ISBN: 9781584885924
Publication Date: 11/09/2007
Pages: 440
Trim Size: 6-1/8 x 9-1/4
Binding(s): Hardback
About the Title
While maintaining the lucidity of the first edition, Discrete Chaos, Second Edition: With Applications in Science and Engineering now includes many recent results on global stability, bifurcation, chaos, and fractals. The first five chapters provide the most comprehensive material on discrete dynamical systems, including trace-determinant stability, bifurcation analysis, and the detailed analysis of the center manifold theory. This edition also covers L-systems and the periodic structure of the bulbs in the Mandelbrot set as well as new applications in biology, chemistry, and physics. The principal improvements to this book are the additions of PHASER software on an accompanying CD-ROM and the MapleEand Mathematica® code available for download online.
Incorporating numerous new topics and technology not found in similar texts, Discrete Chaos, Second Edition presents a thorough, up-to-date treatment of the theory and applications of discrete dynamical systems.
Table of Contents
Preface. The Stability of One-Dimensional Maps. Attraction and Bifurcation. Chaos in One Dimension. Stability of Two-Dimensional Maps. Bifurcation and Chaos in Two Dimensions. Fractals. The Julia and Mandelbrot Sets. Bibliography. Answers to Selected Problems. Index.
Series: Studies in Advanced Mathematics
ISBN: 9781584887454
Publication Date: 02/15/2008
Pages: 320
Trim Size: 6-1/8 x 9-1/4
Binding(s): Paperback
About the Title
The rapid growth of wavelet applications-speech compression and analysis, image compression and enhancement, and removing noise from audio and images-has created an explosion of activity in creating a theory of wavelet analysis and applying it to a wide variety of scientific and engineering problems. It becomes important, then, that engineers and scientists have a working understanding of wavelets. Until now, however, the study of wavelets has been beyond the mathematical grasp of many who need this understanding. Most treatments of the subject involve ideas from functional analysis, harmonic analysis, and other difficult mathematical techniques.
Wavelets and their Scientific Applications offers an introduction to wavelet analysis without mathematical rigor, requiring only algebra and some very basic calculus. The author stresses applications, and explains, using elementary algebra, how wavelet methods are typically applied in analyzing digital data.
Software is available for download through CRC's Website that will enable recording, playing, and modifying sound files, and includes a facility for displaying, printing and modifying IEEE gray field images. Unlike other software packages for wavelet analysis, the author developed this attractive, easy-to-use software without the need for a C++ compiler or MATLABE Throughout the book the author provides numerous suggestions for computer experiments designed to challenge and enhance the reader's comprehension and provide practice in applying the concepts learned.
Wavelets and their Scientific Applications thus provides the perfect vehicle for understanding wavelets and their uses. It provides a fast-track learning opportunity for scientists and mathematicians unfamiliar with wavelet concepts and applications, and it is ideal for anyone without an extensive mathematical background.
Table of Contents
Haar Wavelets. Daubechies Wavelets. Two-Dimensional Wavelets. Frequency Analysis. Beyond Wavelets. Software for Wavelet Analysis.
This unique book provides a collection of more than 200 mathematical problems and their detailed solutions, which contain very useful tips and skills in real analysis. Each chapter has an introduction, in which some fundamental definitions and propositions are prepared. This also contains many brief historical comments on some significant mathematical results in real analysis together with useful references.
Problems and Solutions in Real Analysis may be used as advanced exercises by undergraduate students during or after courses in calculus and linear algebra. It is also useful for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the prime number theorem through several exercises. The book is also suitable for non-experts who wish to understand mathematical analysis.
Readership: Undergraduates and graduate students in mathematical analysis.
Contents:
Sequences and Limits
Infinite Series
Continuous Functions
Differentiation
Integration
Improper Integrals
Series of Functions
Approximation by Polynomials
Convex Functions
Various Proof Ä(2) = Î2/6
Functions of Several Variables
Uniform Distribution
Rademacher Functions
Legendre Polynomials
Chebyshev Polynomials
Gamma Function
Prime Number Theorem
Miscellanies
304pp Pub. date: Nov 2007
ISBN 978-981-277-601-3
ISBN 978-981-277-949-6(pbk)
Series on Knots and Everything
This volume is a result of the author's four decades of research in the field of Fibonacci numbers and the Golden Section and their applications. It provides a broad introduction to the fascinating and beautiful subject of the "Mathematics of Harmony," a new interdisciplinary direction of modern science. This direction has its origins in "The Elements" of Euclid and has many unexpected applications in contemporary mathematics (a new approach to a history of mathematics, the generalized Fibonacci numbers and the generalized golden proportions, the "golden" algebraic equations, the generalized Binet formulas, Fibonacci and ggoldenh matrices), theoretical physics (new hyperbolic models of Nature) and computer science (algorithmic measurement theory, number systems with irrational radices, Fibonacci computers, ternary mirror-symmetrical arithmetic, a new theory of coding and cryptography based on the Fibonacci and "golden" matrices).
The book is intended for a wide audience including mathematics teachers of high schools, students of colleges and universities and scientists in the field of mathematics, theoretical physics and computer science. The book may be used as an advanced textbook by graduate students and even ambitious undergraduates in mathematics and computer science.
Contents:
The Golden Section
Fibonacci and Lucas Numbers
Regular Polyhedrons
Generalizations of Fibonacci Numbers and the Golden Section
Hyperbolic Fibonacci and Lucas Functions
Fibonacci and the gGoldenh Matrices Algorithmic Measurement Theory
Fibonacci Computers
Number Systems with Irrational Radices
Ternary Mirror-Symmetrical Arithmetic
Fibonacci and "Golden" Matrices and a New Theory of Coding
Appendices:
The Most Important Mathematical Results of the Harmony Mathematics
The Museum of Harmony and the Golden Section
Readership: Researchers, teachers and students in mathematics (especially those interested in the Golden Section and Fibonacci numbers), theoretical physics and computer science.
600pp (approx.) Pub. date: Scheduled Spring 2008
ISBN 978-981-277-582-5
Series on Knots and Everything - Vol. 21
LinKnot ? Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics.
The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves.
Hands-on computations using Mathematica or the webMathematica package LinKnot (available online at http://math.ict.edu.yu) and beautiful illustrations facilitate better learning and understanding. LinKnot is also a powerful research tool for experimental mathematics implementation of Caudron's ideas. The use of Conway notation enables experimenting with large families of knots and links.
Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.
Contents:
Notation of Knots and Links
Recognition and Generation of Knots and Links
History of Knot Theory and Applications of Knots and Links
Readership: Researchers interested in knot theory and users of Mathematica.
500pp Pub. date: Nov 2007
ISBN 978-981-277-223-7