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Please I need help in solving numerical differentiation, numerical integration and finding the extrema, Using PYTHON.

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Given a function

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Answer #1

Please let me know if you have any doubts or you want me to modify the answer. And if you find this answer useful then don't forget to rate my answer as thumps up. Thank you! :)

import numpy as np
import matplotlib.pyplot as plt

class Diff:
    def __init__(self, f, h=1E-5):
        self.f = f
        self.h = float(h)

class Diff2(Diff):
    def __init__(self, f, h=1E-5, dfdx_exact=None):
        Diff.__init__(self, f, h)
        self.exact = dfdx_exact

    def error(self, x):
        if self.exact is not None:
            df_numerical = self(x)
            df_exact = self.exact(x)
        return df_exact - df_numerical

class Backward1(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (f(x) - f(x-h))/h

class Forward1(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (f(x+h) - f(x))/h

class Forward3(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (-(1./6)*f(x+2*h) + f(x+h) - 0.5*f(x) - (1./3)*f(x-h))/h

class Central2(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (f(x+h) - f(x-h))/(2*h)

class Central4(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (4./3)*(f(x+h) - f(x-h)) /(2*h) - (1./3)*(f(x+2*h) - f(x-2*h))/(4*h)

class Central6(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (3./2) *(f(x+h) - f(x-h)) /(2*h) - (3./5) *(f(x+2*h) - f(x-2*h))/(4*h) + (1./10)*(f(x+3*h) - f(x-3*h))/(6*h)

class Integrator:
    def __init__(self, a, b, n):
        self.a, self.b, self.n = a, b, n
        self.points, self.weights = self.construct_method()

    def construct_method(self):
        raise NotImplementedError('no rule in class %s'%self.__class__.__name__)

    def integrate(self, f):
        s=0
        for i in range(len(self.weights)):
            s += self.weights[i]*f(self.points[i])
        return s

    def __call__(self, f):
        return self.integrate(f)

class Midpoint(Integrator):
    def construct_method(self):
        a, b, n = self.a, self.b, self.n
        h = (b-a)/float(n)
        x = np.linspace(a + 0.5*h, b - 0.5*h, n)
        w = np.zeros(len(x)) + h
        return x, w

class Trapezoidal(Integrator):
    def construct_method(self):
        x = np.linspace(self.a, self.b, self.n)
        h = (self.b - self.a)/float(self.n - 1)
        w = np.zeros(len(x)) + h
        w[0] /= 2
        w[-1] /= 2
        return x, w

class Simpson(Integrator):
    def construct_method(self):
        if self.n % 2 != 1:
            print('n=%d must be odd, 1 is added'% self.n)
        self.n += 1
        x = np.linspace(self.a, self.b, self.n)
        h = (self.b - self.a)/float(self.n - 1)*2
        w = np.zeros(len(x))
        w[0:self.n:2] = h*1.0/3
        w[1:self.n-1:2] = h*2.0/3
        w[0] /= 2
        w[-1] /= 2
        return x, w

class GaussLegendre2(Integrator):
    def construct_method(self):
        if self.n % 2 != 0:
            print('n=%d must be even, 1 is subtracted' % self.n)
            self.n -= 1
        nintervals = int(self.n/2.0)
        h = (self.b - self.a)/float(nintervals)
        x = np.zeros(self.n)
        sqrt3 = 1.0 / np.math.sqrt(3)
        for i in range(nintervals):
            x[2*i] = self.a + (i+0.5)*h - 0.5*sqrt3*h
            x[2*i+1] = self.a + (i+0.5)*h + 0.5*sqrt3*h
        w = np.zeros(len(x)) + h/2.0
        return x, w

class CalculusCalculator():
    def __init__(self, f, a, b, resolution= 500, differentiation_method= Backward1, integration_method= Midpoint):
        self.f, self.a, self.b = f, a, b
        self.resolution = resolution
        self.differentiation_method = differentiation_method(f)
        self.integration_method = integration_method(a, b, resolution)
        self._integral = self.integration_method(f)
        fx = [f(a)]
        lx = [a]
        minima = []
        minima_value = []
        maxima = []
        maxima_value = []
        h = (b - a) / (resolution-1)
        x = a
        for i in range(resolution-1):
            x += h
            lx.append(x)
            fx.append(f(x))
            if f(x) >= f(x-h) and f(x) >= f(x+h):
                maxima_value.append(f(x))
                maxima.append(x)
            if f(x) <= f(x-h) and f(x) <= f(x+h):
                minima_value.append(f(x))
                minima.append(x)
        lx.append(b)
        fx.append(f(b))
        self.x = lx
        self.fx = fx
        self.maxima = maxima
        self.minima = minima
        self.global_max_value = max(maxima_value + [f(a), f(b)])
        self.global_min_value = min(minima_value + [f(a), f(b)])
        self.global_max = 0
        self.global_min = 0
        for i in self.x:
            if f(i) == self.global_max_value:
                self.global_max = i
            if f(i) == self.global_min_value:
                self.global_min = i

