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MATLAB Programming for Numerical Analysis

Shelve in Applications/Mathematical & Statistical Software MATLAB Programming for Numerical Analysis M ALAB Pgram m ng or um eical Anlysis MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. Programming MATLAB for Numerical Analysis introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. You will first become familiar with the MATLAB environment, and then you will begin to harness the power of MATLAB. You will learn the MATLAB language, starting with an introduction to variables, and how to manipulate numbers, vectors, matrices, arrays and character strings. You will learn about MATLAB’s high-precision capabilities, and how you can use MATLAB to solve problems, making use of arithmetic, relational and logical operators in combination with the common functions and operations of real and complex analysis and linear algebra. You will learn to implement various numerical methods for optimization, interpolation and solving non-linear equations. You will discover how MATLAB can solve problems in differential and integral calculus, both numerically and symbolically, including techniques for solving ordinary and partial differential equations, and how to graph the solutions in brilliant high resolution. You will then expand your knowledge of the MATLAB language by learning how to use commands which enable you to investigate the convergence of sequences and series, and explore continuity and other analytical features of functions in one and several variables.

Robust Predictive Control

The Model Predictive Control Toolbox is a complete set of tools which can be used to implement model predictive control strategies. Model predictive control strategies are often used in chemical engineering and in other industries.

MATLAB Differential and Integral Calculus

Shelve in Applications/Mathematical & Statistical Software MATLAB Differential and Integral Calculus M ALAB Difrential nd Ingral Caculus MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Differential and Integral Calculus introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving a short introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work with ease in differential and integral calculus in one and several variables. Among other core topics of calculus, you will use MATLAB to investigate convergence, find limits of sequences and series and, for the purpose of exploring continuity, limits of functions. Various kinds of local approximations of functions are introduced, including Taylor and Laurent series. Symbolic and numerical techniques of differentiation and integration are covered with numerous examples, including applications to finding maxima and minima, areas, arc lengths, surface areas and volumes. You will also see how MATLAB can be used to solve problems in vector calculus and how to solve differential and difference equations.

MATLAB Differential Equations

M ALAB Difrential Eqations MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Differential Equations introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to the MATLAB environment and MATLAB programming, this book provides all the material needed to work on differential equations using MATLAB. It includes techniques for solving ordinary and partial differential equations of various kinds, and systems of such equations, either symbolically or using numerical methods (Euler’s method, Heun’s method, the Taylor series method, the Runge–Kutta method,...). It also describes how to implement mathematical tools such as the Laplace transform, orthogonal polynomials, and special functions (Airy and Bessel functions), and find solutions of finite difference equations.

Vectors and Matrices

We have already seen how vectors and matrices are represented in MATLAB in the chapter dedicated to variables, however we shall recall the notation.

The MATLAB Environment

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 screen briefly appears, followed by the screen depicted in Figure 1-1, which provides the general environment in which the program works.

Introducing MATLAB and the MATLAB Working Environment

MATLAB is a platform for scientific calculation and high-level programming which uses an interactive environment that allows you to conduct complex calculation tasks more efficiently than with traditional languages, such as C, C++ and FORTRAN. It is the one of the most popular platforms currently used in the sciences and engineering.

Variables, Numbers, Operators and Functions

MATLAB does not require a command to declare variables. A variable is created simply by directly allocating a value to it. For example:

MATLAB Matrix Algebra

M ALAB M atrix Aebra MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Matrix Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. Starting with a look at symbolic and numeric variables, with an emphasis on vector and matrix variables, you will go on to examine functions and operations that support vectors and matrices as arguments, including those based on analytic parent functions. Computational methods for finding eigenvalues and eigenvectors of matrices are detailed, leading to various matrix decompositions. Applications such as change of bases, the classification of quadratic forms and how to solve systems of linear equations are described, with numerous examples. A section is dedicated to sparse matrices and other types of special matrices. In addition to its treatment of matrices, you will also learn how MATLAB can be used to work with arrays, lists, tables, sequences and sets.

Real and Complex Numbers

A rational number is a number of the form p/q, where p and q are integers. That is, the rational numbers are those numbers that can be represented as the quotient of two integers. The way in which MATLAB treats rational numbers is different from the majority of calculators.