Hardback
July 19, 2019 Forthcoming
Reference - 232 Pages - 47 B/W Illustrations
ISBN 9781138051584 - CAT# K33135
This book provides good coverage of the powerful numerical techniques namely, finite element and wavelets, for the solution of partial differential equation to the scientists and engineers with a modest mathematical background. The objective of the book is to provide the necessary mathematical foundation for the advanced level applications of these numerical techniques. The book begins with the description of the steps involved in finite element and wavelets-Galerkin methods. The knowledge of Hilbert and Sobolev spaces is needed to understand the theory of finite element and wavelet-based methods. Therefore, an overview of essential content such as vector spaces, norm, inner product, linear operators, spectral theory, dual space, and distribution theory, etc. with relevant theorems are presented in a coherent and accessible manner. For the graduate students and researchers with diverse educational background, the authors have focused on the applications of numerical techniques which are developed in the last few decades. This includes the wavelet-Galerkin method, lifting scheme, and error estimation technique, etc.
* Computer programs in Mathematica/Matlab are incorporated for easy understanding of wavelets.
* Presents a range of workout examples for better comprehension of spaces and operators.
* Algorithms are presented to facilitate computer programming.
* Contains the error estimation techniques necessary for adaptive finite element method.
This book is structured to transform in step by step manner the students without any knowledge of finite element, wavelet and functional analysis to the students of strong theoretical understanding who will be ready to take many challenging research problems in this area.
Preface
About the authors
1. Overview of finite element method
Some common governing differential equations
Basic steps of finite element method
Element stiffness matrix for a bar
Element stiffness matrix for single variable 2d element
Element stiffness matrix for a beam element
References for further reading
2. Wavelets
Wavelet basis functions
Wavelet-Galerkin method
Daubechies wavelets for boundary and initial value problems
References for further reading
3. Fundamentals of vector spaces
Introduction
Vector spaces
Normed linear spaces
Inner product spaces
Banach spaces
Hilbert spaces
Projection on finite dimensional spaces
Change of basis - Gram-Schmidt othogonalization process
Riesz bases and frame conditions
References for further reading
4. Operators
Mapping of sets, general concept of functions
Operators
Linear and adjoint operators
Functionals and dual space
Spectrum of bounded linear self-adjoint operator
Classification of differential operators
Existence, uniqueness and regularity of solution
References
5. Theoretical foundations of the finite element method
Distribution theory
Sobolev spaces
Variational Method
Nonconforming elements and patch test
References for further reading
6. Wavelet- based methods for differential equations
Fundamentals of continuous and discrete wavelets
Multiscaling
Classification of wavelet basis functions
Discrete wavelet transform
Lifting scheme for discrete wavelet transform
Lifting scheme to customize wavelets
Non-standard form of matrix and its solution
Multigrid method
References for further reading
7. Error - estimation
Introduction
A-priori error estimation
Recovery based error estimators
Residual based error estimators
Goal oriented error estimators
Hierarchical & wavelet based error estimator
References for further reading
Appendix
Combinatorics and finite fields are of great importance in modern applications
such as in the analysis of algorithms, in information and communication theory,
and in signal processing and coding theory. This book contains survey articles
on topics such as difference sets, polynomials, and pseudorandomness.
* A collection of surveys on applications of combinatorics and finite fields
* Covers applications in wireless communication, imaging, check-digit systems,
error-correcting codes, cryptography etc.
* Includes contributions by leading experts in the field
Kai-Uwe Schmidt, Paderborn University, Germany;Arne Winterhof, Radon
Institute for Computational and Applied Mathematics, Austria.
Radon Series on Computational and Applied Mathematics 23
Approx. xii, 350 pages, 7 Figures (bw),
5 Figures (c), 50 Schedule (bw)
Hardcover:
ISBN 978-3-11-064179-0
Date of Publication: July 2019
Language of Publication: English
Subjects: Algebra and Number Theory
Applied Mathematics
Discrete Mathematics
Of interest to: Researchers and graduate
students in discrete mathematics and computer science.
With a new preface by the author
Editions
Paperback 2019
ISBN 9780691191379 336 pp. x 221 b/w illus. 8 tables.
forthcoming July 2019
Leonhard Eulerfs polyhedron formula describes the structure of many objects?from soccer balls and gemstones to Buckminster Fullerfs buildings and giant all-carbon molecules. Yet Eulerfs theorem is so simple it can be explained to a child. From ancient Greek geometry to todayfs cutting-edge research, Eulerfs Gem celebrates the discovery of Eulerfs beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. Using wonderful examples and numerous illustrations, David Richeson presents this mathematical ideafs many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map. Filled with a whofs who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theoremfs development, Eulerfs Gem will fascinate every mathematics enthusiast. This paperback edition contains a new preface by the author.
David S. Richeson is professor of mathematics at Dickinson College.
gThe author has achieved a remarkable feat, introducing a naive reader to a rich history without compromising the insights and without leaving out a delicious detail. . . . An awe-inspiring experience.h?Choice
gThis is an excellent book about a great man and a timeless formula.h
Charles Ashbacher, Journal of Recreational Mathematics
Subject Areas
Mathematics - History & Philosophy
Mathematics - Topology
Mathematics - Geometry - General
Series
Series
Bolyai Society Mathematical Studies
Due 2019-05-31
1st ed. 2019, Approx. 420 p.
Printed book
Hardcover
ISBN 978-3-662-59203-8
Includes 14 contributions of leading researchers in the fields of
combinatorics and computer science
Builds bridges between discrete and continuous mathematics
Includes open problems in various connected areas
This volume collects together research and survey papers written by invited speakers of a
conference celebrating the 70th birthday of Laszlo Lovasz. The topics covered include classical
subjects such as extremal graph theory, coding theory, design theory, applications of linear
algebra and combinatorial optimization, as well as recent trends such as extensions of graph
limits, online or statistical versions of classical combinatorial problems, and new methods of
derandomization. Laszlo Lovasz is one of the pioneers in the interplay between discrete and
continuous mathematics, and is a master at establishing unexpected connections, gbuilding
bridgesh between seemingly distant fields. His invariably elegant and powerful ideas have
produced new subfields in many areas, and his outstanding scientific work has defined and
shaped many research directions in the last 50 years. The 14 contributions presented in this
volume, all of which are connected to Laszlo Lovasz's areas of research, offer an excellent
overview of the state of the art of combinatorics and related topics and will be of interest to
experienced specialists as well as young researchers.
Series
Trends in Mathematics
Due 2019-06-21
1st ed. 2019, XXIV, 263 p. 9
illus., 1 illus. in color.
Printed book
Hardcover
ISBN 978-981-13-7027-4
Presents a collection of research from David F. Anderson as well as other
experts in the field
Provides a valuable source of cutting-edge research in a number of subfields
of commutative algebra
Is useful to graduate students and researchers
This book highlights the contributions of the eminent mathematician and leading algebraist
David F. Anderson in wide-ranging areas of commutative algebra. It provides a balance of
topics for experts and non-experts, with a mix of survey papers to offer a synopsis of
developments across a range of areas of commutative algebra and outlining Andersonfs work.
The book is divided into two sections?surveys and recent research developments?with each
section presenting material from all the major areas in commutative algebra. The book is of
interest to graduate students and experienced researchers alike.