    @property
    def integral(self):
        return self._integral

    def set_differentiation_method(self, differentiation_method):
        self.differentiation_method = differentiation_method(self.f)

    def set_integration_method(self, integration_method):
        self.integration_method = integration_method(self.a, self.b, self.resolution)
        self._integral = self.integration_method(self.f)

    def df(self, x):
        return self.differentiation_method(x)

    def plot(self):
        plt.plot(self.x, self.fx)
        plt.show()

    def plot_derivative(self):
        plt.plot(self.x, [self.df(xx) for xx in self.x])
        plt.show()

    def extrame_points(self):
        print("All minima: ", end= '')
        for x in self.minima:
            print("%.4f"%x, end= ' ')
        print()
        print("All maxima: ", end= '')
        for x in self.maxima:
            print("%.4f"%x, end= ' ')
        print()
        print("Global minimum: %.4f\nGlobal maximum:%.4f"%(self.global_min, self.global_max))

if __name__ == '__main__':
    c = CalculusCalculator(lambda x: x, 0, 6, 500)
    c.plot()
    c.plot_derivative()
    c.extrame_points()
    print(c.df(2.51))
    c.set_differentiation_method(Central4)
    print(c.df(2.51))
    c.set_integration_method(Simpson)
    print(c.integral)

alculusCalculator [/Pycharm Projects/alculusCalculator] -/CalculusCalculator.py [alculusCalculatorl alculusCalculator CalculusCalculator. py CalculusCalculator ¢ - CalculusCalculator. py Project import numpy as np import matplot lib. pyplot as plt | alculusCalculator PycharmProjects/alculusCalc venv CalculusCalcu lator. py External Libraries class Diff: (self, f, h-1E-5 ): der Scratches and Consoles self.ff self.h-float (h) Figure 1 6. 17 5 23 4. 26 29 2 CalculusCalculator Run /Users/swapnil/PycharmP rojects/alculusCalculat 1 pan/zoom, x3.30605 y-3.25714 Python Console 4: Run E 6: TODO Terminal 2 Event Log Packages installed successfully: Installed packages: 'matplotlib (4 minutes agol 4 spaces 118:28 n/a UTF-8 #

alculusCalculator [~/PycharmProjects/alculusCalculator] - ..CalculusCalculator. py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator CalculusCalculator.py Project import numpy |import matplLot lib.pyplot as plt I alculusCalculator PycharmProjects/alculusCalc np venv CalculusCalculator.py External Libraries class Diff: h-16-5): def self.f= f (self, Scratches and Consoles self.h= float ( h ) 1P class Diff2(Diff): 11 e def Diff. self.exact = dfdx exact dfdx_exact-None): intt (self. t. h) 13 14 def error(self, x): if self.exact is not None: 17 df exact = self . exact (x] return df exact 10 df numerical 20 class Backward1(Diff2): de 23 f, hself. e return (f(x) - f(x-h)) /h 25 .h 26 class Forward1(Diff2): 29 Gausslegendre2 construct method(! CalculusCalculator Run: Users/swapnil/PycharmP rojects/alculusCalculator/venv/bin/python /Users/swapnil/PycharmProjects/alcu lusCalculator/CalculusCalculator. py 011 maxima Global minimum: .0000 ep99 m.0000 eeaaaaaaaags5512 500 must be odd, 18.00000000000001 is added Process finis hed with exit code 0 Python Console 4: Run Terminal E 6: TODO 2 Event Log 118:28 n/a UTF-8 4 spaces Packages installed successfully: Installed packages: 'matplotl ib (4 minutes ago)

