Product Description
Many advances have taken place in the field of combinatorial algorithms since Methods of Mathematical Economics first appeared two decades ago. Despite these advances and the development of new computing methods, several basic theories and methods remain important today for understanding mathematical programming and fixed-point theorems. In this easy-to-read classic, readers learn Wolfe's method, which remains useful for quadratic programming, and the Kuhn-Tucker theory, which underlies quadratic programming and most other nonlinear programming methods. In addition, the author presents multiobjective linear programming, which is being applied in environmental engineering and the social sciences.

The book presents many useful applications to other branches of mathematics and to economics, and it contains many exercises and examples. The advanced mathematical results are proved clearly and completely. By providing the necessary proofs and presenting the material in a conversational style, Franklin made Methods of Mathematical Economics extremely popular among students. The addition of a list of errata, new to this edition, should add to the book's popularity as well as its usefulness both in the classroom and for individual study.

The book has three chapters: "Linear Programming," "Nonlinear Programming," and "Fixed-Point Theorems." The first and third chapters include the economic equilibrium theorems of von Neumann and of J. F. Nash, while the second chapter includes Kuhn-Tucker theory and Wolfe's simplex algorithm for quadratic programming. The book concludes with easy, elementary proofs of the famous theorems of Brouwer, of Kakutani, and of Schauder. These fundamental results are usually proved only in advanced texts in topology, economic theory, and nonlinear analysis.

Audience
This book is intended for undergraduate and graduate students of mathematics and economics; it requires no background in these areas except an understanding of elementary calculus and linear algebra.

Contents
Preface to the Classics Edition; Preface; Errata; Chapter 1: Linear Programming. Introduction to Linear Programming; Linear Programs and Their Duals; How the Dual Indicates Optimality; Basic Solutions; The Idea of the Simplex Methods; Separating Planes for Convex Sets; Finite Cones and the Farkas Alternative; The Duality Principle; Perturbations and Parametric Programming; The Simplex Tableau Algorithm; The Revised Simplex Algorithm; A Simplex Algorithm for Degenerate Problems; Multiobjective Linear Programming; Zero-Sum, Two-Person Games; Integer Programming: Gomory's Method; Network Flows; Assignment and Shortest-Route Problems; The Transportation Problem; Chapter 2: Nonlinear Programming. Wolfe's Method for Quadratic Programming; Kuhn-Tucker Theory; Geometric Programming; Chapter 3: Fixed-Point Theorems. Introduction to Fixed Points; Contraction Mappings; Garsia's Proof of the Brouwer Fixed-Point Theorem; Milnor's Proof of the Brouwer Fixed-Point Theorem; Barycentric Coordinates, Sperner's Lemma, and an Elementary Proof of the Brouwer Fixed-Point Theorem; The Schauder Fixed-Point Theorem; Kakutani's Fixed-Point Theorem and Nash's Theorem for n-Person Games; Index. ... Read more

Customer Reviews (1)

Outdated, but has a unique collection of interesting topics
This text attempts to survey the core subjects in optimization and mathematical economics: linear and nonlinear programming, separating plane theorems, fixed-point theorems, and some of their applications.

This text covers only two subjects well: linear programming and fixed-point theorems. The sections on linear programming are centered around deriving methods based on the simplex algorithm as well as some of the standard LP problems, such as network flows and transportation problem. I never had time to read the section on the fixed-point theorems, but I think it could prove to be useful to research economists who work in microeconomic theory. This section presents four different proofs of Brouwer fixed-point theorem, a proof of Kakutani's Fixed-Point Theorem, and concludes with a proof of Nash's Theorem for n-person Games.

Unfortunately, the most important math tools in use by economists today, nonlinear programming and comparative statics, are barely mentioned. This text has exactly one 15-page chapter on nonlinear programming. This chapter derives the Kuhn-Tucker conditions but says nothing about the second order conditions or comparative statics results.

