## Solve Equations in MATLAB

The following tutorials are an introduction to solving linear and nonlinear equations with MATLAB. The solution to linear equations is through matrix operations while sets of nonlinear equations require a solver to numerically find a solution.

#### Solve Linear Equations with MATLAB

Source Code

clear all
A = [3 -9; 2 4];
b = [-42; 2];
% three methods
x = inv(A)*b       % good
x = A\b            % better
x = linsolve(A,b)  % best

#### Solve Nonlinear Equations with MATLAB

Source Code

% Create new file myFunction.m
function F=myFunction(z)
x = z(1);
y = z(2);

F(1)=x^2+y^2-20;
F(2)=y - x^2;
end
% Create new file mySolver.m
clear all
zGuess = [1; 1];
z = fsolve(@myFunction, zGuess);
disp(z)

#### Additional Tutorials

Linear and nonlinear equations can also be solved with Excel and Python. Click on the appropriate link for additional information and source code.

The APMonitor Modeling Language with a MATLAB interface is optimization software for mixed-integer and differential algebraic equations. It is coupled with large-scale solvers for linear, quadratic, nonlinear, and mixed integer programming (LP, QP, NLP, MILP, MINLP). Modes of operation include data reconciliation, real-time optimization, dynamic simulation, and nonlinear predictive control. It is freely available through MATLAB, Python, Julia, or from a web browser interface.