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A First Course in the Numerical Analysis of Differential Equations
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Arieh Iserles
Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and ...
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Numerical Solution of Partial Differential Equations in Science and Engineering
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Leon Lapidus, George Francis Pinder
From the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering: "The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject ...[It] is unique in that it covers equally finite difference and finite element methods."-Burrelle's. "The authors have selected an elementary (but not ...
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Statistical and Computational Inverse Problems
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Jari Kaipio, Erkki Somersalo
The book develops the statistical approach to inverse problems with an emphasis on modeling and computations. The framework is the Bayesian paradigm, where all variables are modeled as random variables, the randomness reflecting the degree of belief of their values, and the solution of the inverse problem is expressed in terms of probability ...
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Soliton Equations and Their Algebro-Geometric Solutions: Volume 1, (1+1)-Dimensional Continuous Models
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Fritz Gesztesy, Helge Holden, Bela Bollobas (Editor)
The focus of this book is on algebro-geometric solutions of completely integrable nonlinear partial differential equations in (1+1)-dimensions, also known as soliton equations. Explicitly treated integrable models include the KdV, AKNS, sine-Gordon, and Camassa-Holm hierarchies as well as the classical massive Thirring system. An extensive ...
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Groups and symmetry
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by
M. A. Armstrong
Groups are important because they measure symmetry. This text, designed for undergraduate mathematics students, provides a gentle introduction to the highlights of elementary group theory. Written in an informal style, the material is divided into short sections each of which deals with an important result or a new idea. Throughout the book, the ...
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Splines and Variational Methods
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P M Prenter
This volume represents an introduction to the numerical solution of boundary value problems by variational methods, with special emphasis placed on the finite element and collocation methods. Assuming only the elements of linear algebra and analysis, Prenter presents just the necessary Hilbert space theory and abstract functional analytic concepts ...
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Numerical Methods for Unconstrained Optimization and Nonlinear Equations
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J E Dennis
This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms ...
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Multivariate Polysplines: Applications to Numerical and Wavelet Analysis
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by
Ognyan Kounchev
Multivariate polysplines are a new mathematical technique that has arisen from a synthesis of approximation theory and the theory of partial differential equations. It is an invaluable means to interpolate practical data with smooth functions. Multivariate polysplines have applications in the design of surfaces and 'smoothing' that are essential ...
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Numerical Solution of Partial Differential Equations by the Finite Element Method
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by
Claes Johnson
Professor Johnson presents an easily accessible introduction to one of the most important methods used to solve partial differential equations. The bulk of the text focuses on linear problems, however a chapter extending the development of non-linear problems is also included, as is one on finite element methods for integral equations. Throughout ...
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Safari Park
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Stuart J Murphy, Steve Bjorkman (Illustrator)
It's four tickets for the River Raft! Just two for the Elephant Twirl! Paul, his sister, and his three cousins each have 20 tickets to spend, and a little simple algebra will help them figure out what rides they can go on at the new amusement park. Full-color illustrations.
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Numerical Solution of Stochastic Differential Equations
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Peter E Kloeden
The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. The book proposes to the reader whose background knowledge is limited to undergraduate level methods for engineering and physics, and easily accessible introductions to SDE ...
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Finite Volume Methods for Hyperbolic Problems
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Randall J Leveque, M J Ablowitz (Editor), S H Davis (Editor)
This book contains an introduction to hyperbolic partial differential equations and a powerful class of numerical methods for approximating their solution, including both linear problems and nonlinear conservation laws. These equations describe a wide range of wave propagation and transport phenomena arising in nearly every scientific and ...
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Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations
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Kathryn Eleda Brenan
Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of ...
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Ordinary Differential Equations Using MATLAB
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John C Polking
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Computer Algebra Recipes: An Advanced Guide to Scientific Modeling
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by
Richard H Enns, George C McGuire
Modern computer algebra systems are revolutionizing the teaching and learning of mathematically intensive subjects in science and engineering, enabling students to explore increasingly complex and computationally intensive models that provide analytic solutions, animated numerical solutions, and complex two- and three-dimensional graphic displays. ...
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Partial Differential Equations: Theory and Technique
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by
George F Carrier, Carl E Pearson
This is the second edition of the well-established text in partial differential equations, emphasizing modern, practical solution techniques. This updated edition includes a new chapter on transform methods and a new section on integral equations in the numerical methods chapter. The authors have also included additional exercises.
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Iterative solution of nonlinear equations in several variables
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by
James M. Ortega, Werner C. Rheinboldt
Iterative Solution of Nonlinear Equations in Several Variables provides a survey of the theoretical results on systems of nonlinear equations in finite dimension and the major iterative methods for their computational solution. Originally published in 1970, it offers a research-level presentation of the principal results known at that time. ...
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Numerical Solution of Partial Differential Equations: An Introduction
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by
K W Morton, D F Mayers (Editor)
Partial differential equations are the chief means of providing mathematical models in science, engineering and other fields. Generally these models must be solved numerically. This book provides a concise introduction to standard numerical techniques, ones chosen on the basis of their general utility for practical problems. The authors emphasise ...
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Perturbation Methods in Applied Mathematics
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J Kevorkian, J D Cole
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Differential Equations with MATLAB
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Brian R Hunt, Ronald L Lipsman, John E Osborn
"Differential Equations with MATLAB" (2nd ed.) by B. Hunt, R. Lipsman, J.Osborn and J.Rosenberg is a supplemental text that can enrich and enhance any first course in ordinary differential equations. Designed to accompany Wiley's "ODE" texts written by Boyce/DiPrima, Borrelli/Coleman and Lomen/Lovelock, this supplement helps instructors move ...
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Numerical Methods for Fluid Dynamics: With Applications in Geophysics
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Dale Durran, J E Marsden (Editor), L Sirov (Editor)
This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows.The book covers both the essentials of building a numerical model and the more sophisticated techiniques that are now available. Finite difference methods, spectral methods, finite element ...
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Numerical solutions of nonlinear differential equations
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Donald Greenspan (Editor), Mathematics Research Center (United States. Army), University of Wisconsin
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Solution Techniques for Elementary Partial Differential Equations
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by
Christian Constanda, Constanda Constanda, Belinda Jack (Contributions by)
Of the many available texts on partial differential equations (PDEs), most are too detailed and voluminous, making them daunting to many students. In sharp contrast, Solution Techniques for Elementary Partial Differential Equations is a no-frills treatment that explains completely but succinctly some of the most fundamental solution methods for ...
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Transform Methods for Solving Partial Differential Equations Es
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by
Dean G Duffy
For most scientists and engineers, the only analytical technique for solving linear partial differential equations is separation of variables. This text uses the power of complex variables to demonstrate how Laplace and Fourier transforms can be harnassed to solve many practical, everyday problems experienced by scientists and engineers. It ...
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Integral methods in science and engineering
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by
Christian Constanda (Preface by)
This book is an outgrowth of the sixth international conference on integral methods in science and engineering. The chapters focus on the solution of mathematical models from various physical domains, using integral methods in conjunction with approximation schemes. "Integral Methods in Science and Engineering" describes the construction and ...
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