Book Description

Emphasis on "cause and effect" in numerical mathematics.
* Flexibility with computing languages--the book is not specific to any one computing language. ... Read more

Reviews (1)

What does it mean?
For those students who have made it through the building blocks of math; algebra, calculus, linear algebra, differential equations, this is a good place to jump off into early applied mathematics.Dr. Epperson has written a good text book that will push your understanding of mathematics to a new level.

Hi Dr. Epp!! ... Read more

Book Description

A principal feature of this book is the substantial care and attention devoted to explaining the basic ideas of the subject. Whenever a new theoretical concept is introduced it is carefully explained by reference to practical examples drawn mainly from the physical sciences. Subjects covered include: spectral analysis which is closely intertwined with the "time domain" approach, elementary notions of Hilbert Space Theory, basic probability theory, and practical analysis of time series data. The inclusion of material on "kalman filtering", state-space filtering", "non-linear models" and continuous time" models completes the impressive list of unique and detailed features which will give this book a prominent position among related literature. The first sectionVolume 1deals with single (univariate) series, while the secondVolume 2treats the analysis of several (multivariate) series and the problems of prediction, forecasting and control. ... Read more

Reviews (2)

Theoretical
This book covers almost all possible aspects of spectral analysis of time series. The problem is that it is almost exclusively theoretical. It should not be used for learning spectral analysis but rather as a reference book. There are very few practical examples but when looking for a proof or an abstract presentation of a particular concept, this book should allow you to understand the theory that lies behind... However, a very good treatment of spectral analysis and very broad coverage of the subject...

Needs more examples but still very good.
I thought James D. Hamiltons book Time Serives Aanlysis was better. It was easier to understand and covered more material, including VAR models and State Space. Still this was and is an excellent book, and it goes into details about multivariate statistics that are not contained in Hamilton's book. I have the same complaint about this book as Hamilton's. Not enough examples. I compare these two books to those of Hosmer and Lemeshow's Applied Logistic Regression where there were nurmerous examples and problems to solve based on data they had provided.

Michael Quigley Director, Statistical Model and Data Mining Wells Fargo Bank ... Read more

Book Description

This book is the only source available thatpresents a unified view of the theory and applications of discrete andcontinuous- time signals.This is the only book to presentthe mathematical point of view, as well as the discrete-time signal processingperspective. It brings together information previously available only inresearch papers, in engineering and applied mathematics. Appropriate for researchers and practitioners in signal processing and appliedmathematics. ... Read more

Reviews (3)

If you don't know anything about Wavelet Analysis Start Here
I have examined most of the popluar books printed on the subject of Wavelet Analysis and this is the best book for those who want to understand what a wavelet is, where is comes from, and how is it is useful for performing Time Scale signal analysis. I strongly suggest starting with this book.

introduction to Wavelets and Wavelets transforms
The introduction to Wavelets and Wavelets transform aplications.

theoretically sound, non-trivial tutorial
This book is a crafted piece as opposed to one of those collections of journal articles that usually leave you wondering. It appears to have a sound theoretical foundation with some clearly presented definitions and theorems. I wouldn't hesitate to spend time with this one. ... Read more

Book Description

This companion volume to Andy Zonst's Understanding the FFT is written in five parts, covering a range of topics from transient circuit analysis to two dimensional transforms.It's an introducton to some of the many applicatons of the FFT, and it's intended for anyone who wants to understand and explore this technology.

The presentation is unique in that it avoids the calculus almost (but not quite) completely.It's a practical "how-to" book, but it also provides down to earth understanding.

This book developes computer programs in BASIC and the reader is encouraged to type these into a computer and run them; however, for those who don't have access to a BASIC compiler you may down load the programs from the internet (contact Citrus Press for URL).

