print 5*0.6 - 0.5*9.81*0.6**2

print 5*0.6 - 0.5*9.81*0.6**2

from numpy import *

def integrate(f, a, b, n=100):
    """
    Integrate f from a to b,
    using the Trapezoidal rule with n intervals.
    """
    x = linspace(a, b, n+1)    # Coordinates of the intervals
    h = x[1] - x[0]            # Interval spacing
    I = h*(sum(f(x)) - 0.5*(f(a) + f(b)))
    return I

# Define my special integrand
def my_function(x):
    return exp(-x**2)

minus_infinity = -20  # Approximation of minus infinity
I = integrate(my_function, minus_infinity, 1, n=1000)
print 'Value of integral:', I

v0 = 5
g = 9.81
t = 0.6
y = v0*t - 0.5*g*t**2
print y

initial_velocity = 5
accel_of_gravity = 9.81
TIME = 0.6
VerticalPositionOfBall = initial_velocity*TIME - \
                         0.5*accel_of_gravity*TIME**2
print VerticalPositionOfBall

# program for computing the height of a ball
# in vertical motion
v0 = 5    # initial velocity
g = 9.81  # acceleration of gravity
t = 0.6   # time
y = v0*t - 0.5*g*t**2  # vertical position
print y

t = 0.6;  y = 1.2342
print 'At t=%g s, y is %.2f m.' % (t, y)

v0 = 5
g = 9.81
t = 0.6
y = v0*t - 0.5*g*t**2

print """
At t=%f s, a ball with
initial velocity v0=%.3E m/s
is located at the height %.2f m.
""" % (t, v0, y)

a = 1      # 1st statement (assignment statement)
b = 2      # 2nd statement (assignment statement)
c = a + b  # 3rd statement (assignment statement)
print c    # 4th statement (print statement)

a = 1;  b = 2;  c = a + b;  print c

myvar = 10
myvar = 3*myvar   # = 30
myvar

myvar = 5.2
prinnt Myvar

v0=3
v0  =  3
v0=   3
v0 = 3

counter = 1
while counter <= 4:
    counter = counter + 1   # correct (4 leading blanks)

while counter <= 4:
counter = counter + 1       # invalid syntax

v0 = 3;  g = 9.81;  t = 0.6
position = v0*t - 0.5*g*t*t
velocity = v0 - g*t
print 'position:', position, 'velocity:', velocity

C = 21
F = (9/5)*C + 32
print F

C = 21
F = (9.0/5)*C + 32
print F

a = 5       # a refers to an integer (int) object
b = 9       # b refers to an integer (int) object
c = 9.0     # c refers to a real number (float) object
d = b/a     # d refers to an int/int => int object
e = c/a     # e refers to float/int => float object
s = 'b/a=%g' % (b/a)  # s is a string/text (str) object
print d, e, s

a = 3              # a is int
b = float(a)       # b is float 3.0
c = 3.9            # c is float
d = int(c)         # d is int 3
d = round(c)       # d is float 4.0
d = int(round(c))  # d is int 4
d = str(c)         # d is str '3.9'
e = '-4.2'         # e is str
f = float(e)       # f is float -4.2

import math
r = math.sqrt(2)
# or
from math import sqrt
r = sqrt(2)
# or
from math import *   # import everything in math
r = sqrt(2)

from math import sin, cos, log
x = 1.2
Q = sin(x)*cos(x) + 4*log(x)   # log is ln (base e)
print Q

v1 = 1/49.0*49
v2 = 1/51.0*51
print '%.16f %.16f' % (v1, v2)

a = 1; b = 2;
computed = a + b
expected = 3
correct = computed == expected
print 'Correct:', correct

a = 0.1; b = 0.2; expected = 0.3
a + b == expected

print '%.17f\n%.17f\n%.17f\n%.17f' % (0.1, 0.2, 0.1 + 0.2, 0.3)

from math import sinh, exp, e, pi
x = 2*pi
r1 = sinh(x)
r2 = 0.5*(exp(x) - exp(-x))
r3 = 0.5*(e**x - e**(-x))
print '%.16f %.16f %.16f' % (r1,r2,r3)

C = 41
F = (9.0/5)*C + 32
print F

F

a = -2
b = 0.5
s = complex(a, b)  # make complex from variables
s

s*w                # complex*complex

s/w                # complex/complex

s.real

s.imag

from sympy import *
t, v0, g = symbols('t v0 g')
y = v0*t - Rational(1,2)*g*t**2
dydt = diff(y, t)                     # 1st derivative
dydt

print 'acceleration:', diff(y, t, t)  # 2nd derivative

y2 = integrate(dydt, t)
y2

y = v0*t - Rational(1,2)*g*t**2
roots = solve(y, t)    # solve y=0 wrt t
roots

x, y = symbols('x y')
f = -sin(x)*sin(y) + cos(x)*cos(y)
simplify(f)

expand(sin(x+y), trig=True)  # requires a trigonometric hint

from math import sin, log
x = 5
r = sin(3*log(10*x))

g = 9.81    # m/s**2
v0 = 15     # km/h
theta = 60  # degrees
x = 0.5     # m
y0 = 1      # m

print """v0    = %.1f km/h
theta = %d degrees
y0    = %.1f m
x     = %.1f m""" % (v0, theta, y0, x)

# convert v0 to m/s and theta to radians:
v0 = v0/3.6
from math import pi, tan, cos
theta = theta*pi/180

y = x*tan(theta) - 1/(2*v0)*g*x**2/((cos(theta))**2) + y0

print 'y     = %.1f m' % y