Most likely, the strange selection and coverage of topics (linear programming takes more than half of the text) simply reflects the fact that the original edition came out in 1980 and also that the author is really an applied mathematician, not an economist.This text is worth a look if you would like to understand fixed-point theorems or how the simplex algorithm works and its applications. Look elsewhere for nonlinear programming or more recent developments in linear programming. ... Read more

Product Description

Peter Kall and János Mayer are distinguished scholars and professors of Operations Research and their research interest is particularly devoted to the area of stochastic optimization. Stochastic Linear Programming is a definitive presentation and discussion of the theoretical properties of the models, the conceptual algorithmic approaches, and the computational issues relating to the implementation of these methods to solve problems that are stochastic in nature.

Product Description

Based on a streamlined presentation of the authors' successful work Linear Systems, this textbook provides an introduction to systems theory with an emphasis on control. The material presented is broad enough to give the reader a clear picture of the dynamical behavior of linear systems as well as their advantages and limitations. Fundamental results and topics essential to linear systems theory are emphasized. The emphasis is on time-invariant systems, both continuous- and discrete-time.

Key features and topics:

* Notes, references, exercises, and a summary and highlights section at the end of each chapter.

* Comprehensive index and answers to selected exercises at the end of the book.

* Necessary mathematical background material included in an appendix.

* Helpful guidelines for the reader in the preface.

* Three core chapters guiding the reader to an excellent understanding of the dynamical behavior of systems.

* Detailed coverage of internal and external system descriptions, including state variable, impulse response and transfer function, polynomial matrix, and fractional representations.

* Explanation of stability, controllability, observability, and realizations with an emphasis on fundamental results.

* Detailed discussion of state-feedback, state-estimation, and eigenvalue assignment.

* Emphasis on time-invariant systems, both continuous- and discrete-time. For full coverage of time-variant systems, the reader is encouraged to refer to the companion book Linear Systems, which contains more detailed descriptions and additional material, including all the proofs of the results presented here.

* Solutions manual available to instructors upon adoption of the text.

A Linear Systems Primer is geared towards first-year graduate and senior undergraduate students in a typical one-semester introductory course on systems and control. It may also serve as an excellent reference or self-study guide for electrical, mechanical, chemical, and aerospace engineers, applied mathematicians, and researchers working in control, communications, and signal processing.

Also by the authors: Linear Systems, ISBN 978-0-8176-4434-5.

Customer Reviews (1)

Very good primer
I used this book for graduate course on linear systems theory. The book covers all important parts of linear systems theory. All the parts are very good explained. I think the style of the book is friendly to newcomers and certainly is suitable for graduate students. Every chapter contains a lot of examples that always help understanding the theory. I really liked studying with this book and I still use it as a reference.
... Read more

Product Description
This reprint of the 1969 book of the same name is a concise, rigorous, yet accessible, account of the fundamentals of constrained optimization theory. Many problems arising in diverse fields such as machine learning, medicine, chemical engineering, structural design, and airline scheduling can be reduced to a constrained optimization problem. This book provides readers with the fundamentals needed to study and solve such problems. Beginning with a chapter on linear inequalities and theorems of the alternative, basics of convex sets and separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions. ... Read more

Customer Reviews (1)

Learn how to write a clear and didactic math book
This book addresses only Nonlinear Programming Theory.
You will not find any algorithms, so that this book is not very practical. I also think the choice of topics could be better.

So, why 5 stars ?

Because of the writing style.

That is, what I like most in this book is the way that Mangasarian wrote it. References to all important equations, definitions, etc. No use of english to explain math subjects but well defined equations. Concise exposition and proof of theorems using math simbols. That is: Math simbols to explain mathematics. Very clear style.

A very good example of how to write an excellent, didactic, precise and clear math book. ... Read more

Product Description
A unique, applied approach to problem solving in linear algebra

Departing from the standard methods of analysis, this unique book presents methodologies and algorithms based on the concept of orthogonality and demonstrates their application to both standard and novel problems in linear algebra. Covering basic theory of linear systems, linear inequalities, and linear programming, it focuses on elegant, computationally simple solutions to real-world physical, economic, and engineering problems. The authors clearly explain the reasons behind the analysis of different structures and concepts and use numerous illustrative examples to correlate the mathematical models to the reality they represent. Readers are given precise guidelines for:
* Checking the equivalence of two systems
* Solving a system in certain selected variables
* Modifying systems of equations
* Solving linear systems of inequalities
* Using the new exterior point method
* Modifying a linear programming problem