alculusCalculator [~/PycharmProjects/alculusCalculator] -...CalculusCalculator.py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalcudator CalculusCalculator.py x Project Pycharm Projects/alcu lu sCalc | alculusCalculator import numpv np import matplot lib. pyplot as plt veny CalculusCalcu lator. py class Diff: def External Libraries 5 (self, h-1E-5) Scratches and Consoles self.f self.h float (h) 11 Eclass Diff2(Diff): dfdx_exact None): def Diff self.exact= dfdx exact self. f. h) 12 14 def error(self, x): if self.exact is not None: 17 df exact self.exact (x l return df_exact 10 df_nunerical class Backward1 (Diff2): def f, h=self. return (f(x) - f(x-h) )/h .h 26 class Forward1( Diff2): 20 def fh=self return (f(x+h) .h f(x))/h class Forward3(Diff2): def 75 f, h=self.f, self return (-(1./6)af (x+2h) + f(x+h ) .h 0.5*f (x) - (1./3) sf (x-h) )/h 39 class Central2 (Diff2) : call (self, x): ля def 42 return (f(xth) f(x-h))/(2*h) GaussLegendre2 construct method) CalculusCalculator Run: Python Console Е 8: торо 4: Run Terminal 2 Event Log 12:1 n/a UTF-8: 4 spaces : Packages installed successfully: Installed packages: 'matplotlib" (5 minutes ago) *ravrites

alculusCalculator [~/PycharmProjects/alculusCalculator] - ./CalculusCalculator.py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator CalculusCalculator.py Project | alculusCalculatorPychamProjects/alcu lusCalc class Central2 ( Diff2) : def call (self, x): f,h=e return (f 47 venv CalculusCalcu lator.py flxsb))/{2#h) 45 External Libraries 45 Scratches and Consoles class Central4 (Diff2) : def all (self, x) : 48 f,haset lflxh) - f(x-h)) /[2#h) - (1./3)e(f(x+2*h) - f(x-2*h) ) / (4eh) return (4./3): 51 class Central6 ( Diff2): ll (self, x) : def f,h=setf Elh) f(x-h) ) /[2*h) - (3./5) (f(x+2*h) - f(x-2«h) ) / (4*h) + (1./10) =(f(x+3+h) . f(x-3*h) ) / (6%h ) return (3./2) *(f(x+ E7 ol class Integrator: (self, , b, n): def 68 self.a, self.b, selr.n = a, b, n self.point .construct method () 63 def construct met hod (self): raise NotImp lemented 64 ( 'no rule in class 4s'self, class , name) 66 def integrate(self, f): for i in range(len (self, weights) ) : Stself.weights [i] *f (self. points [i] ) 69 re turn 72 det retue etr, T): rate (f) TE slass Midpoint(ntegcaeE lf) a. b. n=self.a, self.b, self.n h = (b-a)/float (n) 78 70 DD-7eros (len(x)). b-0.5 h, n) 82 return x. W 83 construct method() GaussLegendre2 Run CalculusCalculator Python Console 4: Run E 6: TODO 2 Event Log Terminal 4 spaces Packages installed successfully: Installed packages: 'matplotlib' (5 minutes ago) 12:1 n/a UTF-8 =

alculusCalculator [~/PycharmProjects/alculusCalculator] - ..CalculusCalculator. py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator , CalculusCalculator.py Project I alculusCalculator /PycharmProjects/alculusCalc 7 class Ostruct metbodicelf); venv 86 e CalculusCalculator.py =np. linspace(self. a, self. b, self.n) loat ( self, n - 1) R7 x External Libraries = n. zeros (len(x))+ h Scratches and Consoles wl0] /-2 coture w class Simpson (Integrator): def construct_method ( self) : 96 if Drint'ned must be odd, 1 is added'& self.n) self.n + 1 99 w=np.zeros ( len (x) ) 102 wTself.n-1:21 . he2.0/3 w[0] /= 2 105 return x 100 class GaussLegendre2(Integrator) : def construct_method ( self ) : 111 e if print'n-d must be even, 1 is subtracted self.n) 114 1 self.n tel.va. alffloat inintervals) = np.zeros (self.n) 117 x 31 for i in rangetnintervals) x[2*i]= self. a + (i+0.5) *h - .5) *h WE00. zeros(len/x)) h/2.8 118 5*sqrt3*h 0.5+sqrt3*h 128 121 return x, w 124 class CalculusCalculato r() : def init (self, f, a, b, resolution= 500, different iation_method Backward1, integration_method=_Mid po int): 121 GaussLegendre2 construct method () CalculusCalculator Run: 4: Pun E 6: TODO Python Console Packages installed successfully: lInstalled packages: 'matplotib) 2 Event Log Terminal (5 minutes agol 12:1 n/a UTE-8 4 spaces :

