Procedural languages are generally well understood and their formal foundations cast in the forms of various lambda-calculi. For object- oriented languages however the situation is not as clear-cut. In this book the authors propose and develop a different approach by developing object calculi in which objects are treated as primitives. Using object calculi,the authors are able to explain both the semantics of objects and their typing rules and demonstrate how to develop all of the most important concepts of object-oriented programming languages: self, dynamic dispatch, classes, inheritance, protected and private methods, prototyping, subtyping, covariance and contravariance, and method specialization. Many researchers and graduate students will find this an important development of the underpinnings of object-oriented programming.

This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.