Calculus¶

In [1]:

n = int(input( " > " ))
print( n - 1 , n , n + 1)

n = int(input( " > " )) print( n - 1 , n , n + 1)

---------------------------------------------------------------------------
StdinNotImplementedError                  Traceback (most recent call last)
Cell In[1], line 1
----> 1 n = int(input( " > " ))
      2 print( n - 1 , n , n + 1)

File /opt/hostedtoolcache/Python/3.8.16/x64/lib/python3.8/site-packages/ipykernel/kernelbase.py:1281, in Kernel.raw_input(self, prompt)
   1279 if not self._allow_stdin:
   1280     msg = "raw_input was called, but this frontend does not support input requests."
-> 1281     raise StdinNotImplementedError(msg)
   1282 return self._input_request(
   1283     str(prompt),
   1284     self._parent_ident["shell"],
   1285     self.get_parent("shell"),
   1286     password=False,
   1287 )

StdinNotImplementedError: raw_input was called, but this frontend does not support input requests.

In [2]:

n = int(input( " > " ))
print( 1000 * (n % 8) + 100 * (n % 8) + 10 * (n % 30) + n % (30) )

n = int(input( " > " )) print( 1000 * (n % 8) + 100 * (n % 8) + 10 * (n % 30) + n % (30) )

---------------------------------------------------------------------------
StdinNotImplementedError                  Traceback (most recent call last)
Cell In[2], line 1
----> 1 n = int(input( " > " ))
      2 print( 1000 * (n % 8) + 100 * (n % 8) + 10 * (n % 30) + n % (30) )

File /opt/hostedtoolcache/Python/3.8.16/x64/lib/python3.8/site-packages/ipykernel/kernelbase.py:1281, in Kernel.raw_input(self, prompt)
   1279 if not self._allow_stdin:
   1280     msg = "raw_input was called, but this frontend does not support input requests."
-> 1281     raise StdinNotImplementedError(msg)
   1282 return self._input_request(
   1283     str(prompt),
   1284     self._parent_ident["shell"],
   1285     self.get_parent("shell"),
   1286     password=False,
   1287 )

StdinNotImplementedError: raw_input was called, but this frontend does not support input requests.

In [3]:

n = int(input( " > " ))
print( n - 1 , n , n + 1)


n = int(input( " > " ))
print( 1000 * (n % 81) + 100 * (n % 81) + 10 * (n % 30) + n % (30) )

n = int(input( " > " )) print( n - 1 , n , n + 1) n = int(input( " > " )) print( 1000 * (n % 81) + 100 * (n % 81) + 10 * (n % 30) + n % (30) )

---------------------------------------------------------------------------
StdinNotImplementedError                  Traceback (most recent call last)
Cell In[3], line 1
----> 1 n = int(input( " > " ))
      2 print( n - 1 , n , n + 1)
      5 n = int(input( " > " ))

File /opt/hostedtoolcache/Python/3.8.16/x64/lib/python3.8/site-packages/ipykernel/kernelbase.py:1281, in Kernel.raw_input(self, prompt)
   1279 if not self._allow_stdin:
   1280     msg = "raw_input was called, but this frontend does not support input requests."
-> 1281     raise StdinNotImplementedError(msg)
   1282 return self._input_request(
   1283     str(prompt),
   1284     self._parent_ident["shell"],
   1285     self.get_parent("shell"),
   1286     password=False,
   1287 )

StdinNotImplementedError: raw_input was called, but this frontend does not support input requests.

In [4]:

for i in range( 1 , 6 ) :
    
    print( ( str(i) + ' ' ) * ( i ))

for i in range( 1 , 6 ) : print( ( str(i) + ' ' ) * ( i ))

1 
2 2 
3 3 3 
4 4 4 4 
5 5 5 5 5 

In [5]:

for i in range(10, 100):

    if i % 7 == 0 or i % 9 == 0:
        continue

    print(i, end=" ")

for i in range(10, 100): if i % 7 == 0 or i % 9 == 0: continue print(i, end=" ")

10 11 12 13 15 16 17 19 20 22 23 24 25 26 29 30 31 32 33 34 37 38 39 40 41 43 44 46 47 48 50 51 52 53 55 57 58 59 60 61 62 64 65 66 67 68 69 71 73 74 75 76 78 79 80 82 83 85 86 87 88 89 92 93 94 95 96 97 

In [6]:

a = int( input( " a = " ))
b = int( input( " b = " ))
if a != b :
    
    print( " different " )
    
else :
    print( " same " )

a = int( input( " a = " )) b = int( input( " b = " )) if a != b : print( " different " ) else : print( " same " )

