how to find upper bound of the absolute value of the line integral of z^2
Question : Find upper bound of the absolute value of the line integral of z^2 along a straight line segment C from 0 to 1 + i. Solution : To…
solved Evaluate the line integral of 1/z
Question : Evaluate the line integral of 1/z along unit circle in counter clockwise direction starting from z = 1 Solution: Since a complex line integral is evaluated as \[\int_{C}{f(z)}dz=\int_{t=a}^{b}f\left(z\left(t\right)\right)\frac{dz(t)}{dt}dt\]…
Solved by Cramer s rule solve the following equations
homework on Cramer s rule Solution: First we shall write system of linear equations in matrix form 3x+4y+z=0 4x-y+z=8 3x+5y+4z=0 in matrix form, \[A=\left[\begin{matrix}3&4&1\\4&-1&1\\3&5&4\\\end{matrix}\right],\ B=\left[\begin{matrix}0\\8\\7\\\end{matrix}\right],\ X=?\] First we shall find…
how to prove that Z-transform of delta sequence is 1
prove that Z-transform of delta sequence is 1 Solution : The definition of delta sequence is defined as \[\delta_n=1 if n=0 0 if n=±1,±2,±3,…\] We know that Z-transform of a…
how to write a python program to integrate ax^2+bx+c from 0 to 1
Question : Write a python program to integrate ax^2+bx+c from 0 to 1 Solution : import scipy from scipy.integrate import quad def f(x): return a*x**2+b*x+c a=1 b=2 c=1 Answer =…
example of Green’s theorem to calculate the line integral
how to use Green's theorem to solve the Assignment Question Solution : First we shall let that D denote the region \[{\left(x,\ y\right):\ 0\ \le\ x\ \le\ 1,\ x^2\ \le\…
solved question Find a power series solution of the differential equation xy′-y=1
Find a power series solution of the differential equation xy′-y=1 Solution :
how to Find all the singular points of differential equations
How to find all the singular points of differential equations Solution :
how to find positive real root of the equation 𝑥𝑒^𝑥 − cos 𝑥 = 0 using Regula Falsi method
Question : Perform three iterations to find positive real root of the equation 𝑥𝑒^𝑥 − cos 𝑥 = 0 using Regula Falsi method Solution : Question : Perform three iterations…
how to use method of false position to find root of x^3 − 5x + 2 = 0
Question : Use method of false position to find root of x^3 − 5x + 2 = 0 lying in the interval (0,1) correct to three decimal places. Solution :…