alculusCalculator [/PycharmProjects/alculusCalculator] -./CalculusCalculator.py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator CalculusCalculator.py Project alculusCalculatorPycharmProjects/alcu lu sCalc cLass Calcus lf f, a, b, resolution=_500, differentiation_method=_Backward1, integration_met hod_Midpo int) : venv CalculusCalculator. py self.f, self.a, self.b f, a, b 128 External Libraries self.differentiation nethod differentiation method(f) self.integration_method= integration method(a, b. resolution) Scratches and Consoles 131 f Teiaatself.integration_method(f) Lx [a] 134 minina value = [0 maxima= [ 137 a)/ (resolution-1) x = a for 148 range(resolution-1) : Lx.append(x) 143 if fix) 2= f (x-h) and f(x) > f(x+h): maxima_value.append (f (x) ) 146 if f(x) = f(x-h) and f(x) = f (x+h ) : minima_value. append ( f (x) ) a. append (x) 149 x.append (b) fx.append(f(b) 152 self.fx = fx пахіпа 155 self.maxima self.global max value = max(maxima value+[f(a), f(b)]) self.globalmin_value = min (minima_va lue + [f(a), f(b)]) 158 self.global min = 0 for i in self.x: 161 лах_value: 1f f(1) .global max if f(i)-self.global min_value : self.global min - i 164 165 167 @property def integral( self) : 168 Gausslegendre2 construct method () CalculusCalculator iRun: Python Console Е 8: торо 4: Run Terminal 2 Event Log 4 spaces: 12:1 n/a UTF-8 : Packages installed successfully: Installed packages: 'matplotlib' (5 minutes ago)

alculusCalculator [/PycharmProjects/alculusCalculator] -./CalculusCalculator. py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator Calculus Calcul ator.py Project I alculusCalculator PycharmProjects/alculusCalc167 @property def integral(self) : return self._integral 168 venv CalculusCalculator.py External Libraries def set diffe rentiation_method ( se lf , differentiation_method ): self.differentiation nethod differentiation method(self. f) 171 Scratches and Consoles def set_integration_method ( self, integration_method) : 174 self intearal self.integration method( selt a, self. b, self,resolution) 177 der self.differentiation_method (x) 18P def I plotiself .x. self. fx) plt.show) 183 def plot derivative(self ): plt.plot(self.x, [self.df(xx) for xx in self.x] ) plt. show) 186 def extrame_points ( self ): r niniea: 100 end 1 print(.4fx, ende') 192 eint("All maxima: ", end ) for x in self. maxima: 105 ("%.4f"x, ende pri print ("Global minimum: *.4f\nG lobal maximum:%. 4f"'%(self. global_min, self.global_max) ) 198 201 if.name = nain c CalculusCalculator ( lambda x: x, 0, 6, 500) 284 205 plot derivative() ,extrame points () 28R h iifferentiation eathnd i fent ralA) construct method() GaussLegendre 2 CalculusCalculator Run: Python Console 4: Bun E 6: TODO Terminal 2 Event Log 12:1 n/a UTF-8 4 spaces î Packages installed successfully: Installed packages: 'matplotlib (5 minutes ago)

alculusCalculator [~/PycharmProjects/alculusCalculator] -CalculusCalculator.py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator CalculusCalculator.py Project self. integral = self.integration method(self. f) | alculusCalculator /Pycharm Projects/alcu lusCalc veny def df(self, x): return self.different iation_method (x) CalculusCalcu lator.py 170 |External Libraries def plot(self): plt.plot ( self.x, self. fx) plt.show) Scratches and Consoles 182 def plot_derivative (self ): 185 PI eself.x, [self.df (xx) for xx in self.x] ) def extra minina: end for x in self.minima: 191 Rrint 4fx, ende print ("All mngxing: ", end' for 194. print) print ("Global minimum: %., 4f\nGlobal max imum : %. 4f'(self. qlobal min, self.global max)) 197 28P 283 i1 rCalculusCalculator( lambda x: x, 0, 6, 580) C.plot () 286 print ( c. df (2 .51) ) 280 Drinttc.dfO ion_method (Central4) . set_integration_method ( Simpson) print(c.integral) 212 214 construct method () GaussLegendre2 CalculusCalculatorx Run: E 6: TODO Python Console Packages installed successfully: Installed packages: 'matolotlib' (5 minutes ago) 4: Run 2 Event Log Terminal 4 spaces: 12:1 n/a UTF-8 5

