Book Description
Special functions, which include the trigonometric functions, have been used for centuries. Their role in the solution of differential equations was exploited by Newton and Leibniz, and the subject of special functions has been in continuous development ever since. In just the past thirty years several new special functions and applications have been discovered. This treatise presents an overview of the area of special functions, focusing primarily on the hypergeometric functions and the associated hypergeometric series. It includes both important historical results and recent developments and shows how these arise from several areas of mathematics and mathematical physics. Particular emphasis is placed on formulas that can be used in computation. The book begins with a thorough treatment of the gamma and beta functions that are essential to understanding hypergeometric functions. Later chapters discuss Bessel functions, orthogonal polynomials and transformations, the Selberg integral and its applications, spherical harmonics, q-series, partitions, and Bailey chains. This clear, authoritative work will be a lasting reference for students and researchers in number theory, algebra, combinatorics, differential equations, applied mathematics, mathematical computing, and mathematical physics.
Customer Reviews:
A Modern Whittaker and Watson, Buy It.......2004-10-24
This book is great. It is the best overview I have ever seen of the primary special functions, as seen from a modern viewpoint. Buy it and you will spend many happy hours reading the theorems it contains, and doing the excercizes at the end of each chapter.
A book comes close to " A course of modern analysis ".......2001-08-07
Though this book cannot be compared to Whittaker and Watson's classic book. It comes quite close to it. I just want to comment on the the area covers are too concentrated and the rigorous manner which is the hall mark of " Modern Analysis " is lacking. Anyway, this book deserves 5 stars.
clean and concise.......2001-02-11
It has a very good style of writing for the nature of mathematics. It is clean, no unnecessary explanation or examples. In a way, one can feel something similar to Axler's. It is an excellent reference book. One should keep this book just as Axler's Linear Algebra Done Right, Numerical Recipe, DE Knuth's Art of Programming.
clean and concise.......2001-02-11
It has a very good style of writing for the nature of mathematics. It is clean, no unnecessary explanation or examples. In a way, one can feel something similar to Axler's. It is an excellent reference book. One should keep this book just as Axler's Linear Algebra Done Right, Numerical Recipe, DE Knuth's Art of Programming.
clean and concise.......2001-02-11
It has a very good style of writing for the nature of mathematics. It is clean, no unnecessary explanation or examples. In a way, one can feel something similar to Axler's. It is an excellent reference book. One should keep this book just as Axler's Linear Algebra Done Right, Numerical Recipe, DE Knuth's Art of Programming.
Book Description
Integrates the traditional approach to differential equations with the modern systems and control theoretic approach to dynamic systems, emphasizing theoretical principles and classic models in a wide variety of areas. Provides a particularly comprehensive theoretical development that includes chapters on positive dynamic systems and optimal control theory. Contains numerous problems.
Customer Reviews:
Good book, but consider a used copy!.......2007-06-14
This "2001 edition" (according to Amazon) was actually copyrighted in 1979. While the book remains very useful, prospective consumers may wish to consider a good used copy in order to save some money.
Although the publication date is misleading, at least Wiley correctly prints the original copyright date within its "new" texts (there are other examples of this practice). Springer-Verlag performs still greater magic. In "Linear and Nonlinear Programming", also by Luenberger, Springer decided to print the copyright date as 2003 instead of 1984, thus giving the impression that the text contains an up-to-date treatment of the subject matter. If I were buying a copy of "Green Eggs and Ham", I would not care about an incorrect copyright date. However, where technical subjects are concerned, this practice borders on fraud (in my view). It is a deliberate attempt to deceive its customers into believing that they are purchasing something more current and relevant than is actually the case.
Excellent treatment of dynamic systems.......2001-05-03
This introduction to dynamic systems is presented with an algebraic formalism which makes things clear and concise. All concepts are explained intuitively as well as formally, having in mind the objective of making things clear. Few books exhibit such a good approach and other reviewers are right when they emphasize the highly pedagogical quality of Luenberger's books ! This is no overstatement.
The advantage of using this algebraic formulation lies in the simplicity as well as the understandability of the state-space approach, which is best explained in those terms. Most books assume that everyone knows what a state space is without explicitly showing what it is really about. This book just uses the reverse assumption, in that you're not asssumed to know everything before getting into it.
