Some programming concepts; intro to using mathematical functions
in python.
----------------
Date : 06 Jan 2013
"""

# Here are a few concepts from programming. First one boots into an
# operating system. The operating system has different applications. We are
# interested in a text editing software and a python interpreter.
#
# The text editing software is a program which allows you to create, edit
# and save text files. Nowadays most text editors do much more than that.
# For example, they support syntax highlighting, auto-indentation, and some
# even allow you to run the code from within the editor (for example vim or
# emacs). The other application we are interested in is a python
# interpreter. This comes pre-installed in linux. Windows and mac users can
# get it from http://www.python.org .

"""
Some computing terms : 
Program / code : the instructions you give the interpreter/compiler.
function : a code which you can "call" from another code.
Module : a set of functions which someone has written and you can use them
in your programs.
package : a collection of related modules packaged together for easy
distribution.
algorithm : a step by step account of how to compute something in plain
english.
pseudo-code : A text which looks like code but is in english. It is
something in between english description and an actual code.
bug : an programming error in the code.
statement : a code comprises of statements. Statements are individual
instructions like 
a = 4 (assignment)
print t (print statement)
a = input("Something") (input statement)
etc.
To emphasaize again: = is an assignment, not a mathematical equality.
Everything is CASE SENSITIVE. aa, aA, Aa are different names.
"""

# Precedence of arithmetic operators.
# ** is evaluated first (left to right) then *, / and after that +, -.

# importing modules : math

# Problem : Consider the vertical motion of a ball. Suppose h = 0 at time t
# = 0, and g = 9.8 m/s/s . Let v0 be the initial velocity. Then the height
# at time t is given by 
t = 1.0
v0 = -1.0
g = - 9.8
h = v0 * t + 0.5 * g * t**2
print "Height at time t = %g is %g" % (t, h)

# Now suppose we want to know the time when it reaches say height hfin = 1.
# We know the formula for t for which
# 0.5 g t^2 + v0 t - hfin = 0
# it is
# t = (-v0 \pm sqrt(v0^2 + 4 * 0.5 g * hfin)) / g
# Let us code it
import math
hfin = 1.0
t1 = (-v0 + math.sqrt(v0**2 - 2 * g * hfin)) / g
t2 = (-v0 - math.sqrt(v0 ** 2 - 2 * g * hfin)) / g
print "The time is either %g or %g" % (t1, t2)

# you can also use 
from math import *
print "Square root of 100 is %g." % sqrt(100)