The potential buyer should understand that presentations are frequently started at an elementary level.This is just a technique to establish the foundation for the subsequent discussion, intended for those who don't already understand the subject (the material usually comes quickly to the problem at hand).The book is written in an informal, tutorial style, and should be managable by anyone with a solid background in high school algebra, trigonometry, and complex arithmetic.Zonst has included the mathematics that might not be available in a high-school curriculum; so, if you managed to work your way through the first book, you should be able to handle this one.

For those familiar with the first edition of this book, the most prominant feature of this revised edition will be its improved coherence and readability. ... Read more

Book Description

From the reviews

"[...] This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. …The high quality of this work, [...] , makes a fascinating subject and its open problem as accessible as possible. [...]"

F.L. Spitzer in Mathematical Reviews, 1986

"[...] However, it can be said that the author has succeeded in what even experts are seldom able to achieve: To write a clearcut and inspiring book on his favorite subject which meets most, if not all requirements which can be imposed on a comprehensive text on an important new field. The author can be congratulated on his excellent presentation of the theory of interacting particle systems. The book is highly recommended to everyone who works on or is interested in this subject: to probabilists, physicists and theoretical biologists. [...]"

G. Rosenkranz in Methods of Information in Medicine, 1986

Book Description

The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills. ... Read more

Book Description

The analysis of time series data is essential to many areas of science, engineering, finance and economics. This introduction to wavelet analysis "from the ground level and up," and to wavelet-based statistical analysis of time series focuses on practical discrete time techniques, with detailed descriptions of the theory and algorithms needed to understand and implement the discrete wavelet transforms. Numerous examples illustrate the techniques on actual time series.The many embedded exercises--with complete solutions provided in the Appendix--allow readers to use the book for self-guided study. Additional exercises can be used in a classroom setting.A Web site offers access to the time series and wavelets used in the book, as well as information on accessing software in S-Plus and other languages. Students and researchers wishing to use wavelet methods to analyze time series will find this book essential. ... Read more

Reviews (5)

Well written.
Well written book. It would be nice to have some "MatLab" problems. Excellent motivational or explanatory examples.

I gave it three stars because most reviewers are far to liberal with their stars. To me 3 stars means worth buying, 4 means a must buy, and 5 means it'll be a classic for a long time.

I equate this book to Mallet's "A Wavelet Tour of Signal Processing". The subject matter is slightly different, but both are very readable.

Reference for time series analysts using wavelets
Few wavelet books offer such a deep insight into wavelet methods
for time series analysts. It goes very deep within the applied
side of wavelet analysis on real time series while not compromising
the mathematical side. A lot of books and papers insist too much
on the mathematical side of wavelets while this one provides just
the right balance between rigor and practical insight. If your
interest does not lie in maths but just in wavelets as a tool,
stick to this one.

As a bonus, it contains a lot of exercices along with answers
at the end of the book...a very good textbook indeed...

First rate all the way
As far as I am concerned,anything Don Percival writes about the topic of wavelets - or digital signal processing - is well worth reading. I was struggling to understand wavelets before I ran across a paper by Percival (and cohorts from the University of Washington) on interpreting remote sensing sea ice data using wavelets. After reading the very clear and compact description of wavelet analysis the light bulb clicked on for me. This book is a must read for anyone interested in wavelets from beginners to experienced practicioners.

introduction to wavelets for time series applications
The purpose of this text is to introduce wavelet methodology targeted toward applications in time series analysis. Emphasis is placed on the discrete wavelet transform and other discrete wavelets. There are many analogies to the spectral analysis of time series that the authors make. The authors do not assume knowledge of Fourier analysis and cover the relevent theory in Chapter 2. Just as the frequency domain methods decompose the variance of a time series into frequency components so to do wavelets decompose the variance according to scales. The authors take great pains in demonstrating this with several wavelets including the DWT and MODWT. Fast transform methods exist for wavelets as well as for Fourier series and they are apparently even simpler and faster for wavelets.

The text tries to be self-contained and the authors start out at a very elementary level. They emphasize applications and practical aspects of wavelets.

