Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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Optimal synthesis, light scattering, and diffraction on a ribbon are just some of the applied problems for which integral equations with difference kernels are employed. The same equations are also met in important mathematical problems such as inverse spectral problems, nonlinear integral equations, and factorization of operators.

On the basis of the operator identity method, the theory of integral operators with difference kernels is developed here, and the connection with many applied and theoretical problems is studied. A number of important examples are analyzed.

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This volume is produced from digital images created through the University of Michigan University Library's large-scale digitization efforts. The Library seeks to preserve the intellectual content of items in a manner that facilitates and promotes a variety of uses. The digital reformatting process results in an electronic version of the original text that can be both accessed online and used to create new print copies. The Library also understands and values the usefulness of print and makes reprints available to the public whenever possible. This book and hundreds of thousands of others can be found in the HathiTrust, an archive of the digitized collections of many great research libraries. For access to the University of Michigan Library's digital collections, please see http://www.lib.umich.edu and for information about the HathiTrust, please visit http://www.hathitrust.org ... Read more

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This volume is the Proceedings of the First Conference on Finite Difference Methods which was held at the University of Rousse, Bulgaria, 10--13 August 1997. The conference attracted more than 50 participants from 16 countries. 10 invited talks and 26 contributed talks were delivered. The volume contains 28 papers presented at the Conference. The most important and widely used methods for solution of differential equations are the finite difference methods. The purpose of the conference was to bring together scientists working in the area of the finite difference methods, and also people from the applications in physics, chemistry and other natural and engineering sciences. ... Read more

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This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

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This book concludes the outstanding series of historical studies of the mathematics in the nineteenth century. Previous volumes have studied logic, algebra, number theory, probability, geometry, and analytic functions. The third volume encompasses: an essay on the development of Chebyshev's theory of approximation of functions, later called "Constructive function theory", a systematic analysis of the history of the theory of ordinary differential equations from Chauchy and certain of his predecessors up to Poincaré and A.M. Lyapunov, an essay of the development of the calculus of variations, and a study of the history of finite differences, in whose development Soviet mathematicians have played a prominent role. This book will be a valuable source of understanding the development of these areas. It provides the general reader, as well as historians of science, not only with the descriptive history but also with a good understanding of the outer and inner motivations and the results and effects of the presented concepts and methods. ... Read more

Customer Reviews (1)

Long shadow.
(It is now in paperback!) I like this book because it highlights
how several of the central questions and ideas in mathematics from the 19th century still cast a long shadow into the present. It is as true for the pioneering work of Abel and Galois, from the early part of the period which is covered, as it is for the discoveries of Chebychev, Markov, and Kolmogorov toward the end. The period starts roughly at the time of the Napoleon wars, and extends up to the Second World War. The articles in this well written book go into mathematical detail (for example, Kummer's theory and work on Fermat's Last Theorem, Dedekin's ideal theory, and cuts,...)and they represent a well chosen treat of papers, written by major players. ... Read more

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In this volume, the authors extend the calculus of finite differences to Dirac's equation. They obtain solutions for particles with negative mass that are completely equivalent to the solutions with positive mass. In addition, they obtain solutions for nuclear distances of the order of 10^-13m and less rather than for the usual atomic distances. They report a number of other deviations from the differential theory, for instance they found a slight deviation in the eigenvalues of an electron in a Coulomb field, similar to the Lamb shift. In two sections some surprising results are shown for the concept of space caused by the replacement of dx by delta x. ... Read more

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Among the subjects reviewed in these Advances, the properties and computation of electromagnetic fields have been considered on several occasions. In particular, the early work of H.F. Harmuth on Maxwell's equations, which was highly controversial at the time, formed a supplement to the series

This volume, unlike previous volumes in the series concentrates solely on the research of professors' Harmuth and Meffert.

These studies raise important and fundamental questions concerning some of the basic areas of physics: electromagnetic theory and quantum mechanics. They deserve careful study and reflection for although the authors do not attempt to provide the definitive answer to the questions, their work is undoubtedly a major step towards such an answer. This volume essential reading for those researchers and academics working applied mathematicians or theoretical physics

Unlike previous volumes, this book concentrates solely on the new research of professors Harmuth and Meffert

Raises important and fundamental questions concerning electromagnetism theory and quantum mechanics

Provides the steps in finding answers for the highly debated questions ... Read more

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The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method.

