Book Description

Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. Its 11 chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.

Book Description

This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirements, and the danger of extrapolation to nonlinear problems methods used on linear problems. Numerical Methods for Partial Differential Equations, Third Edition reflects the great accomplishments that have taken place in scientific computation in the fifteen years since the Second Edition was published. This new edition is a drastic revision of the previous one, with new material on boundary elements, spectral methods, the methods of lines, and invariant methods. At the same time, the new edition retains the self-contained nature of the older version, and shares the clarity of its exposition and the integrity of its presentation.

Key Features
* Material on finite elements and finite differences have been merged, and now constitute equal partners
* Additional material has been added on boundary elements, spectral methods, the method of lines, and invariant methods
* References have been updated, and reflect the additional material
* Self-contained nature of the Second Edition has been maintained
* Very suitable for PDE courses ... Read more

Book Description

It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics.

The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them.

The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented.

The book reflects the unique experience of the authors. It distills a vast mathematical literature, most of which is unknown to the western public, and captures the essence of an abundant problem culture. The target audience includes undergraduates, high school students and their teachers, mathematical contestants (such as those training for Olympiads or the W.L. Putnam Mathematical Competition) and their coaches, as well as anyone interested in essential mathematics.

Book Description

This book contains detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own and graduates in mathematical sciences. ... Read more

Book Description

Time dependent problems frequently pose challenges in areas of science and engineering dealing with numerical analysis, scientific computation, mathematical models, and most importantly—numerical experiments intended to analyze physical behavior and test design. Time Dependent Problems and Difference Methods addresses these various industrial considerations in a pragmatic and detailed manner, giving special attention to time dependent problems in its coverage of the derivation and analysis of numerical methods for computational approximations to Partial Differential Equations (PDEs).

The book is written in two parts. Part I discusses problems with periodic solutions; Part II proceeds to discuss initial boundary value problems for partial differential equations and numerical methods for them. The problems with periodic solutions have been chosen because they allow the application of Fourier analysis without the complication that arises from the infinite domain for the corresponding Cauchy problem. Furthermore, the analysis of periodic problems provides necessary conditions when constructing methods for initial boundary value problems. Much of the material included in Part II appears for the first time in this book.

The authors draw on their own interests and combined extensive experience in applied mathematics and computer science to bring about this practical and useful guide. They provide complete discussions of the pertinent theorems and back them up with examples and illustrations.

For physical scientists, engineers, or anyone who uses numerical experiments to test designs or to predict and investigate physical phenomena, this invaluable guide is destined to become a constant companion. Time Dependent Problems and Difference Methods is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations.

What Every Physical Scientist and Engineer Needs to Know About Time Dependent Problems . . .

Time Dependent Problems and Difference Methods covers the analysis of numerical methods for computing approximate solutions to partial differential equations for time dependent problems. This original book includes for the first time a concrete discussion of initial boundary value problems for partial differential equations. The authors have redone many of these results especially for this volume, including theorems, examples, and over one hundred illustrations.

The book takes some less-than-obvious approaches to developing its material:

• Treats differential equations and numerical methods with a parallel development, thus achieving a more useful analysis of numerical methods
• Covers hyperbolic equations in particularly great detail
• Emphasizes error bounds and estimates, as well as the sufficient results needed to justify the methods used for applications

Time Dependent Problems and Difference Methods is written for physical scientists and engineers who use numerical experiments to test designs or to predict and investigate physical phenomena. It is also extremely useful to numerical analysts, mathematical modelers, and graduate students of applied mathematics and scientific computations. ... Read more

Book Description

Book Description

This English translation of the highly successful German textbook Numerische Mathematik covers the usual classical topics of numerical analysis, and also includes an up-to-date treatment of both splines and linear optimization methods. The text is designed to be used in a first course in numerical analysis at the upper division undergraduate level or at the beginning graduate level. It features a careful balance between mathematical rigor and numerical insight and includes many worked out numerical examples. Each section concludes with an extensive set of exercises which instructors should find useful in helping students to master the material. Moreover, the authors have also provided carefully researched historical notes which will be of particular interest to experts as well as students. ... Read more

