Computational Methods for Modeling of Nonlinear Systems by Anatoli Torokhti and Phil Howlett Book

Computational Methods for Modeling of Nonlinear Systems by Anatoli Torokhti and Phil Howlett


  • Author : Anatoli Torokhti
  • Publisher : Elsevier
  • Release Date : 2007-04-11
  • Genre: Mathematics
  • Pages : 322
  • ISBN 10 : 0080475388

GET BOOK
Computational Methods for Modeling of Nonlinear Systems by Anatoli Torokhti and Phil Howlett Book Description :

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. Best operator approximation Non-Lagrange interpolation Generic Karhunen-Loeve transform Generalised low-rank matrix approximation Optimal data compression Optimal nonlinear filtering

Computational Methods for Modeling of Nonlinear Systems Book

Computational Methods for Modeling of Nonlinear Systems


  • Author : Anatoli Torokhti
  • Publisher : Elsevier Science Limited
  • Release Date : 1967-02-12
  • Genre: Mathematics
  • Pages : 322
  • ISBN 10 : 0124708501

GET BOOK
Computational Methods for Modeling of Nonlinear Systems Book Description :

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Computational Methods for Modeling of Nonlinear Systems Book

Computational Methods for Modeling of Nonlinear Systems


  • Author : Anatoli Torokhti
  • Publisher : Elsevier Science Limited
  • Release Date : 1961
  • Genre: Mathematics
  • Pages : 322
  • ISBN 10 : 012437056X

GET BOOK
Computational Methods for Modeling of Nonlinear Systems Book Description :

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Computational Solution of Nonlinear Systems of Equations Book

Computational Solution of Nonlinear Systems of Equations


  • Author : Eugene L. Allgower
  • Publisher : American Mathematical Soc.
  • Release Date : 1990-04-03
  • Genre: Mathematics
  • Pages : 762
  • ISBN 10 : 0821896946

GET BOOK
Computational Solution of Nonlinear Systems of Equations Book Description :

Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.

Nonlinear Systems  Vol  1 Book

Nonlinear Systems Vol 1


  • Author : Victoriano Carmona
  • Publisher : Springer
  • Release Date : 2019-10-11
  • Genre:
  • Pages : 442
  • ISBN 10 : 3030097811

GET BOOK
Nonlinear Systems Vol 1 Book Description :

Numerical Methods for Nonlinear Engineering Models Book

Numerical Methods for Nonlinear Engineering Models


  • Author : John R. Hauser
  • Publisher : Springer Science & Business Media
  • Release Date : 2009-03-24
  • Genre: Computers
  • Pages : 1013
  • ISBN 10 : 9781402099205

GET BOOK
Numerical Methods for Nonlinear Engineering Models Book Description :

There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.

Numerical Methods for Nonlinear Partial Differential Equations Book

Numerical Methods for Nonlinear Partial Differential Equations


  • Author : Sören Bartels
  • Publisher : Springer
  • Release Date : 2015-01-19
  • Genre: Mathematics
  • Pages : 393
  • ISBN 10 : 9783319137971

GET BOOK
Numerical Methods for Nonlinear Partial Differential Equations Book Description :

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Numerical Methods for Unconstrained Optimization and Nonlinear Equations Book

Numerical Methods for Unconstrained Optimization and Nonlinear Equations


  • Author : J. E. Dennis, Jr.
  • Publisher : SIAM
  • Release Date : 1996-12-01
  • Genre: Equations
  • Pages : 378
  • ISBN 10 : 1611971209

GET BOOK
Numerical Methods for Unconstrained Optimization and Nonlinear Equations Book Description :

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 covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.

Nonlinear Analysis  Problems  Applications and Computational Methods Book

Nonlinear Analysis Problems Applications and Computational Methods


  • Author : Zakia Hammouch
  • Publisher : Springer Nature
  • Release Date : 2020-11-13
  • Genre: Technology & Engineering
  • Pages : 249
  • ISBN 10 : 9783030622992

GET BOOK
Nonlinear Analysis Problems Applications and Computational Methods Book Description :

This book is a collection of original research papers as proceedings of the 6th International Congress of the Moroccan Society of Applied Mathematics organized by Sultan Moulay Slimane University, Morocco, during 7th–9th November 2019. It focuses on new problems, applications and computational methods in the field of nonlinear analysis. It includes various topics including fractional differential systems of various types, time-fractional systems, nonlinear Jerk equations, reproducing kernel Hilbert space method, thrombin receptor activation mechanism model, labour force evolution model, nonsmooth vector optimization problems, anisotropic elliptic nonlinear problem, viscous primitive equations of geophysics, quadratic optimal control problem, multi-orthogonal projections and generalized continued fractions. The conference aimed at fostering cooperation among students, researchers and experts from diverse areas of applied mathematics and related sciences through fruitful deliberations on new research findings. This book is expected to be resourceful for researchers, educators and graduate students interested in applied mathematics and interactions of mathematics with other branches of science and engineering.