In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature:

• Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options
• Early exercise features and approximation using front-fixing, penalty and variational methods
• Modelling stochastic volatility models using Splitting methods
• Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work
• Modelling jumps using Partial Integro Differential Equations (PIDE)
• Free and moving boundary value problems in QF

Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs. ... Read more

Customer Reviews (5)

Bad book
I used this book to solve a rather difficult PDE and in the end i decided that a binomial tree approximation would save me time instead of reading this.
First it is not a beginer's book, second it wastes millions of precious time to the classification of PDEs in a very dense writting style cut in small chapters. In some cases it presents no proofs, or it assumes knowledge of mathematics that does not even cover. For example at some point syas that to check sth toy need Fourier and no presentation of the method is shown. In short to difficult to read, not for a beginner

totally useless!!!
What a joke! This book claims to be adequate for those who have little or no knowledge in the field of PDEs and finite differnces (which is not my case), and believe me you will be just as ignorant after having read the book!

The book is divided into seven parts with the first one dealing with the general theory of PDEs, except that the information content is null! Even the heat equation is not fully solved, whether it is by separation of variables, where the solution is thrown at you in different cases, or by Fourier transform where the author takes the transform of the PDE then conveniently tells you that this can then be solved and converted back into the solution to the problem by "well known" techniques!! Prepostorous!! Furthermore, the entire book is simply a bunch well packed results and definitions with little or no insight as to their practical applications. You will simply learn the EXISTENCE of a certain number of techniques, however you will not have enough information to implement these or gain any insight into them! If you want to learn about PDEs, finite diffenences and their financial applications go for Wilmott, at least the latter won't waste your time!

A practical approach to finite difference methods
This book proved to be a useful reference for practical implementation of finite-difference methods for PDEs:several one- and multi-factor financial derivatives pricing models, including local volatility models and models with stochastic volatilities.The methods described in the text are stable, accurate and reasonably efficient.Stability of FD methods is obviously of top concern to the author (as it should be to readers as well), and he goes into extensive detail evaluating the stability of various techniques.The writing is clear and consistent, though a "notational" index or glossary would have been helpful, particularly in the early going.The author provides several practical examples, which lends a refreshing degree of concreteness to the book.

Well Done
Daniel J.Duffy introduces Finite Difference methods for solving partial differential equations that arise in numerical pricing of derivatives. There are seven sections in the book. They are:
Part I The Continuous Theory of Partial Differential Equations - A short introduction to partial differential equations and their applications to financial engineering.
Part IIFinite Difference Methods: the Fundamentals - There are three chapters that introduce Finite Difference methods to approximate initial value and initial boundary value problems. Another two chapters apply the methods to Black-Scholes equation. He did a nice job to approximate the solutions to problems with small volatility or large drift,...
Part III Applying FDM to One-Factor Instrument Pricing
Part IV FDM for Multidimensional problems
Part VApplying FDM to Multi-Factor Instrument Pricing and
Part VI Free and Moving Boundary Value Problems
There are altogether 18 chapters (about 180 pages) that thoroughly introduce the application of FDM techniques to a wide range of options (pricing) modelling. The exposition is clear and concise.
The last part
Part VII Design and implementation In C++ - The last four chapters design for readers having programming literacy.
To fully appreciate the materials of the book, readers should have at least one year training in partial differential equations and knowledge in financial derivatives at about the same level as John Hull's book - Options, Futures and Other Derivatives, 5e.
If the book contains a few applications to real world data, it will be perfect to primers in this field.

Need more books like this one
Having bought many books in Financial Engineering this is one of the most useful. The source code is atleast alot better than the other books that claim to be the best. I give this book 4 stars and recommend quants to buy this book. ... Read more

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Finite Difference Methods in Heat Transfer presents a clear, step-by-step delineation of finite difference methods for solving engineering problems governed by ordinary and partial differential equations, with emphasis on heat transfer applications. The finite difference techniques presented apply to the numerical solution of problems governed by similar differential equations encountered in many other fields. Fundamental concepts are introduced in an easy-to-follow manner.Representative examples illustrate the application of a variety of powerful and widely used finite difference techniques. The physical situations considered include the steady state and transient heat conduction, phase-change involving melting and solidification, steady and transient forced convection inside ducts, free convection over a flat plate, hyperbolic heat conduction, nonlinear diffusion, numerical grid generation techniques, and hybrid numerical-analytic solutions. ... Read more

Customer Reviews (1)

An authoritative text on FDM in heat transfer
An engineer is constantly engaged in a battle where he tries to balance having enough books on his desk in order to appear well-read, yet not so many as to dilute his collection of "good books."Finite Difference Methods in Heat Transfer is one of those books an engineer cannot be without.It presents the content with an emphasis on solving partial differential equations, i.e. the Poisson and Laplace equations of heat and mass transport, by numerical means, which is ultimately the topic of interest to the practicing engineer.

