Description
DOVER PUBLICATIONS Unbounded Linear Operators Theory And Applications 2006 Edition by GOLDBERG SEYMOUR
This volume presents a systematic treatment of the theory of unbounded linear operators in normed linear spaces with applications to differential equations. Largely self-contained, it is suitable for advanced undergraduates and graduate students, and it only requires a familiarity with metric spaces and real variable theory.After introducing the elementary theory of normed linear spaces--particularly Hilbert space, which is used throughout the book--the author develops the basic theory of unbounded linear operators with normed linear spaces assumed complete, employing operators assumed closed only when needed. Other topics include strictly singular operators; operators with closed range; perturbation theory, including some of the main theorems that are later applied to ordinary differential operators; and the Dirichlet operator, in which the author outlines the interplay between functional analysis and "hard" classical analysis in the study of elliptic partial differential equations.In addition to its readable style, this book's appeal includes numerous examples and motivations for certain definitions and proofs. Moreover, it employs simple notation, eliminating the need to refer to a list of symbols. IntroductionChapter 1 DirectX IntroductionChapter 2 The Game StrandedChapter 3 Direct3D Lighting and ObjectsChapter 4 TexturesChapter 5 Direct3D Text and GUIChapter 6 Special EffectsChapter 7 Basic Scripting SystemsChapter 8 Game Math ReviewChapter 9 Collision DetectionChapter 10 Input Detection and ResponseChapter 11 SoundChapter 12 Model LoadingChapter 13 Model AnimationChapter 14 Scene ManagementChapter 15 Finishing the Game EngineChapter 16 Making the Game: StrandedChapter 17 ConclusionsAppendix A Recommended Books and Web SitesAppendix B C++ PrimerAppendix C About the CD-ROMIndex