Introduction to Computational Mathematics

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

Contents:

• Mathematical Foundations:

  • Mathematical Foundations
  • Algorithmic Complexity, Norms and Convexity
  • Ordinary Differential Equations
  • Partial Differential Equations

• Numerical Algorithms:

  • Roots of Nonlinear Equations
  • Numerical Integration
  • Computational Linear Algebra
  • Interpolation

• Numerical Methods of PDEs:

  • Finite Difference Methods for ODEs
  • Finite Difference Methods for PDEs
  • Finite Volume Method
  • Finite Element Method

• Mathematical Programming:

  • Mathematical Optimization
  • Mathematical Programming

• Stochastic Methods and Data Modelling:

  • Stochastic Models
  • Data Modelling
  • Data Mining, Neural Networks and Support Vector Machine
  • Random Number Generators and Monte Carlo Method

• Computational Intelligence:

  • Evolutionary Computation
  • Swarm Intelligence
  • Swarm Intelligence: New Algorithms

Readership: Advanced undergraduates and graduates in applied mathematics, engineering, computational sciences and scientific computing; computer scientists; algorithm developers; mathematical modellers; data analysts; researchers.
Key Features:

• Introduction to both conventional methods and new algorithms
• Step-by-step examples show how algorithms work
• Suitable for both undergraduates and graduates
• As a comprehensive textbook, it covers all important topics: both conventional methods and new algorithms to reflect the state-of-the-art developments in the field