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Answer 1

Please let me know if you have any doubts or you want me to modify the answer. And if you find this answer useful then don't forget to rate my answer as thumps up. Thank you! :)

import numpy as np
import matplotlib.pyplot as plt

class Diff:
    def __init__(self, f, h=1E-5):
        self.f = f
        self.h = float(h)

class Diff2(Diff):
    def __init__(self, f, h=1E-5, dfdx_exact=None):
        Diff.__init__(self, f, h)
        self.exact = dfdx_exact

    def error(self, x):
        if self.exact is not None:
            df_numerical = self(x)
            df_exact = self.exact(x)
        return df_exact - df_numerical

class Backward1(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (f(x) - f(x-h))/h

class Forward1(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (f(x+h) - f(x))/h

class Forward3(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (-(1./6)*f(x+2*h) + f(x+h) - 0.5*f(x) - (1./3)*f(x-h))/h

class Central2(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (f(x+h) - f(x-h))/(2*h)

class Central4(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (4./3)*(f(x+h) - f(x-h)) /(2*h) - (1./3)*(f(x+2*h) - f(x-2*h))/(4*h)

class Central6(Diff2):
    def __call__(self, x):
        f, h = self.f, self.h
        return (3./2) *(f(x+h) - f(x-h)) /(2*h) - (3./5) *(f(x+2*h) - f(x-2*h))/(4*h) + (1./10)*(f(x+3*h) - f(x-3*h))/(6*h)

class Integrator:
    def __init__(self, a, b, n):
        self.a, self.b, self.n = a, b, n
        self.points, self.weights = self.construct_method()

    def construct_method(self):
        raise NotImplementedError('no rule in class %s'%self.__class__.__name__)

    def integrate(self, f):
        s=0
        for i in range(len(self.weights)):
            s += self.weights[i]*f(self.points[i])
        return s

    def __call__(self, f):
        return self.integrate(f)

class Midpoint(Integrator):
    def construct_method(self):
        a, b, n = self.a, self.b, self.n
        h = (b-a)/float(n)
        x = np.linspace(a + 0.5*h, b - 0.5*h, n)
        w = np.zeros(len(x)) + h
        return x, w

class Trapezoidal(Integrator):
    def construct_method(self):
        x = np.linspace(self.a, self.b, self.n)
        h = (self.b - self.a)/float(self.n - 1)
        w = np.zeros(len(x)) + h
        w[0] /= 2
        w[-1] /= 2
        return x, w

class Simpson(Integrator):
    def construct_method(self):
        if self.n % 2 != 1:
            print('n=%d must be odd, 1 is added'% self.n)
        self.n += 1
        x = np.linspace(self.a, self.b, self.n)
        h = (self.b - self.a)/float(self.n - 1)*2
        w = np.zeros(len(x))
        w[0:self.n:2] = h*1.0/3
        w[1:self.n-1:2] = h*2.0/3
        w[0] /= 2
        w[-1] /= 2
        return x, w

class GaussLegendre2(Integrator):
    def construct_method(self):
        if self.n % 2 != 0:
            print('n=%d must be even, 1 is subtracted' % self.n)
            self.n -= 1
        nintervals = int(self.n/2.0)
        h = (self.b - self.a)/float(nintervals)
        x = np.zeros(self.n)
        sqrt3 = 1.0 / np.math.sqrt(3)
        for i in range(nintervals):
            x[2*i] = self.a + (i+0.5)*h - 0.5*sqrt3*h
            x[2*i+1] = self.a + (i+0.5)*h + 0.5*sqrt3*h
        w = np.zeros(len(x)) + h/2.0
        return x, w

class CalculusCalculator():
    def __init__(self, f, a, b, resolution= 500, differentiation_method= Backward1, integration_method= Midpoint):
        self.f, self.a, self.b = f, a, b
        self.resolution = resolution
        self.differentiation_method = differentiation_method(f)
        self.integration_method = integration_method(a, b, resolution)
        self._integral = self.integration_method(f)
        fx = [f(a)]
        lx = [a]
        minima = []
        minima_value = []
        maxima = []
        maxima_value = []
        h = (b - a) / (resolution-1)
        x = a
        for i in range(resolution-1):
            x += h
            lx.append(x)
            fx.append(f(x))
            if f(x) >= f(x-h) and f(x) >= f(x+h):
                maxima_value.append(f(x))
                maxima.append(x)
            if f(x) <= f(x-h) and f(x) <= f(x+h):
                minima_value.append(f(x))
                minima.append(x)
        lx.append(b)
        fx.append(f(b))
        self.x = lx
        self.fx = fx
        self.maxima = maxima
        self.minima = minima
        self.global_max_value = max(maxima_value + [f(a), f(b)])
        self.global_min_value = min(minima_value + [f(a), f(b)])
        self.global_max = 0
        self.global_min = 0
        for i in self.x:
            if f(i) == self.global_max_value:
                self.global_max = i
            if f(i) == self.global_min_value:
                self.global_min = i

