A First Course in the Calculus of Variations


Book Description

This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.




Qualitative Methods in Nonlinear Dynamics


Book Description

"Presents new approaches to qualitative analysis of continuous, discreteptime, and impulsive nonlinear systems via Liapunov matrix-valued functions that introduce more effective tests for solving problems of estimating the domains of asymptotic stability."




Ecological Time Series


Book Description

This pioneering volume explores time series analysis and interpretation using a wide range of methods and examples from terrestrial, marine, and freshwater ecology. The book challenges readers to discern interdisciplinary processes that can unify fields as diverse as climatology and epidemiology. The first section of the book explores the basic concepts of environmental analysis, reviews state-of-the-art techniques and methodologies, and offers innovative solutions to analytical problems of longer time series with special attention to climate change, providing the reader with the conceptual and methodological tools to analyze environmental data accurately. The second section examines a variety of time scales used to describe change, and the variability within and between different ecosystems, so that diverse systems may be studied in an integrated way. The final section of the book illustrates key concepts and themes, based on the results of major investigations in various time scales, including studies from arctic sites to human epidemiology. Investigating time series in the context of ecological functions such as population processes, community structure, and patch dynamics, this insightful volume will stimulate cross fertilization among the ecological disciplines. The broad spectrum of ideas and applications examined in this volume makes it a useful resource for all ecologists.