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Topic 
MATLAB Examples 
Simultaneous linear equations

screen shot – for Workbook 7.4 
Root of nonlinear equation  Mfile link. As example, solve van der Waal’s equation for molar volume using Newton’s method, fzero(), fminbnd(), interval halving or bisection, successive approximation, the SYMBOLIC toolbox and, since this happens to be a polynomial, roots(). 
Fit polynomial function to 
Fit a polynomial to data using polyfit, polyval and linear algebra

Fitting nonlinear equation to data using “nonlinear regression” (“least squares fit”)
(yes, this example can be inverted and linearized but the methods work on nonlinear equations) 
Problem solution with function lsqcurvefit. You must have the Optimization Toolbox installed in order to use lsqcurvefit. Problem solution with function fminsearch 
Differentiation and integration (quadrature) of data  Integration of data (quadrature) Differentiation of data – RTD tracer experiment FreeMat users: search for Freemat note in file Differentiation of data from Batch Reactor 
Integrate one Ordinary 
Integrating one ODE using Euler’s method Using Matlab’s ode45 function > main file > derivative function file 
Integrate two coupled ODE’s See notes in cell above 
Integrating two ODEs using Euler’s method Using Matlab’s ode45 function > main file > derivative function file 
Integrate Partial Differential Equations (PDE) using the finitedifference method 
Transient 1D diffusion – code, plots and notes Transient 1D diffusion – code only
