Numerical mathematics

Author: Quatoni
Publisher:
Publish Date: 2006-01-01
Features: Numerical mathematics is a branch of mathematics that proposes, develops, analyzes, and applies scientific computing methods to various fields, such as analysis, linear algebra, geometry, approximation theory, functional equations, optimization problems, and differential equations, among others. Other fields, such as physics, natural and biological sciences, engineering, economics, and financial science, also frequently raise problems that require scientific computing for their 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 disciplines. One of the purposes of writing this book is to provide the mathematical foundation for 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, advantages, and disadvantages through examples and counterexamples. For each category of problems 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 in various professional fields and practitioners of scientific computing.