Series: Dolciani Mathematical Expositions
Paperback (ISBN- 0-88385-334-5)
Publication is planned for March 2005 | 262 pages | 229 x 154 mm
Mathematical Delights is a collection of 90 short elementary gems
from algebra, geometry, combinatorics, and number theory. Ross
Honsberger presents us with some surprising results, brilliant
ideas, and beautiful arguments in mathematics, written in his
wonderfully lucid style. The book is a mathematical entertainment
to be read at a leisurely pace. High school mathematics should
equip the reader to handle the problems presented in the book.
The topics are entirely independent and can be read in any order.
A useful set of indices helps the reader locate topics in the
text. Ross Honsberger has published thirteen best-selling books
with the Mathematical Association of America including:
Mathematical Diamonds, Mathematical Chestnuts from Around the
World, From Erdos to Kiev and Ingenuity in Mathematics.
Contents
1. From mathematical miniatures; 2. From the contest problem book
VI; 3. From problem-solving through problems; 4. From Mathematics
magazine; 5. From the college mathematics journal; 6. From the pi
mu epsilon journal; 7. From problems in plene geometry; 8. From
the New Mexico mathematics contest problem book; 9. From
Leningrad olympiads; 10. From the contest problem book V; 11.
From quantum; 12. From the mathematical visitor; 13. From the
desk of Liong-Shin Hahn; 14. From the 2002 New Mexico mathematics
contest; 15. Two solutions by Archilleas Sinefakopoulas; 16.
Alternative solutions by George Evagelopoulos to three problems
from the 1982 West German olympiad; 17. A curious result in
geometry; 18. From the book of prime number records; References;
Index of publications.
Series: Classroom Resource Material
Hardback (ISBN-0-88385-740-5)
Publication is planned for March 2005 | 130 pages | 262 x 184 mm
This is a concise introduction to Fourier series covering
history, major themes, theorems, examples, and applications. It
can be used for self study, or to supplement undergraduate
courses on mathematical analysis. Beginning with a brief summary
of the rich history of the subject over three centuries, the
reader will appreciate how a mathematical theory develops in
stages from a practical problem (such as conduction of heat) to
an abstract theory dealing with concepts such as sets, functions,
infinity, and convergence. The abstract theory then provides
unforeseen applications in diverse areas. Exercises of varying
difficulty are included throughout to test understanding. A broad
range of applications are also covered, and directions for
further reading and research are provided, along with a chapter
that provides material at a more advanced level suitable for
graduate students.
Contents
1. Heat conduction and Fourier series; 2. Convergence of Fourier
series; 3. Odds and ends; 4. Convergence in L2 and L1; 5. Some
applications; A note on normalisation; A brief bibliography;
Index
Inverse and Ill-Posed Problems Series
The problems of determining coefficients of hyperbolic equations
and systems from additional information on their solutions are of
great practical significance. As a rule, the desired coefficients
are important characteristics of the media under consideration.
In this monograph, dynamic type of inverse problems in which the
additional information is given by the trace of the direct
problem solution on a (usually time-like) surface of the domain
is considered.
In this book theoretical and numerical background of the direct
methods are discussed. Theorems of convergence, conditional
stability and other properties of the mentioned above methods are
formulated and proven.
This book is of value and interest for students, postgraduate
students, engineers, and researchers who are interested in the
theory and numerics of inverse problems for hyperbolic equations.
2005; viii+180 pages
ISBN 90-6764-416-1
Contents:
Main definitions and notations
Introduction
CHAPTER 1. FINITE-DIFFERENCE SCHEME INVERSION (FDSI)
Introduction
Volterra operator equations
Definitions and examples
Convergence of FDSI
Numerical examples
CHAPTER 2. LINEARIZED MULTIDIMENSIONAL INVERSE PROBLEM FOR THE
WAVE EQUATION
Introduction
Problem formulation
Linearization
Analyzing the structure of the solution to one-dimensional direct
problem
Existence theorem for the direct problem
Uniqueness of solutions to the inverse problem and regularization
Numerical examples
CHAPTER 3. METHODS OF I.M. GEL'FAND, B.M. LEVITAN AND M. G. KREIN
Introduction
Gel'fand-Levitan-Krein (GLK) equation for one-dimensional inverse
problem
Multidimensional analog of GLK-equations
Gel'fand-Levitan method for wave equation
Discrete analog of the Gel'fand-Levitan equation
Multidimensional discrete analog
Numerical examples
CHAPTER 4. BOUNDARY CONTROL METHOD (BC METHOD)
Introduction. Statement of the problem
BC method in one-dimensional case
BC method for 2D acoustic inverse problem
Numerical examples
CHAPTER 5. PROJECTION METHOD
Introduction
Projection method for solving inverse problem for the wave
equation
Projection method for solving inverse acoustic problem
Numerical examples
Appendix A
Appendix B
Bibliography