The book is organized by chapter into methods for solving PDEs of the elliptic, parabolic, and hyperbolic type; in 1, 2, and 3 dimensions.Each is given a thorough treatment, and the author's knowledge of the the FDM shines as he concisely links the physical meaning of various transport phenomena to its respective term in the PDE.By delineating an otherwise obscure parabolic differential equation into its unsteady, convection, diffusion and source terms, the author imparts an understanding of differential equations that goes beyond a purely mathematical treatment.

The first chapter delves heavily into developing a conceptual understanding of the problem (PDE's), but the book takes off from there.The computational methods described in the book are first-rate, and many of them can be implimented in Excel.With that said, I am confident the reader could be setting up grids and making finite difference approximations the first day of owning this book.The "computational molecule" approach the book takes lends itself well to grid generation in a spreadsheet, although it is not explicity mentioned by the author.The book also includes Fortran code for a Thomas algorithm and domain decomposition algorithms, among others, in the appendices.

All in all, I can't tell you what an outstanding reference this is.I know it's one of the most expensive books on transport phenomena out there, but let me be the first to say it's worth every penny! ... Read more

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Written by a great English mathematician, this classic text begins with the differences of elementary functions and explores interpolation, mechanical quadrature, finite integration, and the summation of series. Several useful tests for the convergence and divergence of series are developed, as is a method for finding the limits of error in series expansions. The latter half of the book discusses difference-equations, including linear, mixed, and partial difference-equations, and concludes with applications to problems in geometry and optics. The text pays particular attention to the connection of the calculus of finite differences with the differential calculus, and more than 200 problems appear in the text (some with solutions). Unabridged republication of the classic 1872 edition.
... Read more

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  Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods.

The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. The authors develop a technique for constructing and justifying ε uniformly convergent difference schemes for boundary value problems with fewer restrictions on the problem data.

Containing information published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter. This part also studies both the solution and its derivatives with errors that are independent of the perturbation parameters.

Co-authored by the creator of the Shishkin mesh, this book presents a systematic, detailed development of approaches to construct ε uniformly convergent finite difference schemes for broad classes of singularly perturbed boundary value problems. ... Read more

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Advances in computer technology have conveniently coincided with trends in numerical analysis toward increased complexity of computational algorithms based on finite difference methods. It is no longer feasible to perform stability investigation of these methods manually—and no longer necessary. As this book shows, modern computer algebra tools can be combined with methods from numerical analysis to generate programs that will do the job automatically.

Comprehensive, timely, and accessible—this is the definitive reference on the application of computerized symbolic manipulations for analyzing the stability of a wide range of difference schemes. In particular, it deals with those schemes that are used to solve complex physical problems in areas such as gas dynamics, heat and mass transfer, catastrophe theory, elasticity, shallow water theory, and more.

Introducing many new applications, methods, and concepts, Computer-Aided Analysis of Difference Schemes for Partial Differential Equations

• Shows how computational algebra expedites the task of stability analysis—whatever the approach to stability investigation
• Covers ten different approaches for each stability method
• Deals with the specific characteristics of each method and its application to problems commonly encountered by numerical modelers
• Describes all basic mathematical formulas that are necessary to implement each algorithm
• Provides each formula in several global algebraic symbolic languages, such as MAPLE, MATHEMATICA, and REDUCE
• Includes numerous illustrations and thought-provoking examples throughout the text

For mathematicians, physicists, and engineers, as well as for postgraduate students, and for anyone involved with numeric solutions for real-world physical problems, this book provides a valuable resource, a helpful guide, and a head start on developments for the twenty-first century. ... Read more

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This book reflects the modern level of the theory ofproblem-solving differential methods in mathematical physics. The mainresults of the stability and convergence of the approximate boundaryproblem solving for many-dimensional equations with partialderivatives are obtained in the works of Russian scientists and arepractically not covered in the monograph and textbooks published inthe West. At the present time the main attention in computationalmathematics is paid to the theory and practice of the method of finiteelements. The books available in English are oriented to the basictraining of specialists. The book is intended for specialists in numerical methods for thesolution of mathematical physics problems; the exposition is easilyunderstood by senior students of universities. ... Read more

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This book provides a primer in inequalities in applied probability theory & statistics. It is intended to be useful to both graduate students and established researchers working in probability theory and statistics, analytic integral inequalities and their applications in demography, economics, physics, biology and other scientific areas. The book is self-contained in the sense that the reader needs only to be familiar with basic real analysis, integration theory and probability theory. All inequalities used in the text are explicitly stated and appropriately referenced. ... Read more

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This text provides a foundation to the theory of error estimation for finite difference/volume schemes for differential equations with rough solutions. Included are applications to mathematical modelling of pollution, transport of phone noise in optical fibres, and economics. ... Read more