Numerical Mathematics

Description

"One of the purposes of this book is to provide the mathematical foundations of numerical methods, to analyze their basic theoretical properties (stability, accuracy, and computational complexity), and to demonstrate their performances on examples and counterexamples, which outline their pros and cons. This is done using the MATLAB 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 MATLAB 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 science. The attention paid to the applications and the related development of software makes it valuable also to researchers and users of scientific computing in a large variety of professional fields."--BOOK JACKET.

First Sentence

A vector space over the numeric field K (K = R or K = C) is a nonempty set V, whose elements are called vectors and in which two operations are defined, called addition and scalar multiplication, that enjoy the following properties: 1. addition is commutative and associative; 2. there exists an element 0 V (the zero vector or null vector) such that v + 0 = v for each v V; 3. 0 . v = 0, 1 . v = v, where 0 and 1 are respectively the zero and the unity of K; 4. for each element v V there exists its opposite, -v, in V such that v + (-v) = 0; 5. the following distributive properties hold K, v, w V, (v + w) = v + w, K, v V, (+)v = v + v; 6. the following associative property holds, K, v V, ()v = (v).

Subjects

Other Editions

• Numerical MathematicsSpringer2000-04-21
• Numerical MathematicsPaperbackSpringer2001-05-04
• Numerical MathematicsSpringer London, Limited2006-01-01
• Numerical MathematicsSpringer2010-01-01
• Numerical MathematicsPaperbackSpringer2010-11-30
• Numerical MathematicsPaperbackSpringer