README.md

Algebraic and Trancedental Equations

Module 1

If we have a function f(x), we will have to manually find a form x = phi(x). This phi(x) is the function that is to be entered in the code.
It is assumed that the function phi(x) passes the convergence condition in the provided interval.
The code will display the first order differential of phi(x) which can be used to check the convergence condition.
We will have to determine the interval where convergence takes place, and then enter the x_ini value into the code.
We should also enter the accuracy_decimal, which is the decimal place accuracy to which answer should be obtained, the number of iterations taken by the code depends on this value.
To prevent the non-convergence condition, the code will proceed till a maximum of 20 iterations is reached.
The code prints the estimated value at the end of every iteration.

If we have an equation of the form f(x) = 0, we will have to enter the f(x) into the code.
We will have to ensure that the function f(x) passes the convergence condition in the provided interval.
We will have to determine the interval where convergence takes place, and then enter the interval into the code.
We should also enter the accuracy_decimal, which is the decimal place accuracy to which answer should be obtained, the number of iterations taken by the code depends on this value.
To prevent the non-convergence condition, the code will proceed till a maximum of 20 iterations is reached.
The code prints the estimated value and the corresponding f(x) value at the end of every iteration.

If we have an equation of the form f(x) = 0, we will have to enter the f(x) into the code.
We will have to ensure that the function f(x) passes the convergence condition in the provided interval.
The code will display the first and the second order differentials of f(x) which can be used to check the convergence condition, and for the calculations.
We will have to determine the interval where convergence takes place, and then enter the interval into the code.
We should also enter the accuracy_decimal, which is the decimal place accuracy to which answer should be obtained, the number of iterations taken by the code depends on this value.
To prevent the non-convergence condition, the code will proceed till a maximum of 20 iterations is reached.
In order to accomodate the Newton Raphson Method for multiple roots, we have incorporated a genralized version into the code. We have provided a m value which we should enter into the code, and it determines the number of occurance of root to be found. For example to find a double root we say m=2, for triple root m=3, and so on.
The code prints the estimated value and the corresponding f(x) value at the end of every iteration.

Given a system of multiple non-linear equations, we solve them.
We enter the system of functions, and the initial values of these variables x, y, etc.
We then find the Jacobian Matrix and use it for the iteration in finding a better estimate for the values of the variables.
In each iteration, the code will display the substituted Jacobian matrix, its inverse and the values of the variables.
The code will display the solution to the system of equations.