Only some basic knowledge in algebra (undergraduate-level) is required but even without experience in algebraic formalism, it is possible to go through the content thanks to the important number of examples and the intuitive explanations.
A must-read !
Excellent supplementary reading of Linear System Theory.......1999-04-24
The economic application examples are interesting for engineering students.
The best mathematical textbook ever written.......1999-02-19
I studied this book for two semesters as a doctoral student, and consider it the best mathematical textbook ever written. Luenberger writes concisely and with great clarity and elegance. His notation is crisp and easy to follow. The book begins with basic concepts of matrix algebra and dynamic equations, and then builds step-by-step to encompass an enormously broad set of applications. The examples are drawn from all over the map, and are great fun to explore. This is a truly mind-expanding text.
Thomas P. Lyon, Associate Professor, Business Economics and Public Policy, Indiana University
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Design Theory (Encyclopedia of Mathematics and its Applications)
Thomas Beth ,
D. Jungnickel , and
H. Lenz
Manufacturer: Cambridge University Press
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Book Description
This volume concludes the second edition of the standard text on design theory. Since the first edition there has been extensive development of the theory and this book has been thoroughly rewritten to reflect this. In particular, the growing importance of discrete mathematics to many parts of engineering and science have made designs a useful tool for applications, a fact that has been acknowledged here with the inclusion of an additional chapter on applications. The volume is suitable for advanced courses and for reference use, not only for researchers in discrete mathematics or finite algebra, but also for those working in computer and communications engineering and other mathematically oriented disciplines. Features include exercises and an extensive, updated bibliography of well over 1800 citations.
Book Description
This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided.
Customer Reviews:
A very good book!.......2007-07-05
I read this book after I had read Karatzas' and Shreve's book "Stochastic Calculus..." and it is probably better to do it the other way round. The mathematical prerequisites are not high, however a good intuitive understanding of measure theory is probably necessary. The pace of the book is leasurely, the proofs are such, that pencil and paper is rarely needed, however no rigor is lost.
The book quickly moves to interesting applications of the theory, which is motivated very well.
It contains a few typographical errors, mostly in the last chapter, and mostly of a harmless nature.
With the necessary mathematical background, it seems to be an ideal introduction to this highly interesting topic of stochastic differential equations!
Excellent introduction on Stochastic Differential Equations.......2007-05-08
A well written book in Mathematics
Stochastic Differential Equations is a branch of mathematics. This book is not just for financial derivatives analysis or modeling. Oksendal first introduces the subject by raising a few stochastic problems (population growth; electric charge in RLC circuit; filtering problems, Dirichlet problems; asset management; optimal portfolio and options pricing) in the first chapter. The subsequent chapters develop notions and techniques which are able to solve wide varieties of stochastic problems (not just those mentioned in the first chapters). The arrangement is impressive in particular for readers who have no previous knowledge about the subject. The readers at least know the target for developing the techniques and would not lose the way when manipulating tons of symbols. Hints and answers to selected problems are invaluable to students for self-study.
To achieve a sound background on stochastic equations is extremely important especially in quantitative finance. It is not an easy job however. QF students may consider going through this book before seriously take Shreve's books on Stochastic Calculus for Finance.
OK intro to stochastic analysis.......2007-03-14
This is a standard work (it is the one I read when I first started looking at this sort of thing) but having taken it off the shelf recently again, I think it is overrated, for several reasons.
First, it is very notation heavy - TeX has seduced Mr. Oksendahl into all sorts of bad habits - I can very easily imagine that the earlier editions (mine is the 5th), which were written with a typewriter, are much more readable.
Second, the proofs are very formal, developed mostly in terms of classical functional analysis (square integrable real functions, geometry of real Hilbert spaces etc.). From the point of view of rigor this is fine, but from the point of view of intuition, not so much, esp. when combined with the heavyweight notation. In fact note that unless you have a decent background in functional analysis, of the sort you are more likely to pick up in a mathematics degree than a finance degree, then you are going to get precisely nowhere with this book.
I don't want to be too negative, and there is lots of good stuff here - just to warn that Oksendahl is not (as one might think) a royal road to the theory of SDEs (depressingly, it may be that Oksendahl is, nevertheless, the best of the bunch out there - it is certainly, all criticism not-withstanding, more accessible than Karatzas and Shreve).
