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This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.
This book provides an introduction to dynamical systems with multiple time scales. The approach it takes is to provide an overview of key areas, particularly topics that are less available in the introductory form. The broad range of topics included makes it accessible for students and researchers new to the field to gain a quick and thorough overview. The first of its kind, this book merges a wide variety of different mathematical techniques into a more unified framework. The book is highly illustrated with many examples and exercises and an extensive bibliography. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.
Improve and Accelerate Software Delivery for Large, Distributed, Complex Projects The Nexus Framework is the simplest, most effective approach to applying Scrum at scale across multiple teams, sites, and time zones. Created by Scrum.org–the pioneering Scrum training and certification organization founded by Scrum co-creator Ken Schwaber–Nexus draws on decades of experience to address the unique challenges teams face in coming together, sharing work, and managing and minimizing dependencies. The NexusTM Framework for Scaling Scrum is a concise book that shows how Nexus helps teams to deliver a complex, multi-platform, software-based product in short, frequent cycles, without sacrificing consistency or quality, and without adding unnecessary complexity or straying from Scrum’s core principles. Using an extended case study, the authors illustrate how Nexus helps teams solve common scaling challenges like reducing cross-team dependencies, preserving team self-organization and transparency, and ensuring accountability. Understand the challenges of delivering working, integrated product increments with multiple teams, and how Nexus addresses them Form a Nexus around a new or existing product and learn how that Nexus sets goals and plans its work Run Sprints within a Nexus, provide transparency into progress, conduct effective Nexus Sprint reviews, and use Nexus Sprint Retrospectives to continuously improve Overcome the distributed team collaboration challenges
The scaling issue remains one of the largest problems in soil science and hydrology. This book is a unique compendium of ideas, conceptual approaches, techniques, and methodologies for scaling soil physical properties. Scaling Methods in Soil Physics covers many methods of scaling that will be useful in helping scientists across a range of soil-rel
Outlines a set of techniques that enables a researcher to explore the hidden structure of large databases. These techniques use proximities to find a configuration of points that reflect the structure in the data.
This is the first book of its kind – explicitly considering uncertainty and error analysis as an integral part of scaling. The book draws together a series of important case studies to provide a comprehensive review and synthesis of the most recent concepts, theories and methods in scaling and uncertainty analysis. It includes case studies illustrating how scaling and uncertainty analysis are being conducted in ecology and environmental science.
The evolution of observational instruments, simulation techniques, and computing power has given aquatic scientists a new understanding of biological and physical processes that span temporal and spatial scales. This has created a need for a single volume that addresses concepts of scale in a manner that builds bridges between experimentalists and