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In [1]:

    
println("hi")

hi



In [3]:

    
f(x) = 10 * x + sin(x)









    Out[3]:





f (generic function with 1 method)



In [4]:

    
f(1)









    Out[4]:





10.841470984807897

Get the Greeks by typing \pi followed by a tab key



In [6]:

    
π









    Out[6]:





π = 3.1415926535897...



In [9]:

    
# this is a comment



In [10]:

    
area(r) = π * r^2









    Out[10]:





area (generic function with 1 method)



In [11]:

    
area(3)









    Out[11]:





28.274333882308138

Use Pkg.add("Gadfly") to add a package



In [14]:

    
using Gadfly









    



INFO: Precompiling module Gadfly.
WARNING: StatsBase.WeightVec is deprecated, use StatsBase.Weights{#1#S, #2#T, #3#V} where #3#V<:AbstractArray{#2#T, 1} where #2#T<:Real where #1#S<:Real instead.
  likely near /Users/amir.ziai/.julia/v0.6/KernelDensity/src/univariate.jl:80



In [16]:

    
g(x) = sin(x)









    Out[16]:





g (generic function with 1 method)



In [17]:

    
plot(g, 0, 10)









    Out[17]:



In [28]:

    
x = abs(3*(4/3-1)-1)









    Out[28]:





2.220446049250313e-16



In [24]:

    
eps()









    Out[24]:





2.220446049250313e-16



In [26]:

    
typeof(ans)









    Out[26]:





Float64



In [27]:

    
typeof(eps())









    Out[27]:





Float64



In [29]:

    
eps() == x









    Out[29]:





true



In [30]:

    
4/3-1









    Out[30]:





0.33333333333333326



In [32]:

    
1 + eps() == 1









    Out[32]:





false



In [35]:

    
eps() / 2 + 1 == 1









    Out[35]:





true

eps() is the machine epsilon
smallest number that can be added to 1 that 1 + eps != 1
sys.float_info.epsilon in python



In [37]:

    
x = 1.0
y = x / 3.0









    Out[37]:





0.3333333333333333



In [38]:

    
x == y * 3.0









    Out[38]:





true



In [43]:

    
1//3









    Out[43]:





1//3



In [45]:

    
1//3 + 2//3 == 1









    Out[45]:





true



In [47]:

    
1//3 + 3 // 4









    Out[47]:





13//12



In [48]:

    
f(x) = (exp(x) - 1) / x - 1









    Out[48]:





f (generic function with 1 method)



In [62]:

    
plot(f, -2, 2)









    Out[62]:



In [65]:

    
f(0.1)









    Out[65]:





0.051709180756477124



In [66]:

    
f(-0.1)









    Out[66]:





-0.048374180359595176



In [68]:

    
f(-0.001)









    Out[68]:





-0.0004998333750219075



In [69]:

    
f(0)









    Out[69]:





NaN



In [70]:

    
f(x) = exp(-1/x^2)









    Out[70]:





f (generic function with 1 method)



In [72]:

    
plot(f, -1, 1)









    Out[72]:



In [73]:

    
a = (1,2,3)









    Out[73]:





(1, 2, 3)



In [76]:

    
typeof(a)









    Out[76]:





Tuple{Int64,Int64,Int64}



In [77]:

    
a = [1, 2, 3]









    Out[77]:





3-element Array{Int64,1}:
 1
 2
 3



In [78]:

    
typeof(a)









    Out[78]:





Array{Int64,1}



In [81]:

    
dot(a, [1,2,3])









    Out[81]:





14



In [84]:

    
f(x) = x^3 + x^2 - 8*x + 4









    Out[84]:





f (generic function with 1 method)



In [85]:

    
plot(f, -4, 4)









    Out[85]:



In [87]:

    
plot(f, -2, 2)









    Out[87]:



In [86]:

    
plot(f, -1, 1)









    Out[86]:



In [1]:

    
function f(x)
    y = x + 1
    return y + 2
end









    Out[1]:





f (generic function with 1 method)



In [2]:

    
f(3)









    Out[2]:





6



In [3]:

    
x -> x * 2









    Out[3]:





(::#1) (generic function with 1 method)



In [4]:

    
function(x) x + 2 end









    Out[4]:





(::#3) (generic function with 1 method)



In [5]:

    
map(x -> x * 2, [1, 2, 3])









    Out[5]:





3-element Array{Int64,1}:
 2
 4
 6



In [7]:

    
maximum([1,2,3])









    Out[7]:





3



In [8]:

    
function f(array)
    max = maximum(array)
    scaled = map(x -> (x / max) * (x / max), array)
    return sqrt(reduce(+, scaled))
end









    Out[8]:





f (generic function with 1 method)



In [9]:

    
f([1,2,3])









    Out[9]:





1.247219128924647



In [10]:

    
f([1,2])









    Out[10]:





1.118033988749895



In [11]:

    
reduce(*, [1,2,3])









    Out[11]:





6



In [13]:

    
a = 1
b = eps() / 2
((a + b) - a) - b









    Out[13]:





-1.1102230246251565e-16