Methods of Nonlinear Analysis

Numerical Methods and Methods of Approximation in Science and Engineering prepares students and other readers for advanced studies involving applied numerical and computational analysis. Focused on bu

Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.

In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called 'solitons' and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such 'soliton equations'. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book, first published in 2003, presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the pre

This book provides a comprehensive, coherent, and intuitive review of panel data methodologies that are useful for empirical analysis. Substantially revised from the second edition, it includes two new chapters on modeling cross-sectionally dependent data and dynamic systems of equations. Some of the more complicated concepts have been further streamlined. Other new material includes correlated random coefficient models, pseudo-panels, duration and count data models, quantile analysis, and alternative approaches for controlling the impact of unobserved heterogeneity in nonlinear panel data models.

This book provides a comprehensive, coherent, and intuitive review of panel data methodologies that are useful for empirical analysis. Substantially revised from the second edition, it includes two new chapters on modeling cross-sectionally dependent data and dynamic systems of equations. Some of the more complicated concepts have been further streamlined. Other new material includes correlated random coefficient models, pseudo-panels, duration and count data models, quantile analysis, and alternative approaches for controlling the impact of unobserved heterogeneity in nonlinear panel data models.

Exploring the analysis of pharmaceuticals, including polymorphic forms, this book discusses regulatory requirements in pharmaceutical product development and pharmaceutical testing. It covers methods

Standard work applies tensorial methods to subjects within realm of advanced college mathematics. Text explains fundamental ideas and notation of tensor theory; covers geometrical treatment of tensor

Analysis of Cosmetic Products, Second Edition, advises the reader from an analytical chemistry perspective on the choice of suitable analytical methods for production monitoring and quality control of

How to apply statistical methods to survey data--a guide to effective analysis of health surveys.With large health surveys becoming increasingly available for public use, researchers with little exper

Bray's monograph considers the multivariate form of analysis of variance (MANOVA). The primary emphasis of the book is on methods for interpreting MANOVA statistical analyses. These are illustrated th

The first edition of Analysis for Longitudinal Data has become a classic. Describing the statistical models and methods for the analysis of longitudinal data, it covers both the underlying statistical

In this fourth and last volume of the series the presentation of methods and techniques for the analysis of foods, nutrients, antinutritional factors and contaminants in foods, is concisely described

The quality of the integration of multiple data sources is key to ensuring that the data can be properly analyzed. This book presents statistical methods for analyzing integrated data, covering uncert

An introduction to biological networks and methods for their analysis Analysis of Biological Networks is the first book of its kind to provide readers with a comprehensive introduction to the structu

The ideas and methods of mathematics, long central to the physical sciences, now play an increasingly important role in a wide variety of disciplines. Analysis provides theorems that prove that result

Analysis of Financial Data teaches the basic methods and techniques of data analysis to finance students, by showing them how to apply such techniques in the context of real-world empirical problems.A

Mixture analysis is very active research topic in statistics and machine learning. It is a good timing for a Handbook to present a broad overview of the methods and applications, suitable for graduate

This book is concerned with statistical methods for the analysis of data collected from a survey. A survey could consist of data collected from a questionnaire or from measurements, such as those take

These notes originate from a one semester course which forms part of the "Math Methods" cycle at Brown. In the hope that these notes might prove useful for reference purposes several additional sectio

Numerical analysis deals with the manipulation of numbers to solve a particular problem. This book discusses in detail the creation, analysis and implementation of algorithms to solve the problems of continuous mathematics. An input is provided in the form of numerical data or it is generated as required by the system to solve a mathematical problem. Subsequently, this input is processed through arithmetic operations together with logical operations in a systematic manner and an output is produced in the form of numbers. Covering the fundamentals of numerical analysis and its applications in one volume, this book offers detailed discussion on relevant topics including difference equations, Fourier series, discrete Fourier transforms and finite element methods. In addition, the important concepts of integral equations, Chebyshev Approximation and Eigen Values of Symmetric Matrices are elaborated upon in separate chapters. The book will serve as a suitable textbook for undergraduate stud

Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich–Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mat

This two-volume (1880-6) teaching aid for the Cambridge Mathematical Tripos greatly influenced the education of Srinivasa Ramanujan (1887-1920).

Covering all aspects of business research, from review of the literature to multivariate analysis, this readable text aimed at advanced undergraduate students intends to help aspiring managers make be

Appropriate for use in developmental research methods or analysis of change courses, this is the first methods handbook specifically designed to meet the needs of those studying development. Leading d

This is a sophisticated and nuanced introduction to critical discourse analysis (CDA) that covers a range of topics in an accessible, engaging style. With international examples and an interd

This is a sophisticated and nuanced introduction to critical discourse analysis (CDA) that covers a range of topics in an accessible, engaging style. With international examples and an interd

First published in 1961, this book provides information on the methods of treating series of observations, the field covered embraces portions of both statistics and numerical analysis. Originally intended as an introduction to the topic aimed at students and graduates in physics, the types of observation discussed reflect the standard routine work of the time in the physical sciences. The text partly reflects an aim to offer a better balance between theory and practice, reversing the tendency of books on numerical analysis to omit numerical examples illustrating the applications of the methods. This book will be of value to anyone with an interest in the theoretical development of its field.

A complete guide to cutting-edge techniques and best practices for applying covariance analysis methodsThe Second Edition of Analysis of Covariance and Alternatives sheds new light on its topic, offer

The Nature of Biological Systems as Revealed by Thermal Methods is a guide for experiments using thermal methods. The Editor has used his many years of experience to create a unique resource that will

The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and

Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equatio

This book assembles and organizes a selected range of methods and techniques that every planning practitioner should know to be successful in the contemporary global urban landscape. The book is uniqu