Numerical Mathematics (Photocopy Edition)

Author: Alfio Quarteroni
Publisher:
Publish Date: 2006-01-17
Features: Numerical mathematics is a branch of mathematics that proposes, develops, analyzes, and applies computational methods in various fields, such as analysis, linear algebra, geometry, approximation theory, functional equations, optimization problems, and differential equations, among others. Other disciplines, such as physics, natural and biological sciences, engineering, economics, and financial science, also frequently pose problems that require computational solutions. Therefore, numerical mathematics can be considered an interdisciplinary field with strong relevance to different disciplines in modern applied science, serving as an important tool for both qualitative and quantitative analysis in these fields. One of the purposes of writing this book is to provide the mathematical foundation of numerical methods, analyzing their fundamental theoretical properties (such as stability, accuracy, and computational complexity), and applying MATLAB, a user-friendly and widely accepted software, to illustrate their characteristics, strengths, and weaknesses through examples and counterexamples. For each type of problem discussed, the book evaluates suitable algorithms, conducts theoretical analysis, and uses a MATLAB program to verify the theoretical results. Each chapter includes examples, exercises, and applies the discussed theories to solve real-world problems. This book is primarily intended for senior undergraduate students and graduate students in engineering, mathematics, physics, and computer science. Its emphasis on practicality and the development of relevant software also makes it valuable for researchers and practitioners in various professional fields and those engaged in scientific computing.