Python Program to print any table of any number entered by user

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#Program to print any table of any number entered by user
#Name and Roll Number
import math

n = int(input('Enter any number whose table you want to print: '))
print('Table of', n, 'is given by\n')

for i in range(1, 11):
    print(n, 'x', i, '=', n * i)

Python program to find solution of quadratic equation

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#program to find solution of quadratic equation
#Name and Roll 
#Quadratic equation is of the order ax^2+bx+c=0

import math

import cmath


print("Quadratic equation is of the order a*x^2+b*x+c=0 \n where a=coefficient of x^2\
 nb=coefficient of b and\nc=constant")
 #taking coefficient a,b and c from user
 
a=float(input("Enter coefficient of(x^2)"))
b=float(input("Enter coefficient of(x)"))
c=float(input("Enter value of constant"))
s=b**2-(4*a*c)

if(s>0):
     s1=((-1*b)+math.sqrt(s))/(2*a)
     s2=((-1*b)-math.sqrt(s))/(2*a)
     print("The roots are real and unequal and are given by \nxt=",s1,"and x2=",s2)   


if(s==0):
         s1=((-1*b)+math.sqrt(s))/(2*a)
         s2=((-1*b)-math.sqrt(s))/(2*a)
         print("The roots are real and equal and are given by \nxt=",s1,"and x2=",s2)   
if(s<0):
         s1=((-1*b)+cmath.sqrt(s))/(2*a)
         s2=((-1*b)-cmath.sqrt(s))/(2*a)
         print("The roots are imaginary and are given by \nxt=",s1,"and x2=",s2)  

Python Program to solve a linear differential equation using SciKit and polt the result in Matplotlib

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#Experiment No 4:Program to solve a linear differential equation using SciKit and polt the result in Matplotlib

#Name and Roll

import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import solve_ivp

print("The general form of the linear differential equation is:")
print("dy/dx+p(x)*y=q(x)\n")

#Get user input for the differential equation coefficients
p = float(input("Enter the coefficient for y (p): "))
q = float(input("Enter the constant term (q): "))
y0 = float(input("Enter the initial condition y(0): "))

#Define the differential equation
def linear_diff_eq(x,y):
    dydx=-p*y+q
    return dydx

#Interval of integration
x_span = (0,10)
#points where the soultion is computed
x_eval = np.linspace(0,10,100)

#Solve the differential equation
solution = solve_ivp(linear_diff_eq,x_span,[y0],t_eval=x_eval)

#Display the complete differential equation on the output screen
equation_str=f"dy/dx+{p}*y={q}"

print(f"The complete differential equation is:{equation_str}")

# Plot the result
plt.plot(solution.t,solution.y[0],label='y(x)')
plt.xlabel('x')
plt.ylabel('y')
plt.title(f'Solution of Linear Differential Equation\n{equation_str}')
plt.legend()
plt.grid(True)
plt.show()

Python Program to plot Hermite Spline on the output screen

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#Program to plot Hermite Spline on the output screen
#Name and Roll

import numpy as np

import matplotlib.pyplot as plt

#User input for start and end points
x0,y0=map(float,input("Enter start point (x0 y0):").split())
x1,y1=map(float,input("Enter end point (x1 y1):").split())
tx0,ty0=map(float,input("Enter start tangent vector (tx0 ty0):").split())
tx1,ty1=map(float,input("Enter end tangent vector (tx1 ty1):").split())

#Generate parameter values
num_points=100
t=np.linspace(0,1,num_points)

#Compute Hermite basis functions/Blending Functions 
h00=(2*t**3)-(3*t**2)+1
h10=(t**3)-(2*t**2) + t
h01=(-2*t**3)+(3*t**2)
h11=t**3 - t**2    

#Compute x and y coordinates
x_curve = h00*x0 + h10*tx0 + h01*x1 + h11*tx1
y_curve = h00*y0 + h10*ty0 + h01*y1 + h11*ty1

#Plot the curve
plt.figure(figsize=(8,6))  
plt.plot(x_curve,y_curve,label="Cubic Hermite Curve")
plt.scatter([x0,x1],[y0,y1],color='red',label="Endpoints")
plt.quiver([x0,x1],[y0,y1],[tx0,tx1],[ty0,ty1],color='green',angles='xy',scale_units='xy',scale=1,label="Tangent Vectors")
plt.legend()
plt.xlabel("X-axis")
plt.ylabel("Y-axis")
plt.title("Parametric Cubic Curve)")
plt.grid()
plt.show()