This self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, Fourier transform, Hilbert transform, and Calderon-Zygmund singular integrals. An ideal ......
Expositions of quantitative methods and algorithms for biological data tend to be scattered through the technical literature, often across different fields, and are thus awkward to assimilate. This book documents one example of this: the relationship between the cell biology idea of metabolic networks and the mathematical idea of polyhedral cones. ......
This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. It presents an outline of the underlying convergence and stability theory while avoiding technical details. Key ideas are illustrated with numerous ......
Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, ......
Continuous-Time, Sampled-Data, and Networked Systems
Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design ......
This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn-Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn-Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. ......
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of ......
Guidelines for Assessment & Instruction in Mathematical Modeling Education
A partnership between SIAM and COMAP, Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIMME) enables the modeling process to be understood as part of STEM studies and research, and taught as a basic tool for problem solving and logical thinking. GAIMME helps define core competencies to include in student experiences, ......
This book is an introduction to both computational inverse problems and uncertainty quantification (UQ) for inverse problems. The book also presents more advanced material on Bayesian methods and UQ, including Markov chain Monte Carlo sampling methods for UQ in inverse problems. Each chapter contains MATLAB (R) code that implements the algorithms ......