Book Description

Numerical Computation of Internal and External Flows Volume 2: Computational Methods for Inviscid and Viscous Flows C. Hirsch, Vrije Universiteit Brussel, Brussels, Belgium This second volume deals with the applications of computational methods to the problems of fluid dynamics. It complements the first volume to provide an excellent reference source in this vital and fast growing area. The author includes material on the numerical computation of potential flows and on the most up-to-date methods for Euler and Navier-Stokes equations. The coverage is comprehensive and includes detailed discussion of numerical techniques and algorithms, including implementation topics such as boundary conditions. Problems are given at the end of each chapter and there are comprehensive reference lists. Of increasing interest, the subject has powerful implications in such crucial fields as aeronautics and industrial fluid dynamics. Striking a balance between theory and application, the combined volumes will be useful for an increasing number of courses, as well as to practitioners and researchers in computational fluid dynamics. Contents Preface Nomenclature Part V: The Numerical Computation of Potential Flows Chapter 13 The Mathematical Formulations of the Potential Flow Model Chapter 14 The Discretization of the Subsonic Potential Equation Chapter 15 The Computation of Stationary Transonic Potential Flows Part VI: The Numerical Solution of the System of Euler Equations Chapter 16 The Mathematical Formulation of the System of Euler Equations Chapter 17 The Lax — Wendroff Family of Space-centred Schemes Chapter 18 The Central Schemes with Independent Time Integration Chapter 19 The Treatment of Boundary Conditions Chapter 20 Upwind Schemes for the Euler Equations Chapter 21 Second-order Upwind and High-resolution Schemes Part VII: The Numerical Solution of the Navier-Stokes Equations Chapter 22 The Properties of the System of Navier-Stokes Equations Chapter 23 Discretization Methods for the Navier-Stokes Equations Index ... Read more

Book Description

The investigation of bounded solutions to systems of differential equations involve some important and challenging problems of perturbation theory of invariant toroidal manifolds. Linear nonautonomous equations arise as mathematical models in mechanics, chemistry, and biology and this monograph is a detailed study of the application of Lyapunov functions with variable sign, expressed in quadratic forms to the solution of problems including; preservation of invariant tori of dynamic systems under perturbation. The volume is a classic contribution to the literature on stability theory and provides a useful source of reference for graduates and researchers. ... Read more

Book Description

Introduction to discrete-event simulation with coverage of computer and statistical issues. Mathematical treatment of the theory is combined with programmed examples of how to put the theory into proper practice. New features of the second edition: Markov chain simulation, gradient estimation, better handling of asynchronous observations, updated treatment of indirect estimation, standardized time series, better ways to generate random fractions and integers, and 37 new problems. ... Read more

Book Description

This text focuses on the topics which are an essential part of the engineering mathematics course:ordinary differential equations, vector calculus, linear algebra and partial differential equations. Advantages over competing texts:1. The text has a large number of examples and problems - a typical section having 25 quality problems directly related to the text.2. The authors use a practical engineering approach based upon solving equations. All ideas and definitions are introduced from this basic viewpoint, which allows engineers in their second year to understand concepts that would otherwise be impossibly abstract. Partial differential equations are introduced in an engineering and science context based upon modelling of physical problems. A strength of the manuscript is the vast number of applications to real-world problems, each treated completely and in sufficient depth to be self-contained.3. Numerical analysis is introduced in the manuscript at a completely elementary calculus level. In fact, numerics are advertised as just an extension of the calculus and used generally as enrichment, to help communicate the role of mathematics in engineering applications.4.The authors have used and updated the book as a course text over a 10 year period.5. Modern outline, as contrasted to the outdated outline by Kreysig and Wylie.6. This is now a one year course. The text is shorter and more readable than the current reference type manuals published all at around 1300-1500 pages. ... Read more

Book Description

Authors Cheney and Kincaid show students of science and engineering the modern computer's potential for solving numerical problems and gives them ample opportunity to hone their skills in programming and problem solving.The text helps students learn about errors that inevitably accompany scientific computing and arms them with methods for detecting, predicting, and controlling these errors.In this edition a discussion of how to locate codes for numerical algorithms on the World Wide Web has been added.A new section on iterative methods for solving large systems of linear equations has also been added.A less scholarly approach and a different menu of topics sets this book apart from the authors' highly regarded NUMERICAL ANALYSIS: MATHEMATICS OF SCIENTIFIC COMPUTING, SECOND EDITION. ... Read more

Reviews (5)

From a student's view......Garbage
I had to use this book for an undergraduate Numerical Analysis class. I'm a Computer Science major with a math minor and this is my last semester. I found this book to be horrible when coupled with an instructor that is equally as horrible. The explainations are too short and lack examples, the problems in each chapter are hard to solve based on the chapter's explaination; they seem to deviate far beyond what was explained in the corresponding chapter. There are some formulas and theorem's mentioned that have no examples to show how they work.

The book is not totally at fault in my case. I also have a horrible instructor and have to rely soley on this book to learn the material. This book just makes it very, very hard to teach myself. My only praise of the book is it's pseudocode for implementing the methods explained. They can easily be used to program them in C++ or other languages.

Overall the book is very confusing but it is still far better than my instructor who doesn't explain anything or answer questions.

