A Practical Guide to the Invariant Calculus

Author: Elizabeth Louise Mansfield
Publisher: Cambridge University Press
ISBN: 9781139487047
Release Date: 2010-04-29
Genre: Mathematics

This book explains recent results in the theory of moving frames that concern the symbolic manipulation of invariants of Lie group actions. In particular, theorems concerning the calculation of generators of algebras of differential invariants, and the relations they satisfy, are discussed in detail. The author demonstrates how new ideas lead to significant progress in two main applications: the solution of invariant ordinary differential equations and the structure of Euler-Lagrange equations and conservation laws of variational problems. The expository language used here is primarily that of undergraduate calculus rather than differential geometry, making the topic more accessible to a student audience. More sophisticated ideas from differential topology and Lie theory are explained from scratch using illustrative examples and exercises. This book is ideal for graduate students and researchers working in differential equations, symbolic computation, applications of Lie groups and, to a lesser extent, differential geometry.

From Frenet to Cartan The Method of Moving Frames

Author: Jeanne N. Clelland
Publisher: American Mathematical Soc.
ISBN: 9781470429522
Release Date: 2017-03-29
Genre: Differential geometry -- Classical differential geometry -- Affine differential geometry

The method of moving frames originated in the early nineteenth century with the notion of the Frenet frame along a curve in Euclidean space. Later, Darboux expanded this idea to the study of surfaces. The method was brought to its full power in the early twentieth century by Elie Cartan, and its development continues today with the work of Fels, Olver, and others. This book is an introduction to the method of moving frames as developed by Cartan, at a level suitable for beginning graduate students familiar with the geometry of curves and surfaces in Euclidean space. The main focus is on the use of this method to compute local geometric invariants for curves and surfaces in various 3-dimensional homogeneous spaces, including Euclidean, Minkowski, equi-affine, and projective spaces. Later chapters include applications to several classical problems in differential geometry, as well as an introduction to the nonhomogeneous case via moving frames on Riemannian manifolds. The book is written in a reader-friendly style, building on already familiar concepts from curves and surfaces in Euclidean space. A special feature of this book is the inclusion of detailed guidance regarding the use of the computer algebra system Mapleā„¢ to perform many of the computations involved in the exercises.

Symmetries and Integrability of Difference Equations

Author: Decio Levi
Publisher: Springer
ISBN: 9783319566665
Release Date: 2017-06-30
Genre: Science

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.

Volterra Integral Equations

Author: Hermann Brunner
Publisher: Cambridge University Press
ISBN: 9781107098725
Release Date: 2017-01-20
Genre: Mathematics

This book offers a comprehensive introduction to the theory of linear and nonlinear Volterra integral equations. It includes applications and an extensive bibliography.

Books in Series

Author:
Publisher:
ISBN: STANFORD:36105015640415
Release Date: 1979
Genre: Monographic series


Forthcoming Books

Author: R.R. Bowker Company. Department of Bibliography
Publisher:
ISBN: 00158119
Release Date: 2002
Genre:


Choice

Author:
Publisher:
ISBN: UCSC:32106007394221
Release Date: 1986
Genre: Academic libraries


Books in Print

Author:
Publisher:
ISBN: STANFORD:36105015915882
Release Date: 1991
Genre: American literature