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Cambridge Tracts in Mathematics (Book #187)
Convexity is important in theoretical aspects of mathematics and also for economists and physicists. In this monograph the author provides a comprehensive insight into convex sets and functions including the infinite-dimensional case and emphasizing the analytic point of view. Chapter one introduces the reader to the basic definitions and ideas that play central roles throughout the book. The restSzego's Theorem and Its Descendants: Spectral Theory for L2 Perturbations of Orthogonal Polynomials
Spectral Theory for L2 Perturbations of Orthogonal Polynomials
This book presents a comprehensive overview of the sum rule approach to spectral analysis of orthogonal polynomials, which derives from Gábor Szego's classic 1915 theorem and its 1920 extension. Barry Simon emphasizes necessary and sufficient conditions, and provides mathematical background that until now has been available only in journals. Topics include background from the theory of meromorphicCase Files Emergency Medicine, Third Edition
Real life cases for the emergency medicine clerkship and shelf-exam You need exposure to high-yield cases to excel on the emergency medicine clerkship and the shelf-exam. Case Files: Emergency Medicine presents 50 real-life cases that illustrate essential concepts in emergency medicine. Each case includes a complete discussion, clinical pearls, references, definitions of key terms, and USMLE-styleMethods of Modern Mathematical Physics (Book #1)
This book is the first of a multivolume series devoted to an exposition of functional analysis methods in modern mathematical physics. It describes the fundamental principles of functional analysis and is essentially self-contained, although there are occasional references to later volumes. We have included a few applications when we thought that they would provide motivation for the reader. LaterAn Introduction to Fourier Series and Integrals
A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley focuses on results of greatest significance to modern readers.Starting with a physical problem, Dr. Seeley sets up and analyzes the mathematicalRecent Trends in Dynamical Systems
Proceedings of a Conference in Honor of Jürgen Scheurle
Springer Proceedings in Mathematics & Statistics (Book #35)
This book presents the proceedings of a conference on dynamical systems held in honor of Jürgen Scheurle in January 2012. Through both original research papers and survey articles leading experts in the field offer overviews of the current state of the theory and its applications to mechanics and physics. In particular, the following aspects of the theory of dynamical systems are covered: -Functionals of Finite Riemann Surfaces
This advanced monograph on finite Riemann surfaces, based on the authors' 1949–50 lectures at Princeton University, remains a fundamental book for graduate students. The Bulletin of the American Mathematical Society hailed the self-contained treatment as the source of "a plethora of ideas, each interesting in its own right," noting that "the patient reader will be richly rewarded." Suitable forSpectral Theory and its Applications
Cambridge Studies in Advanced Mathematics (Book #139)
Bernard Helffer's graduate-level introduction to the basic tools in spectral analysis is illustrated by numerous examples from the Schrödinger operator theory and various branches of physics: statistical mechanics, superconductivity, fluid mechanics and kinetic theory. The later chapters also introduce non self-adjoint operator theory with an emphasis on the role of the pseudospectra. The author'sTowards the Mathematics of Quantum Field Theory
This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language forTopological Methods in the Study of Boundary Value Problems
This textbook is devoted to the study of some simple but representative nonlinear boundary value problems by topological methods. The approach is elementary, with only a few model ordinary differential equations and applications, chosen in such a way that the student may avoid most of the technical difficulties and focus on the application of topological methods. Only basic knowledge of generalLectures on Ordinary Differential Equations
Hailed by The American Mathematical Monthly as "a rigorous and lively introduction," this text explores a topic of perennial interest in mathematics. The author, a distinguished mathematician and formulator of the Hurewicz theorem, presents a clear and lucid treatment that emphasizes geometric methods. Topics include first-order scalar and vector equations, basic properties of linear vector