With few prerequisites, but with plenty of figures and tables, end-of-chapter exercises as well as Java and Mathematica programs available from the authors' Web site, this is an invaluable text/reference for mathematicians, engineers, applied scientists, and graduate students in mathematics. ... Read more

Customer Reviews (1)

Good book!
A linear combination of vectors allows any coefficient - positive or negative. A more powerful concept is the "cone" of a set of vectors which allows only positive combinations (more powerful because a linear space is the union of two cones, but a cone can never be expressed as a linear space). While there are many many good books on the "algebra of linear spaces" (i.e. Linear Algebra) I havent seen any that treat the "algebra of cones" with the thoroughness that this book does. I found this book useful to derive existence proofs in combinatorial optimization although the material is fundamental enough to be applied in many more fields. Best used if you have a reasonably good grasp of linear algebra. ... Read more

Product Description
Linear Programming is a well-written introduction to the techniques and applications of linear programming. It clearly shows readers how to model, solve, and interpret appropriate linear programming problems.

Feiring has presented several carefully-chosen examples which provide a foundation for mathematical modelling and demonstrate the wide scope of the techniques. He subsequently develops an understanding of the Simplex Method and Sensitivity Analysis and includes a discussion of computer codes for linear programming.

This book should encourage the spread of linear programming techniques throughout the social sciences and, since it has been developed from Feiring's own class notes, it is ideal for students, particularly those with a limited background in quantitative methods.

Product Description
An accessible treatment of the modeling and solution of integer programming problems, featuring modern applications and software

In order to fully comprehend the algorithms associated with integer programming, it is important to understand not only how algorithms work, but also why they work. Applied Integer Programming features a unique emphasis on this point, focusing on problem modeling and solution using commercial software. Taking an application-oriented approach, this book addresses the art and science of mathematical modeling related to the mixed integer programming (MIP) framework and discusses the algorithms and associated practices that enable those models to be solved most efficiently.

The book begins with coverage of successful applications, systematic modeling procedures, typical model types, transformation of non-MIP models, combinatorial optimization problem models, and automatic preprocessing to obtain a better formulation. Subsequent chapters present algebraic and geometric basic concepts of linear programming theory and network flows needed for understanding integer programming. Finally, the book concludes with classical and modern solution approaches as well as the key components for building an integrated software system capable of solving large-scale integer programming and combinatorial optimization problems.

Throughout the book, the authors demonstrate essential concepts through numerous examples and figures. Each new concept or algorithm is accompanied by a numerical example, and, where applicable, graphics are used to draw together diverse problems or approaches into a unified whole. In addition, features of solution approaches found in today's commercial software are identified throughout the book.

Thoroughly classroom-tested, Applied Integer Programming is an excellent book for integer programming courses at the upper-undergraduate and graduate levels. It also serves as a well-organized reference for professionals, software developers, and analysts who work in the fields of applied mathematics, computer science, operations research, management science, and engineering and use integer-programming techniques to model and solve real-world optimization problems. ... Read more

Customer Reviews (1)

An Excellent Application Text
A timely, comprehensive, easy-to-read, and self-contained application textbook for integer programming - the first readable text this 30 year veteran has seen in a decade - a must-have for every practitioner. The book is formatted as a traditional textbook, with problems at the end of each chapter, and solutions in the back of the book for many of the more difficult problems. This text is a natural extension of the well-known introductory texts: e.g. Winston. An extensive reference list bridges the practical solutions to the underlying theory. The references are linked from the historical notes at the end of each chapter. The text covers integer programming in 3 major sections: modeling, linear programming theory, and classical and modern solutions.

The modeling section covers all the classical problems: knapsack, production planning, and scheduling - followed by the network models: assignment, transshipment, maxflow, and shortest path.

Since linear programming based branch and bound solutions are state-of-the-art, the second section reviews linear programming fundamentals as both a traditional linear algebra formulation and, in preparation for branch and bound cuts, a geometrical formulation where the columns are the basis vectors spanning the feasible solution space. Figures are extensively used to crystallize the geometric concepts.