Computational Techniques for Modelling Learning in Economics Book

Computational Techniques for Modelling Learning in Economics


  • Author : Thomas Brenner
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Genre: Business & Economics
  • Pages : 391
  • ISBN 10 : 9781461550297

GET BOOK
Computational Techniques for Modelling Learning in Economics Book Description :

Computational Techniques for Modelling Learning in Economics offers a critical overview of the computational techniques that are frequently used for modelling learning in economics. It is a collection of papers, each of which focuses on a different way of modelling learning, including the techniques of evolutionary algorithms, genetic programming, neural networks, classifier systems, local interaction models, least squares learning, Bayesian learning, boundedly rational models and cognitive learning models. Each paper describes the technique it uses, gives an example of its applications, and discusses the advantages and disadvantages of the technique. Hence, the book offers some guidance in the field of modelling learning in computation economics. In addition, the material contains state-of-the-art applications of the learning models in economic contexts such as the learning of preference, the study of bidding behaviour, the development of expectations, the analysis of economic growth, the learning in the repeated prisoner's dilemma, and the changes of cognitive models during economic transition. The work even includes innovative ways of modelling learning that are not common in the literature, for example the study of the decomposition of task or the modelling of cognitive learning.

Mathematical Modeling Book

Mathematical Modeling


  • Author : Ludmilla A. Uvarova
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-03-14
  • Genre: Mathematics
  • Pages : 294
  • ISBN 10 : 9781475733976

GET BOOK
Mathematical Modeling Book Description :

This volume contains review articles and original results obtained in various fields of modern science using mathematical simulation methods. The basis of the articles are the plenary and some section reports that were made and discussed at the Fourth International Mathematical Simulation Conference, held in Moscow on June 27 through July 1, 2000. The conference was devoted to the following scientific areas: • mathematical and computer discrete systems models; • non-linear excitation in condensed media; • complex systems evolution; • mathematical models in economics; • non-equilibrium processes kinematics; • dynamics and structure of the molecular and biomolecular systems; • mathematical transfer models in non-linear systems; • numerical simulation and algorithms; • turbulence and determined chaos; • chemical physics of polymer. This conference was supported by the Russian Ministry of Education, Russian foundation for Basic Research and Federal Program "Integration". This volume contains the following sections: 1. models of non-linear phenomena in physics; 2. numerical methods and computer simulations; 3. mathematical computer models of discrete systems; 4. mathematical models in economics; 5. non-linear models in chemical physics and physical chemistry; 6. mathematical models of transport processes in complex systems. In Sections One and Five a number of fundamental and sufficiently general problems, concerning real physical and physical-chemical systems simulation, is discussed.

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers Book

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers


  • Author : Moysey Brio
  • Publisher : Academic Press
  • Release Date : 2010-09-21
  • Genre: Mathematics
  • Pages : 312
  • ISBN 10 : 0080917046

GET BOOK
Numerical Time Dependent Partial Differential Equations for Scientists and Engineers Book Description :

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical

Computational Techniques for Process Simulation and Analysis Using MATLAB   Book

Computational Techniques for Process Simulation and Analysis Using MATLAB


  • Author : Niket S. Kaisare
  • Publisher : CRC Press
  • Release Date : 2017-09-18
  • Genre: Science
  • Pages : 538
  • ISBN 10 : 9781498762120

GET BOOK
Computational Techniques for Process Simulation and Analysis Using MATLAB Book Description :

MATLAB® has become one of the prominent languages used in research and industry and often described as "the language of technical computing". The focus of this book will be to highlight the use of MATLAB® in technical computing; or more specifically, in solving problems in Process Simulations. This book aims to bring a practical approach to expounding theories: both numerical aspects of stability and convergence, as well as linear and nonlinear analysis of systems. The book is divided into three parts which are laid out with a "Process Analysis" viewpoint. First part covers system dynamics followed by solution of linear and nonlinear equations, including Differential Algebraic Equations (DAE) while the last part covers function approximation and optimization. Intended to be an advanced level textbook for numerical methods, simulation and analysis of process systems and computational programming lab, it covers following key points • Comprehensive coverage of numerical analyses based on MATLAB for chemical process examples. • Includes analysis of transient behavior of chemical processes. • Discusses coding hygiene, process animation and GUI exclusively. • Treatment of process dynamics, linear stability, nonlinear analysis and function approximation through contemporary examples. • Focus on simulation using MATLAB to solve ODEs and PDEs that are frequently encountered in process systems.

