Mathematics of Social Choice is a fun and accessible book that looks at the choices made by groups of people with different preferences, needs, and interests. Divided into three parts, the text first examines voting methods for selecting or ranking candidates. A brief second par…
The linear sampling method is the oldest and most developed of the qualitative methods in inverse scattering theory. It is based on solving a linear integral equation and then using the equation's solution as an indicator function for the determination of the support of the scat…
Mathematical models are used to simulate, and sometimes control, the behavior of physical and artificial processes such as the weather and very large-scale integration (VLSI) circuits. The increasing need for accuracy has led to the development of highly complex models. However,…
Numerical Computing with MATLAB is a lively textbook for an introductory course in numerical methods, MATLAB, and technical computing. The emphasis is on the informed use of mathematical software; in particular, the presentation helps readers learn enough about the mathematical …
This introduction to computer-based problem-solving using the MATLAB environment is highly recommended for students wishing to learn the concepts and develop the programming skills that are fundamental to computational science and engineering (CSE). Through a 'teaching by exampl…
This classic textbook provides a unified treatment of spectral approximation for closed or bounded operators as well as for matrices. Despite significant changes and advances in the field since it was first published in 1983, the book continues to form the theoretical bedrock fo…
This is the first comprehensive treatment of probabilistic Boolean networks (PBNs), an important model class for studying genetic regulatory networks. This book covers basic model properties, including the relationships between network structure and dynamics, steady-state analys…
This book provides an introduction to representative nonrelativistic quantum control problems and their theoretical analysis and solution via modern computational techniques. The quantum theory framework is based on the Schr{uml}odinger picture, and the optimization theory, whic…
Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerf…
Phylogenetics is a topical and growing area of research. Phylogenies (phylogenetic trees and networks) allow biologists to study and graph evolutionary relationships between different species. These are also used to investigate other evolutionary processes--for example, how lang…
An important problem that arises in different disciplines of science and engineering is that of computing limits of sequences of vectors of very large dimension. Such sequences arise, for example, in the numerical solution of systems of linear and nonlinear equations by fixed-po…
The calculation of partial derivatives is a fundamental need in scientific computing. Automatic differentiation (AD) can be applied straightforwardly to obtain all necessary partial derivatives (usually first and, possibly, second derivatives) regardless of a code's complexity. …
Highly oscillatory phenomena range across numerous areas in science and engineering and their computation represents a difficult challenge. A case in point is integrals of rapidly oscillating functions in one or more variables. The quadrature of such integrals has been historica…
This book gives an introduction to the practical treatment of inverse problems by means of numerical methods, with a focus on basic mathematical and computational aspects. To solve inverse problems, we demonstrate that insight about them goes hand in hand with algorithms.
Partial differential equations (PDEs) are used to describe a large variety of physical phenomena, from fluid flow to electromagnetic fields, and are indispensable to such disparate fields as aircraft simulation and computer graphics. While most existing texts on PDEs deal with e…
Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, whic…
Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-…
Ordinary Differential Equations covers the fundamentals of the theory of ordinary differential equations (ODEs), including an extensive discussion of the integration of differential inequalities, on which this theory relies heavily. In addition to these results, the text illustr…