Nilsystems play a key role in the structure theory of measure preserving systems, arising as the natural objects that describe the behavior of multiple ergodic averages. This book is a comprehensive treatment of their role in ergodic theory, covering development of the abstract theory leading to the structural statements, applications of these ......
This first title in SIAM's Spotlights book series is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during ......
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to ......
This volume is an excellent guide for anyone interested in variational analysis, optimization, and PDEs. It offers a detailed presentation of the most important tools in variational analysis as well as applications to problems in geometry, mechanics, elasticity, and computer vision. Among the new elements in this second edition: the section of ......
The Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles
Transcendental equations arise in every branch of science and engineering. While some of these equations are easy to solve, many are not. When confronted with such an equation, this book serves as an indispensable resource. The author's goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations. This ......
Partial differential equations (PDEs) play a central role in modern physics as a tool to model fundamental physical processes. This book, the second of a two-volume set, provides a bridge between the problems addressed by physics and the mathematical tools used to solve them. Topics covered in Volume II include thermoelasticity, viscoelasticity, ......
Second-Order Necessary and Sufficient Optimality Conditions in Calculusof Variations and Optimal Control
This book is devoted to the theory and applications of second-order necessary and sufficient optimality conditions in the calculus of variations and optimal control. The authors develop theory for a control problem with ordinary differential equations subject to boundary conditions of equality and inequality type, and for mixed state-control ......
Some long-standing problems in delay systems are given an elegant and systematic new treatment in this book, which features a methodology developed by the authors. The authors' approach deals with control of nonlinear systems in the presence of long delays, with large and rapid variation in the actuation or sensing path, or in the presence of long ......
This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features ......