---------------------------------------------------------------------------
StdinNotImplementedError                  Traceback (most recent call last)
Cell In[6], line 1
----> 1 a = int( input( " a = " ))
      2 b = int( input( " b = " ))
      3 if a != b :

File /opt/hostedtoolcache/Python/3.8.16/x64/lib/python3.8/site-packages/ipykernel/kernelbase.py:1281, in Kernel.raw_input(self, prompt)
   1279 if not self._allow_stdin:
   1280     msg = "raw_input was called, but this frontend does not support input requests."
-> 1281     raise StdinNotImplementedError(msg)
   1282 return self._input_request(
   1283     str(prompt),
   1284     self._parent_ident["shell"],
   1285     self.get_parent("shell"),
   1286     password=False,
   1287 )

StdinNotImplementedError: raw_input was called, but this frontend does not support input requests.

In [7]:

for i in range( 10 , 100 ) :
    
    if i % 2 == 0 or i % 3 == 0 or i % 5 ==0 : continue
        
    print( i , end =" ")

for i in range( 10 , 100 ) : if i % 2 == 0 or i % 3 == 0 or i % 5 ==0 : continue print( i , end =" ")

11 13 17 19 23 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 

In [8]:

a , b = eval(input( " > "))
ans = 0
for i in range( a , b + 1 ) :
    
    ans += i
    
print( a, "+" , a + 1 , "+" , "..." , "+" , b , "=" , ans )

a , b = eval(input( " > ")) ans = 0 for i in range( a , b + 1 ) : ans += i print( a, "+" , a + 1 , "+" , "..." , "+" , b , "=" , ans )

---------------------------------------------------------------------------
StdinNotImplementedError                  Traceback (most recent call last)
Cell In[8], line 1
----> 1 a , b = eval(input( " > "))
      2 ans = 0
      3 for i in range( a , b + 1 ) :

File /opt/hostedtoolcache/Python/3.8.16/x64/lib/python3.8/site-packages/ipykernel/kernelbase.py:1281, in Kernel.raw_input(self, prompt)
   1279 if not self._allow_stdin:
   1280     msg = "raw_input was called, but this frontend does not support input requests."
-> 1281     raise StdinNotImplementedError(msg)
   1282 return self._input_request(
   1283     str(prompt),
   1284     self._parent_ident["shell"],
   1285     self.get_parent("shell"),
   1286     password=False,
   1287 )

StdinNotImplementedError: raw_input was called, but this frontend does not support input requests.

In [9]:

a , b = eval(input( " > "))
ans = 0
for i in range( a , b + 1 ) :
    
    ans += i
    
print( a, "+" , a + 1 , "+" , "..." , "+" , b , "=" , ans )

a , b = eval(input( " > ")) ans = 0 for i in range( a , b + 1 ) : ans += i print( a, "+" , a + 1 , "+" , "..." , "+" , b , "=" , ans )

---------------------------------------------------------------------------
StdinNotImplementedError                  Traceback (most recent call last)
Cell In[9], line 1
----> 1 a , b = eval(input( " > "))
      2 ans = 0
      3 for i in range( a , b + 1 ) :

File /opt/hostedtoolcache/Python/3.8.16/x64/lib/python3.8/site-packages/ipykernel/kernelbase.py:1281, in Kernel.raw_input(self, prompt)
   1279 if not self._allow_stdin:
   1280     msg = "raw_input was called, but this frontend does not support input requests."
-> 1281     raise StdinNotImplementedError(msg)
   1282 return self._input_request(
   1283     str(prompt),
   1284     self._parent_ident["shell"],
   1285     self.get_parent("shell"),
   1286     password=False,
   1287 )

StdinNotImplementedError: raw_input was called, but this frontend does not support input requests.

In [10]:

n = input( " > " )
print( "*"*( 10 - len(n)) + n )

n = input( " > " ) print( "*"*( 10 - len(n)) + n )

---------------------------------------------------------------------------
StdinNotImplementedError                  Traceback (most recent call last)
Cell In[10], line 1
----> 1 n = input( " > " )
      2 print( "*"*( 10 - len(n)) + n )

File /opt/hostedtoolcache/Python/3.8.16/x64/lib/python3.8/site-packages/ipykernel/kernelbase.py:1281, in Kernel.raw_input(self, prompt)
   1279 if not self._allow_stdin:
   1280     msg = "raw_input was called, but this frontend does not support input requests."
-> 1281     raise StdinNotImplementedError(msg)
   1282 return self._input_request(
   1283     str(prompt),
   1284     self._parent_ident["shell"],
   1285     self.get_parent("shell"),
   1286     password=False,
   1287 )

StdinNotImplementedError: raw_input was called, but this frontend does not support input requests.

