Mathematical And Computational Modeling: With Applications In The Natural And Social Sciences, Engineering, And The Arts

Applied mathematics and computational science play a fundamental role in new discoveries in the sciences and engineering. The methodology of mathematical modeling and computational experiment provides a primary and ubiquitous tool in such discoveries, as well as in the development of new theories and techniques for the solution of important problems arising from the sciences and engineering. This book provides readers with state-of-the-art achievements in the development of this methodology and the associated theories and techniques in diverse areas of human knowledge, promoting interdisciplinary interactions between mathematicians, scientists, and engineers. The book is a valuable source of the methods, ideas, and tools of applied and computational mathematics developed for other disciplines, including natural and social sciences, engineering, and technology. Chapter coverage includes: Numerical Challenges in a Cholesky-decomposed Local Correlation Quantum Chemistry Framework; Magnetic vortices, Abrikosov Lattices, and Automorphic Functions; Variational Principles in Wave-Functional and Density- Functional Formulations of Quantum Mechanics; Ecological and Epidemiological Drivers of Viral Evolution; Data-driven Methods for Dynamical Systems; Smoothness Concepts in Regularization for Nonlinear Inverse Problems in Banach Spaces; Information Integration/Organization and Numerical Harmonic Analysis; Initial and Initial-Boundary Value Problems for First Order Symmetric Hyperbolic Systems with Constraints; Systemic Risk; Satisfaction Approval Voting; and Modeling Musical Rhythm Mutations with Geometric Quantization.

Roderick Melnik, PhD, is Professor in the Department of Mathematics at Wilfrid Laurier University, Canada, where he is also Tier I Canada Research Chair in Mathematical Modeling. He is internationally known for his research in computational and applied mathematics, numerical analysis, and mathematical modeling for scientific and engineering applications. Dr. Melnik is the recipient of many awards, including a number of prestigious fellowships in Italy, Denmark, England and Spain. He has published over 300 refereed research papers and has served on editorial boards of numerous international journals and book series. Currently, Dr. Melnik is Director of the MS2Discovery Interdisciplinary Research Institute in Waterloo, Canada.