First class book on wavelets!!
This book offers a concise highly mathematical accurate analysis treatment of modern wavelet theory. It covers all essential material and should be suitable for those involved in Digital Signal Processing. ... Read more

Book Description

This book deals with the algebraic geometric method of studyingmultivariate splines. Topics treated include: the theory ofmultivariate spline spaces, higher-dimensional splines, rationalsplines, piecewise algebraic variety (including piecewise algebraiccurves and surfaces) and applications in the finite element method andcomputer-aided geometric design. Many new results are given. Audience: This volume will be of interest to researchers andgraduate students whose work involves approximations and expansions,numerical analysis, computational geometry, image processing andCAD/CAM. ... Read more

Book Description

Theory:- The objective of this book is to present themathematical background necessary to study nonlinear analysis,accompanied by numerous problems and solutions. ... Read more

Book Description

This text emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Students learn why the numerical methods work, what type of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are essentially the same as those covered in the authors' top-selling Numerical Analysis text, but in this text, full mathematical justifications are provided only if they are concise and add to the understanding of the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the student that the method is reasonable both mathematically and computationally. ... Read more

Reviews (1)

Good book for Numerical Methods Class
I had previously sat in on a Numerical Analysis class, and I have to say that this book was much better than the one that we were forced to use. The examples were clear, and the text focused much less on proofs and more on how to do problems and calculate their error. The sample programs on disk were also thorough, and included in several different languages (c, fortran, pascal, maple, mathematica, & matlab). ... Read more

Book Description

An outstanding textbook, complete with examples, exercises, and solutions, for an advanced calculus course in which differential forms can be used to introduce the subject. Enriching reading for its modern viewpoint and techniques. The diverse set of topics from which advanced calculus courses are created are presented here in beautiful unifying generalization.

This text has been adopted at: University of California, Davis Layfayette College, Easton, PA Western Illinois University, Macomb University of Michigan, Ann Arbor Eastern Washington University, Cheney ... Read more

Reviews (2)

Best book on Differential Forms for an Undergraduate.
This book is very well written, and being a reprint of a second edition, has very few misprints. Forms and their calculus are introduced in the 3D Euclidean space familiar to students of Calclulus 3 or University Physics. Later in the book the fundamentals like Stokes' Theorem are generalized to higher dimensions and manifolds. This book is suitable for anyone who has had Calculus 3 and is interested in a better way to do multiple-variable calculus. (Just to whet your appetite: after reading this book, you won't have to remember Green's Theorem, Stokes' Theorem, or the Divergence Theorem separately, they are all one compact and simple theorem {the one on the cover} in the language of Differential Forms.)

I, personally, had a lot of trouble with Flanders' and Darling's books on differential forms until I read some outside material on the subject. This book, however, starts off on a more basic level, and does not demand half the mathematical maturity that Flanders or Darling do. For more advanced topics, Flanders and Darling are fine books to go to, after getting the basics right here.

A GEM OF A BOOK ON DIFFERENTIAL FORMS
I can't believe that nonone has ever bothered to review this book. This is an outstanding book, filled with valuable insights. The author introduces differential forms right from the beginning. He provides associations with the utility of differential forms in Mathematical Physics through many examples. There is a lot of material in this book that cannot be covered easily, so the prospective reader is advised to be patient and initially skip sections when necessary. This is a book about advanced calculus via differential forms written with great care by someone who has thought things through very thoroughly. The book has all the attributes of a classic:

1. Excellent explanations and plenty of examples. 2. Conceptual clarity of key ideas, a rare feature these days. 3. Solutions of all the exercises in the book (truly a lot). 4. Rigorous but not terse mathematics.