Computational Methods in Nonlinear Structural and Solid Mechanics Book

Computational Methods in Nonlinear Structural and Solid Mechanics


  • Author : Ahmed K. Noor
  • Publisher : Elsevier
  • Release Date : 2014-05-20
  • Genre: Technology & Engineering
  • Pages : 470
  • ISBN 10 : 9781483145648

GET BOOK
Computational Methods in Nonlinear Structural and Solid Mechanics Book Description :

Computational Methods in Nonlinear Structural and Solid Mechanics covers the proceedings of the Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics. The book covers the development of efficient discretization approaches; advanced numerical methods; improved programming techniques; and applications of these developments to nonlinear analysis of structures and solids. The chapters of the text are organized into 10 parts according to the issue they tackle. The first part deals with nonlinear mathematical theories and formulation aspects, while the second part covers computational strategies for nonlinear programs. Part 3 deals with time integration and numerical solution of nonlinear algebraic equations, while Part 4 discusses material characterization and nonlinear fracture mechanics, and Part 5 tackles nonlinear interaction problems. The sixth part discusses seismic response and nonlinear analysis of concrete structure, and the seventh part tackles nonlinear problems for nuclear reactors. Part 8 covers crash dynamics and impact problems, while Part 9 deals with nonlinear problems of fibrous composites and advanced nonlinear applications. The last part discusses computerized symbolic manipulation and nonlinear analysis software systems. The book will be of great interest to numerical analysts, computer scientists, structural engineers, and other professionals concerned with nonlinear structural and solid mechanics.

Theory of Difference Equations Numerical Methods and Applications by V Lakshmikantham and D Trigiante Book

Theory of Difference Equations Numerical Methods and Applications by V Lakshmikantham and D Trigiante


  • Author : Lakshmikantham
  • Publisher : Elsevier
  • Release Date : 1988-05-01
  • Genre: Mathematics
  • Pages : 322
  • ISBN 10 : 0080958699

GET BOOK
Theory of Difference Equations Numerical Methods and Applications by V Lakshmikantham and D Trigiante Book Description :

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Advanced Methods of Physiological System Modeling Book

Advanced Methods of Physiological System Modeling


  • Author : V.Z. Marmarelis
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-06-29
  • Genre: Technology & Engineering
  • Pages : 272
  • ISBN 10 : 9781475790245

GET BOOK
Advanced Methods of Physiological System Modeling Book Description :

This volume is the third in a series entitled" Advanced Methods of Physiological System Modeling" and the fifth in a series of research volumes published by Plenum under the sponsorship of the Biomedical Simulations Resource (BMSR) at the Uni versity of Southern California in the context of dissemination activities supported by the Biomedical Research Technology Program of the National Center for Research Resources at the National Institutes of Health under Grant No. P41 RR-OI861. These volumes are edited by BMSR principal scientists and report on recent research de velopments in the area of physiological systems modeling, as well as on advanced methods for analysis of physiological signals and data. As in the previous two volumes of this series, the work reported herein is con cerned with the development of advanced modeling methodologies and their novel application to problems of biomedical interest, with emphasis on nonlinear aspects of physiological function. The term "advanced methodologies" is used to indicate that the scope of this work extends beyond the ordinary type of analysis, which is confined traditionally to the linear domain. As the importance of nonlinearities in understanding the complex mechanisms of physiological function is increasingly recognized, the need for effective and practical modeling methodologies that address the issue of nonlinear dynamics in life sciences becomes more and more pressing.

