by Xin-She Yang (University of Cambridge, UK)

Table of Contents (74k)
Preface (44k)
Chapter 1: Mathematical Foundations (237k)

This unique book provides a comprehensive introduction to computational mathematics, which forms an essential part of modern numerical algorithms and scientific computing. It uses a theorem-free approach with just the right balance between mathematics and numerical algorithms. It covers all major topics in computational mathematics with a wide range of carefully selected numerical algorithms, ranging from the root-finding algorithms, numerical integration, numerical methods of partial differential equations, finite element methods, optimization algorithms, stochastic models, to nonlinear curve-fitting and swarm optimization. Especially suitable for undergraduates and graduates in computational mathematics, numerical algorithms, and scientific computing, it can be used as a textbook and/or reference book.

• Mathematical Foundations
• Algorithmic Complexity
• Ordinary Differential Equations
• Partial Differential Equations
• Roots of Nonlinear Equations
• Numerical Integration
• Computational Linear Algebra
• Interpolation
• Finite Difference Methods for ODEs
• Finite Difference Methods for PDEs
• Finite Volume Method
• Finite Element Method
• Mathematical Optimization
• Mathematical Programming
• Stochastic Models
• Data Modelling
• Metaheuristic Methods
• Bee Algorithms
• Swarm Optimization