Having read this book the reader can easily proceed to address more advanced topics without hesitation. I personally would have liked to have seen more applications in mathematical physics but this is by no means a criticism. The author wrote a book that is about the concept of differential forms in advanced calculus and in that he has succeeded admirably. Apparently this book was first published in 1969 and has gone in and out of print over the last three decades. So hurry up, go out and buy this book. ... Read more

Book Description

The theory of elastoplastic media is now a mature branch of solid and structural mechanics, having experienced significant development during the latter half of this century. This monograph focuses on theoretical aspects of the small-strain theory of hardening elastoplasticity. It is intended to provide a reasonably comprehensive and unified treatment of the mathematical theory and numerical analysis, exploiting in particular the great advantages to be gained by placing the theory in a convex analytic context. The book is divided into three parts. The first part provides a detailed introduction to plasticity, in which the mechanics of elastoplastic behavior is emphasized. The second part is taken up with mathematical analysis of the elastoplasticity problem. The third part is devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. The work is intended for a wide audience: this would include specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory. ... Read more

Book Description

The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest.

In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory.

In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader. ... Read more

Reviews (2)

Excellent in content, but somewhat challenging in narrative
Bela Bollobas has the rare gift of having both deep mathematical insights, and the ability to eloquently communicate them in a way that is accessible to the average graduate student. In his book "Modern Graph Theory", Bollobas covers just about every exciting area of the subject, and does so in an up-to-date fashion that gives the reader a big picture of each sub-area of the field. The ability to do this not only seems difficult, but also essential, since he himself has written entire books on two of the chapters (extremal graph theory, and random graphs). Just about every major important theorem (including max-flow/min-cut Theorem, and theorems by Menger, Szemeredi, Kuratowski, Erdos/Stone, and Tutte) can be found here, and thus makes this book indispensable for anyone who does research in graph theory, combinatorics, and/or complexity theory. In my opinion the true highlights of this book are indeed those areas he knows best: extremal graph theory, random graphs, and random walks on graphs, the latter of which may be the best introduction to that subject that one will find in a textbook.

My only complaint, at the cost of perhaps half a star, is that his discussions and proofs often seem difficult to follow, as he will state something that to him seems quite obvious, yet to this reader often seemed a bit subtle, and would hence slow down the reading. Indeed, if these off-handed remarks were included as exercises at the end of each chapter, then the number of excercises would have swelled from the current 600 to well over one thousand ! Speaking of which, these 600+ exercises, although also representing another blessing of this book in that they add another degree of depth, tend to lack "starter" exercises, and go straight to the theory. But this is to be expected from a graduate text.

Finally, for the reader whose research significantly intersects with graph theory, but may not be ready or willing to be initiated by Bollabas into the world of graph theory, I would recommend Dietsel's graduate text on the subject. His book covers similar topics, but may be more clearly and transparently, but with less depth and insight.

A good introduction book
My profile is the following: I am a phD student in theoretical computer science and I needed a good introduction book to graph theory.

This book is just what I needed... ... Read more

Book Description

Real Analysis and Foundations is an advanced undergraduate and first-year graduate textbook that introduces students to introductory topics in real analysis (or real variables), point set topology, and the calculus of variations. This classroom-tested book features over 350 end-of-chapter exercises that clearly develop and reinforce conceptual topics. It also provides an excellent review chapter on math foundations topics, as well as accessible coverage of classical topics, such as Weirstrass Approximation Theorem, Ascoli-Arzela Theorem and Schroeder-Bernstein Theorem. Explanations and discussions of key concepts are so well done that Real Analysis and Foundations will also provide valuable information for professional aerospace and structural engineers. ... Read more

Book Description

Here is a clear exposition of nonparametric smoothing methods for statisticians.The focus is applied rather than theoretical, with a large number of illustrations from different disciplines. ... Read more

Book Description

This edition is a comprehensive introduction to the basic ideas of modern mathematicalanalysis. Coverage proceeds form the elementary level to advanced and researchlevels. Additions to this edition include Rademacher's theorem on differentiability ofLipschitz Functions, deeper formulas on change of variables in multiple integrals, andrecent results on the extension of differentiable functions. ... Read more