Unknown - MATHEMATICS with MATLAB. GRAPHICS and LINEAR ALGEBRA

introduction MATLAB can be used as a high level programming language including data structures, variables, functions, vectors, matrix, arrays, instructions for flow control, management of inputs/outputs and even object-oriented programming. MATLAB programs are often written into files called M-files. AnM-file is nothing more than a MATLAB code (script) that executes a series of commands or functions that accept arguments and produce an output. MATLAB is able to implement a number of algorithms which provide numerical solutions to certain problems which play a central role in the solution of non-linear equations. Such algorithms are easy to construct in MATLAB and are stored as M-files. Also MATLAB allows you to easily manipulate and operate on formulae and expressions symbolically.

It is possible to expand, factor and simplify polynomials and rational and trigonometric expressions; find algebraic solutions of polynomial equations and systems of equations; evaluate derivatives and integrals symbolically; find symbolic solutions of differential equations; manipulate powers, limits and many other facets of algebraic series. MATLAB is a platform for scientific computing that can work in almost all areas of the experimental sciences and engineering. Logically, this software allows you to work in the field of graphics and linera algebra, featuring some pretty extensive capabilities. The commands that implements Matlab, about working with graphics and matrix algebra are quite high and very efficient. Matlab functions for working with two-dimensional and three-dimensional graphics, statistical graphs, curves and surfaces in explicit, implicit, parametric and polar coordinates. Additional work perfectly implements the twisted curves, surfaces , meshes , contours , contours, volumes and graphical interpolation.

MATLAB allows you to work with ease in the field of Linear Algebra. Its matrix structure facilitates the treatment of matrix algebra, vector and matrix variables and functions, vector spaces, equations and systems, algebraic expressions, polynomials, linear applications, quadratic forms, diagonalization and other typical tasks of linear algebra.

INTRODUCTION TO MATLAB The MATLAB language, based on matrices, is the most natural way to express computational mathematics. The integrated graphics facilitate the visualization of the data and the obtaining of information from them. The desktop environment invites you to experience, explore and discover. All of these MATLAB tools and functions are rigorously tested and designed to work together.

Mathematical functions offer a wide variety of calculation methods to analyze data, develop algorithms and create models. The main functions use libraries optimized for processors that allow quick calculations of vectors and matrices. You can use MATLAB as a powerful numerical computer. While most calculators handle numbers only to a preset degree of precision, MATLAB performs exact calculations to any desired degree of precision. In addition, unlike calculators, we can perform operations not only with individual numbers, but also with objects such as arrays. Most of the topics of classical numerical analysis are treated by this software.

It supports matrix calculus, statistics, interpolation, least squares fitting, numerical integration, minimization of functions, linear programming, numerical and algebraic solutions of differential equations and a long list of further methods that well meet as this book progresses. To start MATLAB, simply double-click on the shortcut icon to the program on the Windows desktop. Alternatively, if there is no desktop shortcut, the easiest and most common way to run the program is to choose programs from the Windows Start menu and select MATLAB . Having launched MATLAB by either of these methods, the welcome screenbriefly appears, followed by the screen depicted in Figure 1-1, which provides the general environment in whichthe program works. The most important elements of the MATLAB screen are the following: The Command Window: This runs MATLAB functions . The Current Folder: This shows MATLAB files and execute files (such as opening and search for content operations).

The Workspace: This shows the present contents of the workspace and allows you to make changes to it. The Men Options: This shows the most important work options with the program (Figure 1-2). Options palettes (HOME, PLOTS and APPS): This allows you to access to the main MATLAB options, graphic options and predefined applications. Figure 1-1 Figure 1-2 The Command Window(Figure 1-3) is the main way to communicate with MATLAB. It appears on the desktop when MATLAB starts and is used to execute all operations and functions. The entries are written below the prompt >> and, once completed, they run afterpressing Enter .

The first line of Figure 1-3 defines a matrix and, after pressing Enter, the results itself is displayed as output. Figure 1-3 In the Command Window is possible to work with operations, functions, graphics and MATLAB code in general. Simply enter an expression with valid MATLAB syntax and pressing Enter is executed. Also it is possible to evaluate previously executed operations. To do this, simply select the syntax you wish to evaluate, right-click, and choose the option Evaluate Selection from the resulting pop-up menu (Figures 1-4 and 1-5). Figure 1-4 Figure 1-5 Figure 1-6 Figure 1-7 MATLAB is sensitive to the use of uppercase and lowercase characters, and blank spaces can be used before and after minus signs, colons and parentheses. Figure 1-4 Figure 1-5 Figure 1-6 Figure 1-7 MATLAB is sensitive to the use of uppercase and lowercase characters, and blank spaces can be used before and after minus signs, colons and parentheses.

MATLAB also allows you to write several commands on the same line, provided they are separated by semicolons (Figure 1-8). Entries are executed sequentially in the order they appear on the line. Every command which ends with a semicolon will run, but will not display its output. Long entries that will not fit on one line can be continued onto a second line by placing dots at the end of the first line (Figure 1-9).