Basic but Good
This is a good, basic, undergraduate text covering scientific computing. It gives a nice, broad overview of some basic topics, problems for the student to solve, and is generic as far as programming languages are concerned.

That being said, for my use this book was not detailed enough and failed to go into sufficient detail into many different areas (such as the eigenproblem). It is definantly an undergrad text and would be an excellent choice for a 300-level math or computer science class, it also provides a good general background in numerical computing. In that regard this book is a fine choice.

Reader from Belgium compares to the wrong book
The description "it looks like they cut the 2nd edition in half and labeled it '4th edition'" would be approximately correct if you talk about the 2nd edition of the much more advanced text by approximately the same authors, "Numerical Analysis: Mathematics of Scientific Computing" by Kincaid, Cheney and Cheney, which was published in 1995 and does conform to the description "covered so much in detail". If you expect graduate level coverage, that is the book to get, not this one, which is an undergraduate text, and aimed at students that don't major in math.

A concise text for introductory numerical analysis
I am a mathematics professor at a liberal art college. This is one of the few textbooks that is suitable for our students who are mathematics majors or related sciences majors. The approach is mathematical and computer science oriented, rather than cookbook type or overwhemingly applied. I and my colleages use this text and recommend it.

Total piece of crap
Our professor for numerical analysis at the university told us to get this book because it covered so much in detail. He has the 2nd edition for some time now. I just got my 4th edition and it looks like they cut the 2nd edition in half and labeled it '4th edition'. Get another book instead. ... Read more

Reviews (1)

Some new and unexpected results
To the best of my knowledge, this is the third book that Henry Ibstedt has written about the natural numbers. In it, he investigates some of the problems first posed by Florentin Smarandache. The specific problems are:

1) Expressing an integer as the sum of consecutive integers.
2) Alternating iterations of the Pseudo-Smarandache and Euler phi function.
3) Alternating iterations of the Pseudo-Smarandache and the sum of divisors function.
4) Recursively-defined sequences that return integers for a large number of iterations and then suddenly do not.
5) The behavior of the Smarandache partial-perfect additive sequence.
6) Continued fractions created from one or two Smarandache sequences.
7) Smarandache additive k-k and subtractive k-k relationships.
8) Sequences of integers formed by concatenating consecutive integers.
9) The prime factors of the Smarandache symmetric sequence.

The Pseudo-Smarandache function Z(n) is the smallest positive integer m such that n evenly divides 1 + 2 + . . . + m. The Smarandache partial-perfect additive sequence has the recursive definition:

1) a(1) = a(2) = 1
2) a(2k+1) = a(k+1) - 1, k >0
3) a(2k+2) = a(k+1) +1, k > 0.

The Smarandache function, S(n) is the smallest integer m such that m! is divisible by n and a Smarandache additive k-k relationship is a situation where

S(n) + S(n+1) + . . . +S(n+k-1) = S(n+k+1) + . . . +S(n+k+k).

A subtractive k-k relationship is formed by replacing the additions by subtraction. The symmetric sequence is defined by performing the repeated concatenations

11, 1221, 123321, 12344321, 1234554321, 123456654321, 12345677654321, 1234567887654321, 123456789987654321, 1234567891010987654321, . . .

Ibstedt pushes the knowledge of these sequences beyond what was previously known. Once again, we learn that the natural numbers are the possessors of more properties than humans seem capable of comprehending. The mathematics is purely recreational in nature, and there are similarities to some major unsolved problems. The alternating iterations of the Pseudo-Smarandache function with classical functions of number theory demonstrates the falling into a cyclic behavior that is similar to the famous Collatz conjecture. It seems likely that there is a fundamental, albeit unknown, property of the natural numbers that remains to be discovered that will explain such behaviors.
Problems in mathematics are often solved by thinking outside the lines, using the results of similar, yet distinct operations to gain insight. As time goes on, I grow more convinced that the behavior of some of the Smarandache problems will yield insights into other problems. Ibstedt demonstrates some new and sometimes unexpected results, as he delves deeper into problems that are easy to understand but difficult to resolve. ... Read more

Book Description

This research monograph addresses recent developments of wavelet concepts in the context of large scale numerical simulation. It offers a systematic attempt to exploit the sophistication of wavelets as a numerical tool by adapting wavelet bases to the problem at hand. This includes both the construction of wavelets on fairly general domains and the adaptation of wavelet bases to the particular structure of function spaces governing certain variational problems. Those key features of wavelets that make them a powerful tool in numerical analysis and simulation are clearly pointed out. The particular constructions are guided by the ultimate goal to ensure the key features also for general domains and problem classes. All constructions are illustrated by figures and examples are given. ... Read more

Book Description

Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.