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.

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Contents:Mathematical Foundations:Mathematical FoundationsAlgorithmic Complexity, Norms and ConvexityOrdinary Differential EquationsPartial Differential EquationsNumerical Algorithms:Roots of Nonlinear EquationsNumerical IntegrationComputational Linear AlgebraInterpolationNumerical Methods of PDEs:Finite Difference Methods for ODEsFinite Difference Methods for PDEsFinite Volume MethodFinite Element MethodMathematical Programming:Mathematical OptimizationMathematical ProgrammingStochastic Methods and Data Modelling:Stochastic ModelsData ModellingData Mining, Neural Networks and Support Vector MachineRandom Number Generators and Monte Carlo MethodComputational Intelligence:Evolutionary ComputationSwarm IntelligenceSwarm 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 algorithmsStep-by-step examples show how algorithms workSuitable for both undergraduates and graduatesAs 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