In the final, integer programming methods are covered in general: branch and bound, cutting plane, and group theoretic - focusing on using the methods in combinations, especially, branch and bound with cutting plane. Detailed, but tractable, examples with figures are included every step of the way emphasizing how and why the algorithms work. Rarely introduced in a text are 3 modeling languages that can actually be used in commercial applications.

An excellent application text - enjoy.
... Read more

Customer Reviews (2)

From the author of Approximate Dynamic Programming
If you believe in the axiom "less is more," this is an outstanding book.This is the book that attracted me to the field of dynamic programming.The presentation is exceptionally clear, and gives an introduction to the simple, elegant problems that makes the field so addictive.It takes only a few afternoons to go through the entire book.In fact, it was memories of this book that guided the introduction to my own book on approximate dynamic programming (see chapter 2).

Once you have been drawn to the field with this book, you will want to trade up to Puterman's much more thorough presentation in Markov Decision Processes: Discrete Stochastic Dynamic Programming (Wiley Series in Probability and Statistics).But be forewarned - this elegant theory, which uses a "flat representation" of states (where states are numbered 1, 2, ..., S), suffers from the well-known curse of dimensionality, limiting its practical application.If your interests are drawn to real problems, you might consider my recent book Approximate Dynamic Programming: Solving the Curses of Dimensionality (Wiley Series in Probability and Statistics), which puts far more emphasis on modeling and practical algorithms drawn from the field of approximate dynamic programming.Other important references in this field are Neuro-Dynamic Programming (Optimization and Neural Computation Series, 3), and Reinforcement Learning: An Introduction (Adaptive Computation and Machine Learning).

Warren B. Powell
Professor
Princeton University

Good Examples BUT...a little too theoretical
I've used this book for a graduate course in Dynamic Programming.Having used many of Mr. Ross's books (undergraduate and graduate), I found this one lacks the detail and lucidity (particularly the end of chapterproblems...I believe in "learning by doing"... i.e. solve lots ofproblems!) that I have come to know of his books (e.g. A First Course inProbability and Introduction to Probability Models).The bright spot ofthe book is its examples, which are interesting and fairly detailed. ... Read more

Product Description
A complete and accessible introduction to the real-world applications of approximate dynamic programming

With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines—Markov design processes, mathematical programming, simulation, and statistics—to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems.

Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues.

With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming:

• Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects

• Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics

• Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms

• Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book

Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts. ... Read more

Customer Reviews (4)

Great coverage, great depth
The author had a challenge: how to introduce an algorithmic framework with a wide scope were different historical path have led to similar concepts but expressed and applied differently? Given this difficulty, I give the author five stars for the result. The subject is "approached" differently over each early chapter, this has the advantage of providing a true depth of subject. (The disadvantage is that it may confuse the reader). Then in the later chapters, Dr. Powell solidifies the subject by generalizing its application and by providing multiple proofs with different levels of sophistications. It is therefore not an easy book, but it is very readable, thanks to many excellent examples of applications of the concepts.

Approximate Dynamic Programming for practioners
Our consulting firm has successfully collaborated with Dr. Powell for years and I have seen first hand how ADP solves large scale, real world problems that would frankly be intractable by many traditional traditional operations research or optimization techniques.While consulting firms and other business jealously guard their intellectual property, it is terrific for all of us that academics are rewarded for precisely the opposite.I would highly recommend for any serious practitioner to grab a copy of this book and study it.Probably one of the best $100s you will have spent in a while.

Approximate Dynamic Programming for practitioners and education
In this book Warren nicely blends his practical experience in modeling and solving complex dynamic and stochastic problems occurring in a variety of industries (transportation, the financial sector,energy, etc) with algorithmical and theoretical aspects of approximate dynamic programming. The book can be either used as a textbook in undergraduate or graduate courses, or for practitioners to learn about recent advances in this exciting area. Indeed, I have already used it twice as a textbook for a graduate course, and on the other hand, I have recommended it to several practitioners. Without doubt, this is an important contribution in approximate dynamic programming.

I strongly recommend the book for all practitioners facing large-scale complex dynamic programs. It is also an excellent textbook.

