Undergraduate Convexity: Problems And Solutions
by Mikkel Slot Nielsen and Victor Ulrich Rohde
This solutions manual thoroughly goes through the exercises found in Undergraduate Convexity: From Fourier and Motzkin to Kuhn and Tucker. Several solutions are accompanied by detailed illustrations and intuitive explanations. This book will pave the way for students to easily grasp the multitude of solution methods and aspects of convex sets and convex functions. Companion Textbook here
"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." Proceedings of the Edinburgh Mathematical Society
Dirichlet Forms and Related Topics (Springer Proceedings in Mathematics & Statistics, #394)
This conference proceeding contains 27 peer-reviewed invited papers from leading experts as well as young researchers all over the world in the related fields that Professor Fukushima has made important contributions to. These 27 papers cover a wide range of topics in probability theory, ranging from Dirichlet form theory, Markov processes, heat kernel estimates, entropy on Wiener spaces, analysis on fractal spaces, random spanning tree and Poissonian loop ensemble, random Riemannian geometry,...
In these lecture notes, we will analyze the behavior of random walk on disordered media by means of both probabilistic and analytic methods, and will study the scaling limits. We will focus on the discrete potential theory and how the theory is effectively used in the analysis of disordered media. The first few chapters of the notes can be used as an introduction to discrete potential theory.Recently, there has been significant progress on the theory of random walk on disordered media such as fr...
Tensor Spaces and Numerical Tensor Calculus (Springer Series in Computational Mathematics)
Lineare Funktionen in der Berufsfachschule. Planung und Durchfuhrung einer Unterrichtsreihe
by Andreas Wolf
Nonlinear Analysis and Variational Problems (Springer Optimization and Its Applications, #35)
The chapters in this volume, written by international experts from different fields of mathematics, are devoted to honoring George Isac, a renowned mathematician. These contributions focus on recent developments in complementarity theory, variational principles, stability theory of functional equations, nonsmooth optimization, and several other important topics at the forefront of nonlinear analysis and optimization.
Applications of Tensor Analysis (Dover Books on Mathematics)
by A. J. McConnell
Morse Theory Of Gradient Flows, Concavity And Complexity On Manifolds With Boundary
by Gabriel Katz
This monograph is an account of the author's investigations of gradient vector flows on compact manifolds with boundary. Many mathematical structures and constructions in the book fit comfortably in the framework of Morse Theory and, more generally, of the Singularity Theory of smooth maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly rich. This geometric setting leads organically to many encounters w...
This is a book that the author wishes had been available to him when he was student. It reflects his interest in knowing (like expert mathematicians) the most relevant mathematics for theoretical physics, but in the style of physicists. This means that one is not facing the study of a collection of definitions, remarks, theorems, corollaries, lemmas, etc. but a narrative - almost like a story being told - that does not impede sophistication and deep results.It covers differential geometry far be...
Functions of One Complex Variable II (Graduate Texts in Mathematics, #159)
by John B Conway
This book discusses a variety of problems which are usually treated in a second course on the theory of functions of one complex variable, the level being gauged for graduate students. It treats several topics in geometric function theory as well as potential theory in the plane, covering in particular: conformal equivalence for simply connected regions, conformal equivalence for finitely connected regions, analytic covering maps, de Branges' proof of the Bieberbach conjecture, harmonic function...
Lectures on Choquet's Theorem (Lecture Notes in Mathematics, #1757)
by Robert R. Phelps
A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated...
Distributionen als Loesungen von Anfangswertproblemen
by Daphne Von Harrach
This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weigh...
Seminaire de Theorie Du Potentiel, Paris, 1976-1977, No. 3 (Lecture Notes in Mathematics, #681)
Potential Theory (Lecture Notes in Mathematics, #408)
by John Wermer
This advanced calculus text is suitable for mathematicians, engineers and physicists. For this second edition the artwork has been completely revised and there is a new section on simple connectedness. Enabling students to gain a thorough understanding of the divergence, gradiant, curl and Laplacian vectors, this text is presented in an informal style with steady exposition.
Hodge Decomposition - A Method for Solving Boundary Value Problems (Lecture Notes in Mathematics, #1607)
by Gunter Schwarz
Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects. It aims at developing a method for solving boundary value problems. Analysing a Dirichlet form on the exterior algebra bundle allows to give a refined version of the classical decomposition results of Morrey. A projection technique leads to existence and regularity t...
New Developments in the Visualization and Processing of Tensor Fields