var("x,y")
plot_vector_field((sin(x),cos(y)),(x,-3,3),(y,-3,3))

#1 Mathematical functions: two ways to define
def mathfunc(x):
    return 3*x^2

#Parameters and symbolic variables
f(x) = 3*x^2

f(3)

# define a function of x to the power of 19
g(x) = x^19
g(2)

#2 Symbolic variables

type(x)

# x is the default 'symbolic variable'
# Make other sybolic variables?

var("a,b,c")

type(b)

b = 7

type(b)

#2 Making lists of integers 1 to 5
#syntax:  srange(lower, upper, stepsize)
srange(5)
#default argument values

#Practice: Making a list with even numbers starting from 2 and ends at 50, inclusive.

#hint: srange(lower, last value to include +b, stepsize), where 0<b<=stepsize
srange(2, 53,2)

srange(5)

#Iterations
#use the list as counter or index

f(x) = 3*x^2
val = 3
for i in srange(5):
     val = f(val)
val

f(x) = 3*x^2
vals = [1,3,5,7,9]
newvals = []
for i in srange(5):
     newvals.append(f(vals[i]))
newvals

# Exercise : apply a function g(x) = 6*x for 100 times, initial val 9

#Store intermediate values in a list named vals? Hint: the function is always applied on the last element in list

#example 4
f(x) = 2*x #Define the function we want to iterate
#Create list of numbers defining how many times to iterate
count = srange(0,10)
#Create a list to hold the results. The first value is 3.
vals = [3]
for i in count:
    a = vals[i] #Grab the last item in the results list
    b = f(a) # Plug a into the function. Put the output in b.
    vals.append(b) # Put b into the list of results.
list_plot(vals) # Plot the results

def iterate(iter,j):
    f(x) = 2*x #Define the function we want to iterate
#Create list of numbers defining how many times to iterate
    count = srange(iter)
#Create a list to hold the results. The first value is 3.
    vals = [3]
    for i in count:
        a = vals[i] #Grab the last item in the results list
        b = j(a) # Plug a into the function. Put the output in b.
        vals.append(b) # Put b into the list of results.
    return vals # Plot the results
g(x) = 3*x
list_plot(iterate(5,g))

f(x) = 2*x #Define the function we want to iterate
#Create list of numbers defining how many times to iterate
count = srange(0,10)
#Create a list to hold the results. The first value is 3.
vals = [3]
for i in count:
    a = vals[i] #Grab the last item in the results list
    b = f(a) # Plug a into the function. Put the output in b.
    vals.append(b) # Put b into the list of results.
list_plot(vals) # Plot the results

def my_func(iter, init, g):
    #f(x) = 2*x
    vals = [init]
    count = srange(0,iter)
    for i in count:
        a = vals[i] #Grab the last item in the results list
        b = g(a) # Plug a into the function. Put the output in b.
        vals.append(b) # Put b into the list of results.
    return(vals)
f(x) = 2*x
list_plot(my_func(10, 5,f))

my_func()

︠46242af9-542a-443c-abfa-fa53daf40a1a︠
# (1) simplify?
# (2) wrap in function?
#inputs...
#~0 no input
#~1 iteration no.
#~2 init
#~3 function

︠d11286a4-2553-4437-bd2e-1c9fed4cb77e︠