Perspectives from the author
This book represents a paradigm shift in the presentation of dynamic programming/stochastic optimization.Classical treatments of dynamic programming/neuro-dynamic programming/reinforcement learning typically assume small "action spaces," and often assume the presence of a one-step transition matrix.By contrast, authors working with decision vectors in the presence of uncertainty often turn to stochastic linear programming.But these techniques typically struggle when applied to multistage applications.It is extremely hard to solve most of these problems without taking advantage of the presence of a state variable that captures previous history.

I have adopted the notational style where S is the state of the system, and x is a decision, using the language of math programming.x may have many thousands of dimensions for some problem classes (although the book considers many classical problems where decisions are relatively simple).

The challenge that arises when x is a vector when we use dynamic programming is the expectation within the max/min operator.Bellman's equation is typically written

V(S_t) = max (C(S_t,x) + discount * E{V(S_{t+1})|S_t} )

If x is a vector, we generally need the power of math programming to solve the maximization problem.The challenge is the expectation.We avoid this using the post-decision state variable, which is the state immediately after we have made a decision, but before any time has passed (bringing new information).Denoted S^x_t, the post-decision state variable is a deterministic function of S and x.If V^x(S^x_t) is the value function around the post-decision state variable, we obtain

V(S_t) = max (C(S_t,x) + discount * V^x(S^x_t)

The book provides a number of practical examples of this, but the key is that the maximization problem is now a deterministic problem.The final step is that we have to replace V^x() with a suitably chosen approximation.If our maximization problem is a linear, nonlinear or integer programming problem, we have to choose an approximation for V^x() that allows these algorithmic tools to be used. ... Read more

Product Description

From the reviews: "Do you know M.Padberg's Linear Optimization and Extensions? […] Now here is the continuation of it, discussing the solutions of all its exercises and with detailed analysis of the applications mentioned. Tell your students about it. […] For those who strive for good exercises and case studies for LP this is an excellent volume." Acta Scientiarum Mathematicarum

Customer Reviews (2)

Computational and Mathematical Excellence
For nearly 30 years, Padberg has been a leader in computational integer programming and in combinatorial optimization theory.

In practice, Padberg has helped to design and implement "branch-and-cut" methods for finding exact optimal solutions to large traveling salesman problems, and this approach is a method of choice for finding approximately optimal solutions to tough industrial problems.The book provides the mathematical and computational background for understanding branch-and-cut; the established mathematical texts by Nemhauser and Wolsey and by Schrijver are less detailed and more condensed, and omit numerical issues.The treatment of modern simplex algorithms for linear programming---updating LU factorizations and using column- and constraint-generation and -purging---is excellent, and a large bibliography contains recent references.Besides industrial and Berlin-airlift scheduling problems, the book contains TSP examples of circuit-board wiring, U.S. state capitals, and Odysseus!

Three more highlights: The double description algorithm receives a complete description, and this is useful for combinatorial geometers.The discussion of integer-arithmetic and complexity theory is very readable, and these technical topics are slighted by interior-point books (besides Wright's quickie), despite their importance in integer programming and combinatorial optimization. The discussion of interior-point algorithms emphasizes projective geometry, a beautiful theory that has inspired so much of optimization theory---besides Karmarkar's interior-point algorithm,Dantzig's simplex algorithm, Fenchel duality, Davidon's conic algorithm for nonlinear optimization, etc.).

The book is not a comprehensive survey of linear programming,
and lacks a treatment of Nesterov's theory of self-concordant barrier-functions.Also, no treatment is given of pivoting algorithms besides Dantzig's (e.g., Terlaky's criss-cross method, Todd's oriented matroid algorithm).