Adaptive Learning Methods for Nonlinear System Modeling Book

Adaptive Learning Methods for Nonlinear System Modeling


  • Author : Danilo Comminiello
  • Publisher : Butterworth-Heinemann
  • Release Date : 2018-06-11
  • Genre: Technology & Engineering
  • Pages : 388
  • ISBN 10 : 9780128129777

GET BOOK
Adaptive Learning Methods for Nonlinear System Modeling Book Description :

Adaptive Learning Methods for Nonlinear System Modeling presents some of the recent advances on adaptive algorithms and machine learning methods designed for nonlinear system modeling and identification. Real-life problems always entail a certain degree of nonlinearity, which makes linear models a non-optimal choice. This book mainly focuses on those methodologies for nonlinear modeling that involve any adaptive learning approaches to process data coming from an unknown nonlinear system. By learning from available data, such methods aim at estimating the nonlinearity introduced by the unknown system. In particular, the methods presented in this book are based on online learning approaches, which process the data example-by-example and allow to model even complex nonlinearities, e.g., showing time-varying and dynamic behaviors. Possible fields of applications of such algorithms includes distributed sensor networks, wireless communications, channel identification, predictive maintenance, wind prediction, network security, vehicular networks, active noise control, information forensics and security, tracking control in mobile robots, power systems, and nonlinear modeling in big data, among many others. This book serves as a crucial resource for researchers, PhD and post-graduate students working in the areas of machine learning, signal processing, adaptive filtering, nonlinear control, system identification, cooperative systems, computational intelligence. This book may be also of interest to the industry market and practitioners working with a wide variety of nonlinear systems. Presents the key trends and future perspectives in the field of nonlinear signal processing and adaptive learning. Introduces novel solutions and improvements over the state-of-the-art methods in the very exciting area of online and adaptive nonlinear identification. Helps readers understand important methods that are effective in nonlinear system modelling, suggesting the right methodology to

Computational Methods in Systems Biology Book

Computational Methods in Systems Biology


  • Author : Corrado Priami
  • Publisher : Springer Science & Business Media
  • Release Date : 2003-02-07
  • Genre: Computers
  • Pages : 214
  • ISBN 10 : 9783540006053

GET BOOK
Computational Methods in Systems Biology Book Description :

Rovereto,December2002 CorradoPriami ProgrammeCommitteeofCMSB 2003 CorradoPriami(Chair),UniversityofTrento(Italy), CharlesAu?ray,CNRS,Villejuif(France), CosimaBaldari,Universit`adiSiena(Italy), AlexanderBockmayr,Universit ́eHenriPoincar ́e(France), LucaCardelli,MicrosoftResearchCambridge(UK), VincentDanos,Universit ́eParisVII(France), PierpaoloDegano,Universitad ` iPisa(Italy), Francois ̧ Fages,INRIA,Rocquencourt(France), DrabløsFinn,NorwegianUniversityofScienceandTechnology,Trondheim(N- way), MonikaHeiner,BrandenburgUniversityofTechnologyatCottbus(Germany), InaKoch,UniversityofAppliedSciencesBerlin,(Germany), JohnE.

Nonlinear System Identification Book
Score: 5
From 1 Ratings

Nonlinear System Identification


  • Author : Oliver Nelles
  • Publisher : Springer Science & Business Media
  • Release Date : 2001
  • Genre: Computers
  • Pages : 785
  • ISBN 10 : 3540673695

GET BOOK
Nonlinear System Identification Book Description :

Written from an engineering point of view, this book covers the most common and important approaches for the identification of nonlinear static and dynamic systems. The book also provides the reader with the necessary background on optimization techniques, making it fully self-contained. The new edition includes exercises.

Advances in the Efficiency of Computational Methods and Applications Book

Advances in the Efficiency of Computational Methods and Applications


  • Author : Ioannis K. Argyros
  • Publisher : World Scientific
  • Release Date : 2000
  • Genre: Mathematics
  • Pages : 546
  • ISBN 10 : 9810243367

GET BOOK
Advances in the Efficiency of Computational Methods and Applications Book Description :

This invaluable textbook creates a general framework for the study of optimal iterative procedures for problems that are solved approximately. Emphasis is given to the efficiency of numerical methods. For generality the setting is abstract, but the book presents many applications to practical problems, allowing the reader to take advantage of the most modern high speed calculating devices, and provides examples to illustrate concepts and major theorems. The examples are selected from astrophysics (radiative transfer and the kinetic theory of gases), mechanics (elasticity), economics (predator -- prey problems), the n-dimensional Euclidean space and other applied areas. The book will benefit not only senior undergraduates, graduates, graduate students and researchers in the field but also those who wish to obtain information about specific results or techniques that take into account the particular nature of the equation.