    @property
    def integral(self):
        return self._integral

    def set_differentiation_method(self, differentiation_method):
        self.differentiation_method = differentiation_method(self.f)

    def set_integration_method(self, integration_method):
        self.integration_method = integration_method(self.a, self.b, self.resolution)
        self._integral = self.integration_method(self.f)

    def df(self, x):
        return self.differentiation_method(x)

    def plot(self):
        plt.plot(self.x, self.fx)
        plt.show()

    def plot_derivative(self):
        plt.plot(self.x, [self.df(xx) for xx in self.x])
        plt.show()

    def extrame_points(self):
        print("All minima: ", end= '')
        for x in self.minima:
            print("%.4f"%x, end= ' ')
        print()
        print("All maxima: ", end= '')
        for x in self.maxima:
            print("%.4f"%x, end= ' ')
        print()
        print("Global minimum: %.4f\nGlobal maximum:%.4f"%(self.global_min, self.global_max))

if __name__ == '__main__':
    c = CalculusCalculator(lambda x: x, 0, 6, 500)
    c.plot()
    c.plot_derivative()
    c.extrame_points()
    print(c.df(2.51))
    c.set_differentiation_method(Central4)
    print(c.df(2.51))
    c.set_integration_method(Simpson)
    print(c.integral)

alculusCalculator [/Pycharm Projects/alculusCalculator] -/CalculusCalculator.py [alculusCalculatorl alculusCalculator CalculusCalculator. py CalculusCalculator ¢ - CalculusCalculator. py Project import numpy as np import matplot lib. pyplot as plt | alculusCalculator PycharmProjects/alculusCalc venv CalculusCalcu lator. py External Libraries class Diff: (self, f, h-1E-5 ): der Scratches and Consoles self.ff self.h-float (h) Figure 1 6. 17 5 23 4. 26 29 2 CalculusCalculator Run /Users/swapnil/PycharmP rojects/alculusCalculat 1 pan/zoom, x3.30605 y-3.25714 Python Console 4: Run E 6: TODO Terminal 2 Event Log Packages installed successfully: Installed packages: 'matplotlib (4 minutes agol 4 spaces 118:28 n/a UTF-8 #

alculusCalculator [~/PycharmProjects/alculusCalculator] - ..CalculusCalculator. py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator CalculusCalculator.py Project import numpy |import matplLot lib.pyplot as plt I alculusCalculator PycharmProjects/alculusCalc np venv CalculusCalculator.py External Libraries class Diff: h-16-5): def self.f= f (self, Scratches and Consoles self.h= float ( h ) 1P class Diff2(Diff): 11 e def Diff. self.exact = dfdx exact dfdx_exact-None): intt (self. t. h) 13 14 def error(self, x): if self.exact is not None: 17 df exact = self . exact (x] return df exact 10 df numerical 20 class Backward1(Diff2): de 23 f, hself. e return (f(x) - f(x-h)) /h 25 .h 26 class Forward1(Diff2): 29 Gausslegendre2 construct method(! CalculusCalculator Run: Users/swapnil/PycharmP rojects/alculusCalculator/venv/bin/python /Users/swapnil/PycharmProjects/alcu lusCalculator/CalculusCalculator. py 011 maxima Global minimum: .0000 ep99 m.0000 eeaaaaaaaags5512 500 must be odd, 18.00000000000001 is added Process finis hed with exit code 0 Python Console 4: Run Terminal E 6: TODO 2 Event Log 118:28 n/a UTF-8 4 spaces Packages installed successfully: Installed packages: 'matplotl ib (4 minutes ago)

