Mathematics Research Guide

Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods. Computation in the research is prominent. Computational mathematics emerged as a distinct part of applied mathematics by early 1950s. This new and important book gathers the latest research from around the globe in the study of this dynamic field and highlights such topics as: coherence-homotopies of higher order, Vandermonde Systems: theory and application, numerical conformal mappings for waveguides, computational study of 3D affine transformation, commutativity formulas for fundamental group entropy, the completion of fuzzy metric spaces, and others.

This book covers core computational science concepts and techniques. It shows how to apply a model, select a numerical method, implement computer simulations, and assess the ensuing results. Providing a wealth of MATLAB, Fortran, and C++ code online for download, the second edition includes a new chapter with sections on the finite element method, shallow water waves, and the driven cavity problem. It introduces multiprocessor/multicore computers, parallel MATLAB, and MPI in the chapter on high-performance computing, as well as updates and adds code and documentation.