OVERVIEW

Chapter 2 covered numerical methods that are quite useful in solving chemical engineering problems, which translate into C programs. MATLAB, however, is a mathematical programming language, so it already has numerous existing functions that can perform numerical computation. Some of these functions were developed based on the algorithm we learned when we developed functions in C.

In this chapter, we will further explore MATLAB existing functions including:

The Matrix Method for Linear Equations

• The inv() Function

• Matrix Left Division (\)

Regression and Curve Fitting

• The polyfit() Function

• The polyval() Function

• Coefficient of Determination and Standard Error of Estimate

Finding Roots

• The roots() Function

• The fzero() Function

Interpolation

• One-dimensional Interpolation

• Two-dimensional Interpolation

Numerical Integration

• Trapezoidal Integration

• Quadrature

Ordinary Differential Equations (ODE)

The ode2 3 () and ode4 5 () Functions

All program listings discussed in this chapter can be found on the CD-ROM.

\Program Listings\Chapter 7\PL7 l.m    Program Listing 7.1\Program Listings\Chapter 7\PL7 2.m    Program Listing 7.2\Program Listings\Chapter 7\coefdet.m  Program Listing 7.3\Program Listings\Chapter 7\stderr.m   Program Listing 7.4\Program Listings\Chapter 7\PL7 5.m    Program Listing 7.5\Program Listings\Chapter 7\PL7 6.m    Program Listing 7.6\Program Listings\Chapter 7\odeapp.m   Program Listing 7.7\Program Listings\Chapter 7\PL7 8.m    Program Listing 7.8

THE MATRIX METHOD FOR LINEAR EQUATIONS

Let us consider a set of linear equations

where:

x ₁, x ₂ . x _n are unknown varibles

a ₁₁, a ₁₂