Computational Technologies : a First Course

In this book we describe the basic elements of present computational technologies that use the algorithmic languages C/C++. The emphasis is on GNU compilers and libraries, FOSS for the solution of computational mathematics problems and visualization of the obtained data. At the beginning, a brief introduction to C is given with emphasis on its easy use in scientific and engineering computations. We describe the basic elements of the language, such as variables, data types, executable statements, functions, arrays, pointers, dynamic memory and file management. After that, we present some observations on the C++ programming language. We discuss the issues of program compiling, linking, and debugging. A quick guide to Eclipse is also presented in the book. The main features for editing, compiling, debugging and application assembling are considered. As examples, we solve the standard problems of computational mathematics: operations with vectors and matrices, linear algebra problems, solution of nonlinear equations, numerical differentiation and integration, interpolation, initial value problems for ODEs and so on. Finally, basic features of computational technologies are illustrated with model problems. All programs are implemented in C/C++ with using the GSL library. Gnuplot is employed to visualize the results of computations. * Provides a brief introduction to the basic tools for mathematical scientific computing * Numerical solutions of model problems are explained along examples from various fields of science and engineering

In this book we describe the basic elements of present computational technologies that use the algorithmic languages C/C . The emphasis is on GNU compilers and libraries, FOSS for the solution of computational mathematics problems and visualization of the obtained data.

At the beginning, a brief introduction to C is given with emphasis on its easy use in scientific and engineering computations. We describe the basic elements of the language, such as variables, data types, executable statements, functions, arrays, pointers, dynamic memory and file management. After that, we present some observations on the C programming language. We discuss the issues of program compiling, linking, and debugging. A quick guide to Eclipse is also presented in the book. The main features for editing, compiling, debugging and application assembling are considered. As examples, we solve the standard problems of computational mathematics: operations with vectors and matrices, linear algebra problems, solution of nonlinear equations, numerical differentiation and integration, interpolation, initial value problems for ODEs and so on. Finally, basic features of computational technologies are illustrated with model problems. All programs are implemented in C/C with using the GSL library. Gnuplot is employed to visualize the results of computations.

Contents 7 Preface 9 Introduction 11 1 An introduction to C 13 1.1 Syntax 13 1.2 Constants and variables 15 1.3 Expressions and operators 18 1.4 Statements 21 1.5 Arrays 25 1.6 Pointers 27 1.7 Functions 29 1.8 Structures 32 1.9 Input/output 33 1.10 Program structure 37 2 C++ programming basics 41 2.1 Enhanced features 41 2.2 Classes 44 2.3 Function and operator overloading 48 2.4 Inheritance 50 2.5 Input/output 53 2.6 Standard libraries 59 3 GCC distilled 63 3.1 General information 63 3.2 Available documentation 65 3.3 Compilation workflow 72 3.4 Compiling a C/C++ program 77 3.5 Libraries and linking programs 79 3.6 Debugging 82 3.7 The make utility 86 4 The Eclipse IDE in a nutshell 91 4.1 The Eclipse architecture and GUI 91 4.2 Working with projects 98 4.3 Editing a source code 105 4.4 Debugging applications 111 5 The GSL scientific library 115 5.1 Preliminaries 115 5.2 Functions and constants 116 5.3 Combinatorics 122 5.4 Linear algebra 130 5.5 Numerical differentiation and integration 141 5.6 Cauchy problem for systems of ODEs 151 5.7 Solution of equations 160 5.8 Interpolation and approximation of functions 176 5.9 Fast Fourier transforms and Chebyshev approximations 186 6 Visualization of computed data 193 6.1 Basics 193 6.2 Data handling 200 6.3 Data interpolation 203 6.4 Using styles 207 6.5 Graph decoration 214 7 Mathematical modeling 221 7.1 Approximation of experimental data 221 7.2 Predator-prey system 225 7.3 Water infiltration 231 7.4 Torsion of cylindrical bars 239 Bibliography 245 Index 247