This is an elementary and self-contained introduction to nonlinear functional analysis and its applications, especially in bifurcation theory.

A graduate text explaining how methods of nonlinear analysis can be used to tackle nonlinear differential equations. Suitable for mathematicians, physicists and engineers, topics covered range from elementary tools of bifurcation theory and analysis to critical point theory and elliptic partial differential equations. The book is amply illustrated with many exercises.

This volume covers a diverse collection of topics dealing with some of the fundamental concepts and applications embodied in the study of nonlinear dynamics. Each of the 15 chapters contained in this compendium generally fit into one of five topical areas: physics applications, nonlinear oscillators, electrical and mechanical systems, biological and behavioral applications or random processes. The authors of these chapters have contributed a stimulating cross section of new results, which provide a fertile spectrum of ideas that will inspire both seasoned researches and students.

There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.

Nonlinear Contingency Analysis is a guide to treating clinically complex behavior problems such as delusions and hallucinations. It’s also a framework for treating behavior problems, one that explores solutions based on the creation of new or alternative consequential contingencies rather than the elimination or deceleration of old or problematic thoughts, feelings, or behaviors. Chapters present strategies, analytical tools, and interventions that clinicians can use in session to think about clients’ problems using decision theory, experimental analysis of behavior, and clinical research and practice. By treating thoughts and emotions not as causes of behavior but as indicators of the environmental conditions that are responsible for them, patients can use that knowledge to make changes that not only result in changes in behavior, but in the thoughts and feelings themselves.

R is the most widely used open-source statistical and programming environment for the analysis and visualization of biological data. Drawing on Gregg Hartvigsen's extensive experience teaching biostatistics and modeling biological systems, this text is an engaging, practical, and lab-oriented introduction to R for students in the life sciences. Underscoring the importance of R and RStudio in organizing, computing, and visualizing biological statistics and data, Hartvigsen guides readers through the processes of entering data into R, working with data in R, and using R to visualize data using histograms, boxplots, barplots, scatterplots, and other common graph types. He covers testing data for normality, defining and identifying outliers, and working with non-normal data. Students are introduced to common one- and two-sample tests as well as one- and two-way analysis of variance (ANOVA), correlation, and linear and nonlinear regression analyses. This volume also includes a section on advanced procedures and a chapter introducing algorithms and the art of programming using R.

Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.