alculusCalculator [~/PycharmProjects/alculusCalculator] -...CalculusCalculator.py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalcudator CalculusCalculator.py x Project Pycharm Projects/alcu lu sCalc | alculusCalculator import numpv np import matplot lib. pyplot as plt veny CalculusCalcu lator. py class Diff: def External Libraries 5 (self, h-1E-5) Scratches and Consoles self.f self.h float (h) 11 Eclass Diff2(Diff): dfdx_exact None): def Diff self.exact= dfdx exact self. f. h) 12 14 def error(self, x): if self.exact is not None: 17 df exact self.exact (x l return df_exact 10 df_nunerical class Backward1 (Diff2): def f, h=self. return (f(x) - f(x-h) )/h .h 26 class Forward1( Diff2): 20 def fh=self return (f(x+h) .h f(x))/h class Forward3(Diff2): def 75 f, h=self.f, self return (-(1./6)af (x+2h) + f(x+h ) .h 0.5*f (x) - (1./3) sf (x-h) )/h 39 class Central2 (Diff2) : call (self, x): ля def 42 return (f(xth) f(x-h))/(2*h) GaussLegendre2 construct method) CalculusCalculator Run: Python Console Е 8: торо 4: Run Terminal 2 Event Log 12:1 n/a UTF-8: 4 spaces : Packages installed successfully: Installed packages: 'matplotlib" (5 minutes ago) *ravrites

alculusCalculator [~/PycharmProjects/alculusCalculator] - ./CalculusCalculator.py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator CalculusCalculator.py Project | alculusCalculatorPychamProjects/alcu lusCalc class Central2 ( Diff2) : def call (self, x): f,h=e return (f 47 venv CalculusCalcu lator.py flxsb))/{2#h) 45 External Libraries 45 Scratches and Consoles class Central4 (Diff2) : def all (self, x) : 48 f,haset lflxh) - f(x-h)) /[2#h) - (1./3)e(f(x+2*h) - f(x-2*h) ) / (4eh) return (4./3): 51 class Central6 ( Diff2): ll (self, x) : def f,h=setf Elh) f(x-h) ) /[2*h) - (3./5) (f(x+2*h) - f(x-2«h) ) / (4*h) + (1./10) =(f(x+3+h) . f(x-3*h) ) / (6%h ) return (3./2) *(f(x+ E7 ol class Integrator: (self, , b, n): def 68 self.a, self.b, selr.n = a, b, n self.point .construct method () 63 def construct met hod (self): raise NotImp lemented 64 ( 'no rule in class 4s'self, class , name) 66 def integrate(self, f): for i in range(len (self, weights) ) : Stself.weights [i] *f (self. points [i] ) 69 re turn 72 det retue etr, T): rate (f) TE slass Midpoint(ntegcaeE lf) a. b. n=self.a, self.b, self.n h = (b-a)/float (n) 78 70 DD-7eros (len(x)). b-0.5 h, n) 82 return x. W 83 construct method() GaussLegendre2 Run CalculusCalculator Python Console 4: Run E 6: TODO 2 Event Log Terminal 4 spaces Packages installed successfully: Installed packages: 'matplotlib' (5 minutes ago) 12:1 n/a UTF-8 =

alculusCalculator [~/PycharmProjects/alculusCalculator] - ..CalculusCalculator. py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator , CalculusCalculator.py Project I alculusCalculator /PycharmProjects/alculusCalc 7 class Ostruct metbodicelf); venv 86 e CalculusCalculator.py =np. linspace(self. a, self. b, self.n) loat ( self, n - 1) R7 x External Libraries = n. zeros (len(x))+ h Scratches and Consoles wl0] /-2 coture w class Simpson (Integrator): def construct_method ( self) : 96 if Drint'ned must be odd, 1 is added'& self.n) self.n + 1 99 w=np.zeros ( len (x) ) 102 wTself.n-1:21 . he2.0/3 w[0] /= 2 105 return x 100 class GaussLegendre2(Integrator) : def construct_method ( self ) : 111 e if print'n-d must be even, 1 is subtracted self.n) 114 1 self.n tel.va. alffloat inintervals) = np.zeros (self.n) 117 x 31 for i in rangetnintervals) x[2*i]= self. a + (i+0.5) *h - .5) *h WE00. zeros(len/x)) h/2.8 118 5*sqrt3*h 0.5+sqrt3*h 128 121 return x, w 124 class CalculusCalculato r() : def init (self, f, a, b, resolution= 500, different iation_method Backward1, integration_method=_Mid po int): 121 GaussLegendre2 construct method () CalculusCalculator Run: 4: Pun E 6: TODO Python Console Packages installed successfully: lInstalled packages: 'matplotib) 2 Event Log Terminal (5 minutes agol 12:1 n/a UTE-8 4 spaces :

