Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections highlighting various developments of the main equations treated in that chapter. For advanced students, the book introduces functional equations in abstract domains like semigroups, groups, and Banach spaces. Functional equations covered include: Cauchy Functional Equations and Applications The Jensen Functional Equation Pexider's Functional Equation Quadratic Functional Equation D'Alembert Functional Equation Trigonometric Functional Equations Pompeiu Functional Equation Hosszu Functional Equation Davison Functional Equation Abel Functional Equation Mean Value Type Functional Equations Functional Equations for Distance Measures The innovation of solving functional equations lies in finding the right tricks for a particular equation. Accessible and rooted in current theory, methods, and research, this book sharpens mathematical competency and prepares students of mathematics and engineering for further work in advanced functional equations.

Image Processing with MATLAB (R): Applications in Medicine and Biology explains complex, theory-laden topics in image processing through examples and MATLAB (R) algorithms. It describes classical as well emerging areas in image processing and analysis. Providing many unique MATLAB codes and functions throughout, the book covers the theory of probability and statistics, two-dimensional fast Fourier transform, nonlinear diffusion filtering, and partial differential equation (PDE)-based image denoising techniques. It presents intensity-based image segmentation methods, including thresholding techniques as well as K-means and fuzzy C-means clustering techniques. The authors also explore Markov random field (MRF)-based image segmentation, boundary and curvature analysis methods, and parametric and geometric deformable models. The final chapters focus on three specific applications of image processing and analysis. Reducing the need for the trial-and-error way of solving problems, this book helps readers understand advanced concepts by applying algorithms to real-world problems in medicine and biology. A solutions manual is available for instructoes wishing to convert this reference to classroom use.

Introduction to Functional Equations grew out of a set of class notes from an introductory graduate level course at the University of Louisville. This introductory text communicates an elementary exposition of valued functional equations where the unknown functions take on real or complex values. In order to make the presentation as manageable as possible for students from a variety of disciplines, the book chooses not to focus on functional equations where the unknown functions take on values on algebraic structures such as groups, rings, or fields. However, each chapter includes sections highlighting various developments of the main equations treated in that chapter. For advanced students, the book introduces functional equations in abstract domains like semigroups, groups, and Banach spaces. Functional equations covered include: Cauchy Functional Equations and Applications The Jensen Functional Equation Pexider's Functional Equation Quadratic Functional Equation D'Alembert Functional Equation Trigonometric Functional Equations Pompeiu Functional Equation Hosszu Functional Equation Davison Functional Equation Abel Functional Equation Mean Value Type Functional Equations Functional Equations for Distance Measures The innovation of solving functional equations lies in finding the right tricks for a particular equation. Accessible and rooted in current theory, methods, and research, this book sharpens mathematical competency and prepares students of mathematics and engineering for further work in advanced functional equations.