In [11]:

for i in range(5) :
    
    print( " * " * ( i + 1 ))

for i in range(5) : print( " * " * ( i + 1 ))

 * 
 *  * 
 *  *  * 
 *  *  *  * 
 *  *  *  *  * 

Practice

In [12]:

import pylab

def f(x):
    return pylab.cos(x)**2 / pylab.sqrt(pylab.maximum(1, 2*x-1))
    
a, b, n = 0, 10*pylab.pi, 100
xs = pylab.linspace(a,b,n)
ys = f(xs)
pylab.plot(xs,ys)

pylab.show()

import pylab def f(x): return pylab.cos(x)**2 / pylab.sqrt(pylab.maximum(1, 2*x-1)) a, b, n = 0, 10*pylab.pi, 100 xs = pylab.linspace(a,b,n) ys = f(xs) pylab.plot(xs,ys) pylab.show()

In [13]:

import pylab, numpy

def factorial(n) :
    
    f = 1
    for i in range(2, n+1) :
        f *= i
    return f

def taylor_poly(n, x) :
    
    s = 0
    for k in range(n) :
        s = s + ((-1) ** (k) * (x ** (2 * k)) / factorial(2 * k)) + ((-1) ** (k) * (x ** ((2 * k) + 1)) / factorial((2 * k) + 1))

    return s    

a, b, m = 0 , 3 * numpy.pi, 100
xs = numpy.linspace(a, b, m)

n = 10
for i in range(1, n+1) :
    ys = taylor_poly(i, xs)
    pylab.plot(xs, ys, label = "P" + str(2 * i - 1))

pylab.plot(xs,numpy.sin(xs) + numpy.cos(xs), label = "sin(x)+cos(x)")
pylab.title("HW1"
            "-"
            "Taylor polynomilas with different orders for sin(x)+cos(x)")
pylab.legend()
pylab.grid()
pylab.xlabel("X")
pylab.ylabel("Y")
pylab.ylim(-2, 2)
pylab.show()

import pylab, numpy def factorial(n) : f = 1 for i in range(2, n+1) : f *= i return f def taylor_poly(n, x) : s = 0 for k in range(n) : s = s + ((-1) ** (k) * (x ** (2 * k)) / factorial(2 * k)) + ((-1) ** (k) * (x ** ((2 * k) + 1)) / factorial((2 * k) + 1)) return s a, b, m = 0 , 3 * numpy.pi, 100 xs = numpy.linspace(a, b, m) n = 10 for i in range(1, n+1) : ys = taylor_poly(i, xs) pylab.plot(xs, ys, label = "P" + str(2 * i - 1)) pylab.plot(xs,numpy.sin(xs) + numpy.cos(xs), label = "sin(x)+cos(x)") pylab.title("HW1" "-" "Taylor polynomilas with different orders for sin(x)+cos(x)") pylab.legend() pylab.grid() pylab.xlabel("X") pylab.ylabel("Y") pylab.ylim(-2, 2) pylab.show()

In [14]:

import pylab
a , b , n = -4 , 4 , 500

def g(t):
    glist = []
    for i in range(0,n):
        if t[i]%pylab.pi>0 and t[i]%pylab.pi<pylab.pi/2:
            glist.append(1)
        else:
            glist.append(-1)
    return glist
    
gxs = pylab.linspace(a,b,n)
gys = g(gxs)

pylab.plot(gxs,gys)
pylab.grid()
pylab.show()

def dg(s):
    dglist=[]
    h = (b-a)/(n-1)
    for j in range(0,n):
        if abs((g(s+h)[j]-g(s)[j])/h) < 100:
            dglist.append((g(s+h)[j]-g(s)[j])/h)
        else:
            dglist.append(0)
    return dglist

dgxs = pylab.linspace(a,b,n)
dgys = dg(dgxs)

pylab.plot(dgxs,dgys)
pylab.show()

def h(u):
    return 1.2732*pylab.sin(2*u)+0.4244*pylab.sin(6*u)+0.25465*pylab.sin(10*u)+0.18189*pylab.sin(14*u)+0.14147*pylab.sin(18*u)
hxs = pylab.linspace(a,b,n)
hys = h(hxs)
pylab.plot(hxs,hys)
pylab.show()

def dh(v):
    p = (b-a)/(n-1)
    return (h(v+p)-h(v))/p
    
dhxs = pylab.linspace(a,b,n)
dhys = dh(dhxs)
pylab.plot(dhxs,dhys)
pylab.show()

import pylab a , b , n = -4 , 4 , 500 def g(t): glist = [] for i in range(0,n): if t[i]%pylab.pi>0 and t[i]%pylab.pi