Introduction To Computational Mathematics

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.

Contents: 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.