Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Numerical mathematics is the branch of mathematics that proposes, develops, analyzes and applies methods from scientific computing to several fields including analysis, linear algebra, geometry, approximation theory, functional equations, optimization and differential equations. Other disciplines, such as physics, the natural and biological sciences, engineering, and economics and the financial sciences frequently give rise to problems that need scientific computing for their solutions. As such, numerical mathematics is the crossroad of several disciplines of great relevance in modern applied sciences, and can become a crucial tool for their qualitative and quantitative analysis. One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, computational complexity) and demonstrate their performance on examples and counterexamples which outline their pros and cons. This is done using the MATLABTM software environment which is user-friendly and widely adopted. Within any specific class of problems, the most appropriate scientific computing algorithms are reviewed, their theoretical analyses are carried out and the expected results are verified on a MATLABTM computer implementation. Every chapter is supplied with examples, exercises and applications of the discussed theory to the solution of real-life problems. This book is addressed to senior undergraduate and graduate students with particular focus on degree courses in engineering, mathematics, physics and computer sciences. The attention which is paid to the applications and the related development of software makes it valuable also for researchers and users of scientific computing in a large variety of professional fields. In this second edition, the readability of pictures, tables and program headings has been improved. Several changes in the chapters on iterative methods and on polynomial approximation have also been added. From the reviews of the first edition: "This is an excellent and modern textbook in numerical mathematics! It is primarily addressed to undergraduate students in mathematics, physics, computer science and engineering. But you will need a weekly 4 hour lecture for 3 terms lecture to teach all topics treated in this book! Well known methods as well as very new algorithms are given. The methods and their performances are demonstrated by illustrative examples and computer examples. Exercises shall help the reader to understand the theory and to apply it. MATLAB-software satisfies the need of user-friendliness. [....] In the reviewers opinion, the presented book is the best textbook in numerical mathematics edited in the last ten years." Zentralblatt für Mathematik 2001, 991.38387.

Numerical analysis --- 519.61 --- 519.61 Numerical methods of algebra --- Numerical methods of algebra --- Mathematical analysis --- Mathematical Sciences --- Applied Mathematics --- Mathematics. --- Applied mathematics. --- Engineering mathematics. --- Numerical analysis. --- Applications of Mathematics. --- Mathematics, general. --- Numerical Analysis. --- Appl.Mathematics/Computational Methods of Engineering. --- wiskunde --- Mathematics --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Math --- Science --- Numerical analysis - Textbooks --- Analyse numérique. --- Manuels d'enseignement

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.

Iterative methods (Mathematics) --- Numerical solutions of algebraic equations --- 519.61 --- 681.3*G13 --- 519.61 Numerical methods of algebra --- Numerical methods of algebra --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Linear systems. --- Itération (Mathématiques) --- Systèmes linéaires --- Linear systems --- Systems, Linear --- Differential equations, Linear --- System theory --- Iteration (Mathematics) --- Numerical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Modern computer algebra systems are revolutionizing the teaching and learning of mathematically intensive subjects in science and engineering, enabling students to explore increasingly complex and computationally intensive models that provide analytic solutions, animated numerical solutions, and complex two- and three-dimensional graphic displays. This self-contained text benefits from a spiral structure that regularly revisits the general topics of graphics, symbolic computation, and numerical simulation with increasing intricacy at each turn. The text is built around a large number of computer algebra worksheets or "recipes" that have been designed using MAPLE to provide tools for problem solving and to stimulate critical thinking. No prior knowledge of MAPLE is assumed. All relevant commands are introduced on a need-to-know basis and are indexed for easy reference. Each recipe is associated with a scientific model or method and an interesting or amusing story designed to both entertain and enhance concept comprehension and retention. All recipes are included on the CD-ROM enclosed with the book. Aimed at third- and fourth-year undergraduates in science and engineering, the text contains numerous examples in disciplines that will challenge students progressing in mathematics, physics, engineering, game theory, and physical chemistry. Computer Algebra Recipes: An Advanced Guide to Mathematical Modeling can serve as an effective computational science text, with a set of problems following each section of recipes to enable readers to apply and confirm their understanding. The book may also be used as a reference, for self-study, or as the basis of an online course.

analyse (wiskunde) --- Computer. Automation --- Computer architecture. Operating systems --- algebra --- simulaties --- vormgeving --- informatica --- Artificial intelligence. Robotics. Simulation. Graphics --- Mathematical physics --- Mathematical control systems --- Engineering sciences. Technology --- Planning (firm) --- mathematische modellen --- ingenieurswetenschappen --- wiskunde --- Mathematical logic --- fysica --- 517.91 --- Science --- 519.61 --- 519.67 --- Natural science --- Science of science --- Sciences --- 517.91 Differential equations --- Differential equations --- 519.61 Numerical methods of algebra --- Numerical methods of algebra --- 519.67 Machine, graphical and other methods of computational mathematics --- Machine, graphical and other methods of computational mathematics --- Numerical solutions --- Numerical solutions&delete& --- Computer programs. --- Mathematical models --- Maple (Computer file) --- Mathematical models. --- Algebra. --- Algebra --- Engineering mathematics. --- Mathematical physics. --- Computer software. --- Mathematical Modeling and Industrial Mathematics. --- Symbolic and Algebraic Manipulation. --- Mathematical and Computational Engineering. --- Mathematical Methods in Physics. --- Mathematical Software. --- Data processing. --- Software, Computer --- Computer systems --- Physical mathematics --- Physics --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Natural sciences --- Computer science—Mathematics. --- Applied mathematics. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Models, Mathematical --- Simulation methods --- Numerical solutions&delete&&delete& --- Computer programs