Very good book - would not mind more on finance.......2007-02-08
Very good book. However the math prerequisite is at quite a high level. Especially the probability theory introduction could be a little less fast-paced. As my main interest was on the financial application I would not have minded a little more on that topic and a little less on e.g. filtering or stochatsic control in return.
good intro book.......2006-02-03
This is a good intro book. It brings you really fast to Ito's Formula and SDE. Somebody said that the Kolmogorov's backward eq in chapter 8 is wrong. This is false, it is just expressed in a different way than the usual form. However, with a change of time, you are all set.
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Control of Quantum-Mechanical Processes and Systems (Mathematics and its Applications)
A.G. Butkovskiy , and
Yu.I. Samoilenko
Manufacturer: Springer
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Binding: Hardcover
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ASIN: 0792306899 |
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- First Aid to those outside the EE community
- Systems theory done right!
|
Introduction to Mathematical Systems Theory : A Behavioral Approach (Texts in Applied Mathematics, Vol. 26)
Jan Willem Polderman , and
Jan C. Willems
Manufacturer: Springer
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ASIN: 0387982663 |
Book Description
This is a book about modelling, analysis and control of linear time- invariant systems. The book uses what is called the behavioral approach towards mathematical modelling. Thus a system is viewed as a dynamical relation between manifest and latent variables. The emphasis is on dynamical systems that are represented by systems of linear constant coefficients. In the first part of the book the structure of the set of trajectories that such dynamical systems generate is analyzed. Conditions are obtained for two systems of differential equations to be equivalent in the sense that they define the same behavior. It is further shown that the trajectories of such linear differential systems can be partitioned in free inputs and bound outputs. In addition the memory structure of the system is analyzed through state space models. The second part of the book is devoted to a number of important system properties, notably controllability, observability, and stability. An essential feature of using the behavioral approach is that it allows these and similar concepts to be introduced in a representation-free manner. In the third part control problems are considered, more specifically stabilization and pole placement questions. This text is suitable for advanced undergraduate or beginning graduate students in mathematics and engineering. It contains numerous exercises, including simulation problems, and examples, notably of mechanical systems and electrical circuits.
Customer Reviews:
First Aid to those outside the EE community.......2006-12-02
The book starts off with an extremely useful modeling term: "Exclusion Law." This term describes a notion that any closed system of physical laws/equations (Newton's, etc.) state what's included (possible) and what's excluded (impossible) from its (a certain set of physical laws/equations) interpretation of reality.
Most of the concepts in this text will be nothing new to those who already have a bachelor of science in electrical engineering. Still, learning from the author's choice of words and his arrangement of materials will provide one with a very effective way of communicating modeling ideas to those outside the EE community or to those who are somehow academically juvenile (for example, speaking with someone who had to suffer a poor signals and systems instructor or with anyone who had to deal with a similar academic situation).
Here's a quote from page 12:
"Now it becomes necessary to consider two cases:"
From page 1:
"We view a mathematical model as an exlcusion law. A mathematical model expresses the OPINION that some things can happen, are possible, while others cannot, are declared impossible. Thus Kepler claims that planetary orbits that do not satisfy his three famous laws are impossible. In particular, he judges nonelliptical orbits as unphysical. ... Economic production functions tell us that certain amounts of raw materials, capital, and labor are needed in order to manufacture a finished product: it prohibits the creation of finished products unless the required resources are available."
And from page 8:
"Dynamical Systems.... The adjective dynamical refers to phenomena with a delayed reaction, phenomena with an aftereffect, with transients, oscillations, and, perhaps, an approach to equilibrium. ...a mathematical model in which the objects of interest are functions of time..."
Systems theory done right!.......2004-04-06
This is an excellent book on mathematical control theory. As opposed to the classical state-space approach, the behavioural theory gives a more fundamental and natural way of looking at physical systems. The book deals with the notions of controllability, observability, stability and feedback in a beautiful mathematical framework. A more appropriate title would be "Systems theory done right"!