alculusCalculator [/PycharmProjects/alculusCalculator] -./CalculusCalculator.py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator CalculusCalculator.py Project alculusCalculatorPycharmProjects/alcu lu sCalc cLass Calcus lf f, a, b, resolution=_500, differentiation_method=_Backward1, integration_met hod_Midpo int) : venv CalculusCalculator. py self.f, self.a, self.b f, a, b 128 External Libraries self.differentiation nethod differentiation method(f) self.integration_method= integration method(a, b. resolution) Scratches and Consoles 131 f Teiaatself.integration_method(f) Lx [a] 134 minina value = [0 maxima= [ 137 a)/ (resolution-1) x = a for 148 range(resolution-1) : Lx.append(x) 143 if fix) 2= f (x-h) and f(x) > f(x+h): maxima_value.append (f (x) ) 146 if f(x) = f(x-h) and f(x) = f (x+h ) : minima_value. append ( f (x) ) a. append (x) 149 x.append (b) fx.append(f(b) 152 self.fx = fx пахіпа 155 self.maxima self.global max value = max(maxima value+[f(a), f(b)]) self.globalmin_value = min (minima_va lue + [f(a), f(b)]) 158 self.global min = 0 for i in self.x: 161 лах_value: 1f f(1) .global max if f(i)-self.global min_value : self.global min - i 164 165 167 @property def integral( self) : 168 Gausslegendre2 construct method () CalculusCalculator iRun: Python Console Е 8: торо 4: Run Terminal 2 Event Log 4 spaces: 12:1 n/a UTF-8 : Packages installed successfully: Installed packages: 'matplotlib' (5 minutes ago)

alculusCalculator [/PycharmProjects/alculusCalculator] -./CalculusCalculator. py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator Calculus Calcul ator.py Project I alculusCalculator PycharmProjects/alculusCalc167 @property def integral(self) : return self._integral 168 venv CalculusCalculator.py External Libraries def set diffe rentiation_method ( se lf , differentiation_method ): self.differentiation nethod differentiation method(self. f) 171 Scratches and Consoles def set_integration_method ( self, integration_method) : 174 self intearal self.integration method( selt a, self. b, self,resolution) 177 der self.differentiation_method (x) 18P def I plotiself .x. self. fx) plt.show) 183 def plot derivative(self ): plt.plot(self.x, [self.df(xx) for xx in self.x] ) plt. show) 186 def extrame_points ( self ): r niniea: 100 end 1 print(.4fx, ende') 192 eint("All maxima: ", end ) for x in self. maxima: 105 ("%.4f"x, ende pri print ("Global minimum: *.4f\nG lobal maximum:%. 4f"'%(self. global_min, self.global_max) ) 198 201 if.name = nain c CalculusCalculator ( lambda x: x, 0, 6, 500) 284 205 plot derivative() ,extrame points () 28R h iifferentiation eathnd i fent ralA) construct method() GaussLegendre 2 CalculusCalculator Run: Python Console 4: Bun E 6: TODO Terminal 2 Event Log 12:1 n/a UTF-8 4 spaces î Packages installed successfully: Installed packages: 'matplotlib (5 minutes ago)

alculusCalculator [~/PycharmProjects/alculusCalculator] -CalculusCalculator.py [alculusCalculator] alculusCalculator CalculusCalculator. py CalculusCalculator CalculusCalculator.py Project self. integral = self.integration method(self. f) | alculusCalculator /Pycharm Projects/alcu lusCalc veny def df(self, x): return self.different iation_method (x) CalculusCalcu lator.py 170 |External Libraries def plot(self): plt.plot ( self.x, self. fx) plt.show) Scratches and Consoles 182 def plot_derivative (self ): 185 PI eself.x, [self.df (xx) for xx in self.x] ) def extra minina: end for x in self.minima: 191 Rrint 4fx, ende print ("All mngxing: ", end' for 194. print) print ("Global minimum: %., 4f\nGlobal max imum : %. 4f'(self. qlobal min, self.global max)) 197 28P 283 i1 rCalculusCalculator( lambda x: x, 0, 6, 580) C.plot () 286 print ( c. df (2 .51) ) 280 Drinttc.dfO ion_method (Central4) . set_integration_method ( Simpson) print(c.integral) 212 214 construct method () GaussLegendre2 CalculusCalculatorx Run: E 6: TODO Python Console Packages installed successfully: Installed packages: 'matolotlib' (5 minutes ago) 4: Run 2 Event Log Terminal 4 spaces: 12:1 n/a UTF-8 5