Practical scientific computing
Scientific computing is about developing mathematical models, numerical methods and computer implementations to study and solve real problems in science, engineering, business and even social sciences. Mathematical modelling requires deep understanding of classical numerical methods. This essential...
| Autor principal: | |
|---|---|
| Otros Autores: | |
| Formato: | Libro electrónico |
| Idioma: | Inglés |
| Publicado: |
Cambridge, England ; Philadelphia, Pennsylvania ; New Delhi, India :
Woodhead Publishing
2011.
|
| Edición: | 1st edition |
| Colección: | Woodhead Publishing in mathematics
|
| Materias: | |
| Ver en Biblioteca Universitat Ramon Llull: | https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009628575106719 |
Tabla de Contenidos:
- Cover; Practical scientific computing; Copyright; Table of contents; Preface; Acknowledgements; Part I; 1 Introduction; 1.1 Getting started; 1.2 Interpreter; 1.3 Program; 2 Expressions; 2.1 Matrix; 2.2 Real number; 2.3 Complex number; 2.4 Boolean; 2.5 String; 2.6 Structure; 2.7 Cell; 2.8 Range expression; 2.9 Boolean expression; 2.10 Relational expression; 2.11 Numerical expression; 3 Statements; 3.1 Assignment statement; 3.2 Loop statements; 3.3 Conditional statements; 3.4 Continue and break statements; 4 Programming; 4.1 Program; 4.2 Function; 4.3 Procedure; 4.4 Java programming
- 4.5 C programming5 Architecture; 5.1 Front-end; 5.2 Back-end; 5.3 User interface; 5.4 Gnuplot interface; 5.5 Execution engine; 6 Plotting; 6.1 Simple function plot (fplot); 6.2 Two-dimensional plots; 6.3 Three-dimensional plots; Part II; 7 Solving nonlinear equations; 7.1 Calculation of roots with the use of iterative functions; 7.2 Exercises; 8 Solving systems of linear equations; 8.1 Linear algebra background; 8.2 Systems of linear equations; 8.3 Types of matrices that arise from applications and analysis; 8.4 Error sources; 8.5 Condition number; 8.6 Direct methods; 8.7 Iterative methods
- 8.8 Exercises9 Computational eigenvalue problems; 9.1 Basic facts concerning eigenvalue problems; 9.2 Localization of eigenvalues; 9.3 Power method; 9.4 Inverse iteration; 9.5 Iteration with a shift of origin; 9.6 The qr method; 9.7 Exercises; 10 Introduction to finite difference schemes for ordinary differential equations; 10.1 Elementary example of a finite difference scheme; 10.2 Approximation and stability; 10.3 Numerical solution of initial value problems; 10.4 Numerical solution and value problems; 10.5 Error estimation and control; 10.6 Exercises; 11 Interpolation and approximation
- 11.1 Interpolation11.2 Approximation of functions and data representation; 11.3 Exercises; Bibliography