A good reference for Linear Programming Theory
This book is certainly a very good reference for theoretical topics of linear programming. It covers the Simplex method and the Ellipsoid algorithms. It also covers the geometry of linear programming (polyhedraand polytopes, etc). It certainly covers more topics than most other linearprogramming texts.As expected, a book writen for theoretical topics iscertainly not easy to read, especially for people with no training in doingrigorous mathematical proofs. Also, not many examples or illustrations aregiven in this book, and this might be a problem for some readers. ... Read more

Product Description
Linear programming is widely used in industry to solve complex planningand resource allocation problems. This book provides practitioners aswell as students of this general methodology with an easily accessibleintroduction to the new class of algorithms known as interior-pointmethods for linear programming. In addition to presenting thetheoretical and algorithmic background necessary for dealing withspecific interior-point linear programming algorithms, it offers areview of modeling linear programming problems, a review of the simplexalgorithm that has been used to solve linear programming problems in thepast, and a complete user's guide to the software that is included withthe book. Foundations of Computing series, Research Reports and Notes ... Read more

Customer Reviews (1)

Exploring Interior Point Linear Programming
Very good, easy to understand introduction of interior point methods.No advanced methods included, but does discuss implementation issues.Also a nice intro to the simplex method. ... Read more

Product Description
Introduces multiple criteria and multiple constraint levels linear programming which is an extension of linear programming and multiple criteria linear programming. ... Read more

Product Description
Linear programming represents one of the major applications of mathematics to business, industry, and economics. It provides a methodology for optimizing an output given that is a linear function of a number of inputs. George Dantzig is widely regarded as the founder of the subject with his invention of the simplex algorithm in the 1940's. This second volume is intended to add to the theory of the items discussed in the first volume. It also includes additional advanced topics such as variants of the simplex method, interior point methods (early and current methods), GUB, decomposition, integer programming, and game theory.Graduate students in the fields of operations research, industrial engineering, and applied mathematics will find this volume of particular interest. ... Read more

Customer Reviews (1)

interesting book
There is an example of piecewise linear convex problem which Iwas looking for. ... Read more

Product Description
Now in an accessible paperback edition, this classic work is just as relevant as when it first appeared in 1974, due to the increased use of nonlinear waves. It covers the behavior of waves in two parts, with the first part addressing hyperbolic waves and the second addressing dispersive waves. The mathematical principles are presented along with examples of specific cases in communications and specific physical fields, including flood waves in rivers, waves in glaciers, traffic flow, sonic booms, blast waves, and ocean waves from storms. ... Read more

Customer Reviews (3)

Good book
I took some graduate level courses from Dr. Whitham at CalTech in 1973 while this book was still in draft form, and he was the head of the Applied Mathematics department. He was an excellent lecturer, and this book has long been an exemplar of that style as well as the pioneer book in the treatment of non linear waves. To my knowledege it was the first textbook to treat solitons. The book is very subtle in its treatment of physics, and the adept reader will note the bearing of dispersion relations on the foundations of quantum mechanics.

good backround
Most treatment of waves involves their role in electromagnetic spectra. The writer provides the historical account of the derivation of these algebraic (read numerical analysis) versions which implement in MathCad andMatlab well. The book's material on water waves is worth the price alone.However, only at the end,does the author venture into the world ofnon-linear dynamics which is so important to this area. Most of the booktreats the wave phenomenology as most physicists will in the kinematicalsense trying to linearize everything and avoiding the path if it can't belinearized. (In this sense most of the arguements and examples arestructured in the conservation of mass and energy). This is great, howeverfor the construction of first order linear diff. equations forimplementation in Mathcad or Matlab. If one were not aware of bifurcations,limit-cycles or even total response waves from control theory, one wouldstill be left feeling secure that water waves are standing waves. (They arenot). Early research breaks them up into first part(Airy)long-standing(middle of the wave) and orgin to get around this problem.Book does not approach treatment as a diffusion problem.

The most understandable treatment of waves I have read!
Linear and Nonlinear Waves provides an excellent treatment of the wave phenomena.This is a very complex and mathematically intesive subject, which Whitham conveys in an understandable and followable manner.He takes the approach that the reader has some knowlege of the subject, but writes at an introductory graduate level.This book will give any mathematician or engineer interested in waves an excellent introduction and bring them to a superior understanding. ... Read more

Product Description

Linear Genetic Programming presents a variant of Genetic Programming that evolves imperative computer programs as linear sequences of instructions, in contrast to the more traditional functional expressions or syntax trees. Typical GP phenomena, such as non-effective code, neutral variations, and code growth are investigated from the perspective of linear GP. This book serves as a reference for researchers; it includes sufficient introductory material for students and newcomers to the field.

