The theory of traveling waves described by parabolic equations and systems is a rapidly developing branch of modern mathematics. This book presents a general picture of current results about wave solutions of parabolic systems, their existence, stability, and bifurcations. The main part of the book contains original approaches developed by the authors.
Download link
Archive for the ‘Mathematics’ Category
Traveling Wave Solutions of Parabolic Systems
Saturday, November 7th, 2009Unsolved Problems in Mathematical Systems and Control Theory
Thursday, November 5th, 2009This book provides clear presentations of more than sixty important unsolved problems in mathematical systems and control theory. Each of the problems included here is proposed by a leading expert and set forth in an accessible manner. Covering a wide range of areas, the book will be an ideal reference for anyone interested in the latest developments in the field, including specialists in applied mathematics, engineering, and computer science.
Download link
Von Neumann Algebras and Local Quantum Theory
Thursday, November 5th, 2009These notes are based on lectures given many years ago at the Institute of Physics, University of Sao Paulo, Brazil. The material includes an introduction to von Neumann algebras and modular theory and the beginnings of algebraic quantum theory.
Download link
What is String Theory?
Thursday, November 5th, 2009The first part is an introduction to conformal field theory and string perturbation theory. The second part deals with the search for a deeper answer to the question posed in the title. Contents: Conformal Field Theory; String Theory; Vacua and Dualities; String Field Theory or Not String Field Theory; Matrix Models.
Download link
Why the Boundary of a Round Drop Becomes a Curve of Order Four
Thursday, November 5th, 2009Description:
This book concerns the problem of evolution of a round oil spot surrounded by water when oil is extracted from a well inside the spot. It turns out that the boundary of the spot remains an algebraic curve of degree four in the course of evolution. This text discusses this topic and other recent work in the theory of fluid flows with a moving boundary.
Download link
A Problem Course in Mathematical Logic
Thursday, November 5th, 2009A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Moore-method.
Download link
A Problem Text in Advanced Calculus
Thursday, November 5th, 2009This is a text on Advanced Calculus written for a more “theoretical” course, usually taken by majors in mathematics and physical sciences (and often called elementary analysis or intermediate analysis), it concentrates on conceptual development and proofs. It is intended for students of mathematics and others who have completed (or nearly completed) a standard introductory calculus sequence and who wish to understand where all those rules and formulas come from.
A First Course in Linear Algebra
Thursday, November 5th, 2009A First Course in Linear Algebra is an introductory textbook aimed at college-level sophomores and juniors. Typically such a student will have taken calculus, but this is not a prerequisite. The book begins with systems of linear equations, then covers matrix algebra, before taking up finite-dimensional vector spaces in full generality. The final chapter covers matrix representations of linear transformations, through diagonalization, change of basis and Jordan canonical form. Along the way, determinants and eigenvalues get fair time.
Download link
A First Course in Complex Analysis
Thursday, November 5th, 2009These are the lecture notes of a one-semester undergraduate course which we taught at SUNY Binghamton. For many of our students, Complex Analysis is their first rigorous analysis (if not mathematics) class they take, and these notes reflect this very much. We tried to rely on as few concepts from real analysis as possible. In particular, series and sequences are treated “from scratch.” This also has the (maybe disadvantageous) consequence that power series are introduced very late in the course.
Download link
A Course of Modern Analysis
Thursday, November 5th, 2009This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever
Download link