Kategoria BISAC: Mathematics >> Mathematical Analysis

The use of elementary linear algebra in presenting the topics of multi- variable calculus is more extensive than usual in this book. It makes many of these topics easier to understand and remember. The book will prepare readers for more advanced math courses and also for courses in physical...

Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B.C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D.M. Bressoud), theta functions in complex analysis (H.M. Farkas),...

This book is motivated by stimulating problems in contact mechanics, emphasizing antiplane frictional contact with linearly elastic and viscoelastic materials. It focuses on the essentials with respect to the qualitative aspects of several classes of variational inequalities (VIs). Clearly presented, easy to follow, and well-referenced, this work treats almost entirely VIs of the second kind, with much of the material being state-of-the-art.

From reviews of the first edition:

"In the world of mathematics, the 1980's might well be described as the "decade of the fractal." Starting with Benoit Mandelbrot's remarkable text The Fractal Geometry of Nature, there has been a deluge of books, articles and television programmes about the beautiful mathematical objects, drawn by computers using recursive or iterative algorithms, which Mandelbrot christened fractals. Gerald Edgar's book is a significant addition to this deluge. Based on a course given to talented high- school students at Ohio University in 1988, it is, in fact,...

There is a range of literature dealing with the blow-up behavior of evolution equations, but this book 's fresh approach elucidates the theory by focusing on methodology, eschewing large-scale technical computations in favor of a simple illustrative equation.

In this text the authors consider the Korteweg-de Vries (KdV) equation (u_t = - u_xxx + 6uu_x) with periodic boundary conditions. Derived to describe long surface waves in a narrow and shallow channel, this equation in fact models waves in homogeneous, weakly nonlinear and weakly dispersive media in general.

Viewing the KdV equation as an infinite dimensional, and in fact integrable Hamiltonian system, we first construct action-angle coordinates which turn out to be globally defined. They make evident that all solutions of the periodic KdV equation are...