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Stability and Control of Discrete Processes (Applied Mathematical Sciences)
J. P. Lasalle
Manufacturer: Springer
ProductGroup: Book
Binding: Paperback
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ASIN: 0387964118 |
Book Description
This book presents a self-contained and up-to-date account of the theory of viscosity solutions for first order partial differential equations of Hamilton-Jacobi type and its interplay with Bellman's Dynamic Programming approach to optimal control and differential games, as it developed after the beginning of the eighties with the pioneering work of M. Crandall and P.L. Lions. The book begins with a long introduction where the authors present in a rather informal way the main ideas and themes of the book, beginning with the classical derivation of the Hamilton-Jacobi-Bellman equation from the Dynamic Programming Optimality Principle and the characterization of the value function as the unique viscosity solution of this equation. This is followed by a treatment of the general theory of continuous viscosity solutions and its applications to a number of problems in deterministic optimal control theory for nonlinear systems(infinite and finite horizon, minimal time, optimal stopping, impulse control, problems with state constraints, etc.)The second part of the book develops the theory of discontinuous viscosity solutions and its applications to asymptotic problems (singular perturbations, ergodic problems, etc.), to some approximation schemes for the value function and for optimal feedback controls based on Dynamic Programming. The last chapter and appendix deal, respectively, with differential games and nonlinear H-infinity control.
The book will be of interest to scientists involved in the theory of optimal control of deterministic linear and nonlinear systems. In particular it will appeal to system theorists wishing to learn about a recent mathematical theory providing a correct framework for the classical method of Dynamic Programming and mathematicians interested in new recent methods for first order nonlinear PDEs. The books historical notes provide a guide to a fairly complete bibliography including more than 500 titles. Some suggestions of how to present the material to students will make it ideal as a graduate course text as well as a self-teaching tool for practicing control mathematicians and engineers.
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Robust Nonlinear Control Design: State-Space and Lyapunov Techniques (Systems & Control: Foundations & Applications)
Randy A. Freeman , and
Petar V. Kokotovic
Manufacturer: Birkhauser
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Binding: Hardcover
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ASIN: 0817639306 |
Book Description
This book presents recent advances in the theory and design of robust nonlinear control systems. In the first part of the book, the authors provide a unified framework for state-space and Lyapunov techniques by combining concepts from set valued analysis, Lyapunov stability theory, and game theory. Within this unified framework, the authors then develop a variety of new control design methods suitable for systems described by low-order nonlinear ordinary differential equations. This book emphasizes global controller designs - that is designs for the entire region of model validity. Because linear theory deals well with local system behavior (except for critical cases in which Jacobian linearization fails), the authors focus on achieving robustness and performance for large deviations from a given operation condition.
The purpose of the book is to summarize new Lyapunov design techniques for nonlinear systems and to raise important issues concerning large-signal robustness and performance. The authors have been the first to address some of these issues and they report their findings in this text. For example, they identify two potential sources of excessive control effort in Lyapunov design techniques and show how such effort can be greatly reduced.
The researcher who wishes to enter the field of robust nonlinear control might use this book as a source of new research topics. For those already active in the field, the book can serve as a reference to a recent body of significant work. Finally, the design engineer faced with a nonlinear control problem will benefit from the new techniques presented here.
Book Description
This volume presents an introduction to the common ground between operator theory and linear systems theory. Pure mathematical topics are included such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be suitable for a course in functional analysis. The book also includes applications to partial differential equations, the stability and stabilization of linear systems, power signal spaces, and delay systems, treated from an input/output point of view.
Books:
- Spreadsheet Modeling and Decision Analysis (with CD-ROM and Microsoft Project 2003 120 day version)
- Spreadsheet Modeling and Decision Analysis (with CD-ROM and Microsoft Project 2003 120 day version)
- Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming (Systems & Control: Foundations & Applications)
- System Reliability Theory: Models, Statistical Methods, and Applications, Second Edition
- Technical Analysis of the Financial Markets: A Comprehensive Guide to Trading Methods and Applications (New York Institute of Finance)
- The Art Student Survival Guide
- The Continuum Concept: In Search of Happiness Lost (Classics in Human Development)
- The Data Warehouse Lifecycle Toolkit : Expert Methods for Designing, Developing, and Deploying Data Warehouses
- The Econometric Modelling of Financial Time Series
- The Feynman Lectures on Physics Volumes 1-2
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