Product Description
Fundamentals of Algorithms 2Computational scientists often encounter problems requiring the solution of sparse systems of linear equations. Attacking these problems efficiently requires an in-depth knowledge of the underlying theory, algorithms, and data structures found in sparse matrix software libraries. Here, Davis presents the fundamentals of sparse matrix algorithms to provide the requisite background. The book includes CSparse, a concise downloadable sparse matrix package that illustrates the algorithms and theorems presented in the book and equips readers with the tools necessary to understand larger and more complex software packages.With a strong emphasis on MATLAB® and the C programming language, Direct Methods for Sparse Linear Systems equips readers with the working knowledge required to use sparse solver packages and write code to interface applications to those packages. The book also explains how MATLAB performs its sparse matrix computations.This invaluable book is essential to computational scientists and software developers who want to understand the theory and algorithms behind modern techniques used to solve large sparse linear systems. The book also serves as an excellent practical resource for students with an interest in combinatorial scientific computing.Preface; Chapter 1: Introduction; Chapter 2: Basic algorithms; Chapter 3: Solving triangular systems; Chapter 4: Cholesky factorization; Chapter 5: Orthogonal methods; Chapter 6: LU factorization; Chapter 7: Fill-reducing orderings; Chapter 8: Solving sparse linear systems; Chapter 9: CSparse; Chapter 10: Sparse matrices in MATLAB; Appendix: Basics of the C programming language; Bibliography; Index. "Overall, the book is magnificent. It fills a long-felt need for an accessible textbook on modern sparse direct methods.Its choice of scope is excellent.."John Gilbert, Professor, Department of Computer Science, University of California, Santa Barbara. ... Read more

Customer Reviews (2)

Good for using As-Is, not so much for adding onto
This books provides a decent library of sparse matrix functions. However, it can be difficult to understand the code at times because the author chose to use cryptic variable names.

Good concise refrence
Overall, I would say this is a pretty good book. I picked it up looking for something a bit deeper (and hopefully faster-executing) than what is found in the usual numerical analysis books, and that is what I got. Davis carefully steps through the code he developed, CSparse, from the bottom to the top. Sometimes the explanations are hard to follow, but I think that is because I'm an engineer, not a computer scientist, so mybackground really isn't on par with what it should be before reading this book.

The code (in C and/or Matlab) that is presented is very terse, and seems to combine as many operations per line as possible. If it weren't for the text, trying to understand what is going on in the code would be impossible. Spartan coding has its place, surely, but not in textbooks.

The book is missing two things. One, parallelism. Seriously- its 2008 (the fact that the book came out in 2006 doesn't change my claim)- multicore processors are everywhere, and clusters are becoming cheaper and more ubiquitous. If a reader is interested enough in this topic to want to take advantage of sparsity, chances are they want to solve large sparse linear systems. Second, the proof that's in the pudding is in the tasting. Davis only ever mentions the theoretical execution times of the various algorithms and pieces of algorithms. I would like to see a graph (that is, an x-y plot) of run time vs matrix size for the various methods (as well as the theoretical predictions). Not only that, but let's see it for a finite element problem with an unstructured mesh over a non-trivial geometry....you know, a real problem.

If nothing else, this book is a concise reference for the modern methods for treating sparse linear systems. The last book exclusive to the topic was some 20 years ago, and a lot of research has happened since then. If the algorithms presented in the book don't help you (which I doubt), then at least Davis cites several references to point you in the right direction. ... Read more

Product Description
In THEORY AND APPLICATION OF THE LINEAR MODEL, Franklin A. Graybill integrates the linear statistical model within the context of analysis of variance, correlation and regression, and design of experiments. With topics motivated by real situations, it is a time tested, authoritative resource for experimenters, statistical consultants, and students. ... Read more

Customer Reviews (3)

Graduate Level Text
This is a good reference text for the fundamentals,It is usedat the Georgia Institute of Technology for a graduate math class.

Amazon is slow
Amazon can't get copies of this book so don't even try ordering it from them. They said they ordered this title from the publisher twelve weeks ago and told me I would have it in 4-6 weeks

general linear model
estimation in the full rank model hypothesis testing in the full rank model estimation in the less than full rank model hypothesis testing in the less than full rank model ... Read more