Here is some example code in the order of contour, euler method, and slope field

Question

Here is some example code in the order of contour, euler method, and slope field.

M be the integer corresponding to the first letter of your last name. For example, if your last name begins wi th "A", M-1 and if your last name begins with "Z", M-26. Let Let k 1/M and consider the logistic equation dy/dt y (M y) Construct a single figure including 1. a slope field for 0 s 3, -M/2 s y s 3M/2 2. an uler's method solution for initial condition y (0)SM/2 for 0 sts 3 using A t 0.1 3. contours for the function Ft exp(-t The title of the figure should say, "Logistic Equation S Fr E M. and solution curves by FirstName LastName" where you use your actual first and last names.

Explanation / Answer

# FB - 201104096
import science
# initial Order lyric (y' = f(x, y)) problem solver victimization mathematician methodology
# xa: initial price of experimental variable
# xb: final price of experimental variable
# ya: initial price of variable quantity
# n : variety of steps (higher the better)
# Returns price of y at xb.
def Euler(f, xa, xb, ya, n):
h = (xb - xa) / float(n)
x = xa
y = ya
for i in range(n):
y += h * f(x, y)
x += h
return y

# Second Order lyric (y'' = f(x, y, y')) problem solver victimization mathematician methodology
# y1a: initial price of calculation of variable quantity
def Euler2(f, xa, xb, ya, y1a, n):
h = (xb - xa) / float(n)
x = xa
y = ya
y1 = y1a
for i in range(n):
y1 += h * f(x, y, y1)
y += h * y1
x += h
return y

if __name__ == "__main__":
print Euler(lambda x, y: math.cos(x) + science.sin(y), 0, 1, 1, 1000)

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