MATLAB-Programming

Solving some numerical problems with MATLAB programming language to improve ,expand and practice my skills at MATLAB.

1st# Bisection Method :

Writing a MATLAB function that uses Bisection Method to iteratively estimate the positive real root of the equation ln(𝑥) = 0.7 in the interval [xl, xu] until εa is less than εs.

2nd# Maclaurin series approximation :

Writing a MATLAB function that calculates the approximate value of arctan(x) using the Maclaurin series approximation:

arctan(𝑥) = 𝑥 −𝑥^3/3 +𝑥^5/5 −𝑥^7/7 + ⋯ 

3rd# linear& nonlinear regression :

I . Writing a MATLAB function that accepts n values of 𝑥 and 𝑦, perform Linear Regression and returns values of r2 and, the model parameters 𝑎 and 𝑎0.

II. Writing another MATLAB function that accepts n values of 𝑥 and 𝑦 (provided as arrays), checks for Linear, Power and Saturation growth rate models, and estimate the values of parameters 𝑎 and 𝑎0 (or 𝛼 and 𝛽, whichever is applicable).

4th# 1st Order differential Equation using Mid-point method :

Writing a MATLAB function that solves 1st ODE using Mid-point method to solve The accumulation of mass in a reactor.

𝑉(dc/dt)=Qcin-Qc0