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Numerical Methods For Roots Of Polynomials

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Numerical Methods for Roots of Polynomials

Numerical Methods for Roots of Polynomials   Book
Author : J.M. McNamee
Publisher : Elsevier
Release : 2007-08-17
ISBN : 9780080489476
Language : En, Es, Fr & De

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Book Description :

Numerical Methods for Roots of Polynomials - Part I (along with volume 2 covers most of the traditional methods for polynomial root-finding such as Newton’s, as well as numerous variations on them invented in the last few decades. Perhaps more importantly it covers recent developments such as Vincent’s method, simultaneous iterations, and matrix methods. There is an extensive chapter on evaluation of polynomials, including parallel methods and errors. There are pointers to robust and efficient programs. In short, it could be entitled “A Handbook of Methods for Polynomial Root-finding . This book will be invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in several decades Gives description of high-grade software and where it can be down-loaded Very up-to-date in mid-2006; long chapter on matrix methods Includes Parallel methods, errors where appropriate Invaluable for research or graduate course

Numerical Methods for Roots of Polynomials

Numerical Methods for Roots of Polynomials   Book
Author : J.M. McNamee,Victor Pan
Publisher : Newnes
Release : 2013-07-19
ISBN : 008093143X
Language : En, Es, Fr & De

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Book Description :

Numerical Methods for Roots of Polynomials - Part II along with Part I (9780444527295) covers most of the traditional methods for polynomial root-finding such as interpolation and methods due to Graeffe, Laguerre, and Jenkins and Traub. It includes many other methods and topics as well and has a chapter devoted to certain modern virtually optimal methods. Additionally, there are pointers to robust and efficient programs. This book is invaluable to anyone doing research in polynomial roots, or teaching a graduate course on that topic. First comprehensive treatment of Root-Finding in several decades with a description of high-grade software and where it can be downloaded Offers a long chapter on matrix methods and includes Parallel methods and errors where appropriate Proves invaluable for research or graduate course

Numerical Methods for Engineers and Scientists Second Edition

Numerical Methods for Engineers and Scientists  Second Edition  Book
Author : Joe D. Hoffman,Steven Frankel
Publisher : CRC Press
Release : 2001-05-31
ISBN : 9780824704438
Language : En, Es, Fr & De

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Book Description :

Emphasizing the finite difference approach for solving differential equations, the second edition of Numerical Methods for Engineers and Scientists presents a methodology for systematically constructing individual computer programs. Providing easy access to accurate solutions to complex scientific and engineering problems, each chapter begins with objectives, a discussion of a representative application, and an outline of special features, summing up with a list of tasks students should be able to complete after reading the chapter- perfect for use as a study guide or for review. The AIAA Journal calls the book "...a good, solid instructional text on the basic tools of numerical analysis."

Initial Approximations and Root Finding Methods

Initial Approximations and Root Finding Methods Book
Author : Nikolay V. Kyurkchiev
Publisher : Wiley-VCH
Release : 1998-10-27
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Polynomials as mathematical objects have been studied extensively for a long time, and the knowledge collected about them is enormous. Polynomials appear in various fields of applied mathematics and engineering, from mathematics of finance up to signal theory or robust control. The calculation of the roots of a polynomial is a basic problems of numerical mathematics. In this book, an update on iterative methods of calculating simultaneously all roots of a polynomial is given: a survey on basic facts, a lot of methods and properties of those methods connected with the classical task of the approximative determination of roots. For the computer determination the choice of the initial approximation is of special importance. Here the authors offers his new ideas and research results of the last decade which facilitate the practical numerical treatment of polynomials.

Object Oriented Implementation of Numerical Methods

Object Oriented Implementation of Numerical Methods Book
Author : Didier H. Besset
Publisher : Morgan Kaufmann
Release : 2001
ISBN : 9781558606791
Language : En, Es, Fr & De

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Book Description :

"There are few books that show how to build programs of any kind. One common theme is compiler building, and there are shelves full of them. There are few others. It's an area, or a void, that needs filling. this book does a great job of showing how to build numerical analysis programs." -David N. Smith, IBM T J Watson Research Center Numerical methods naturally lend themselves to an object-oriented approach. Mathematics builds high- level ideas on top of previously described, simpler ones. Once a property is demonstrated for a given concept, it can be applied to any new concept sharing the same premise as the original one, similar to the ideas of reuse and inheritance in object-oriented (OO) methodology. Few books on numerical methods teach developers much about designing and building good code. Good computing routines are problem-specific. Insight and understanding are what is needed, rather than just recipes and black box routines. Developers need the ability to construct new programs for different applications. Object-Oriented Implementation of Numerical Methods reveals a complete OO design methodology in a clear and systematic way. Each method is presented in a consistent format, beginning with a short explanation and following with a description of the general OO architecture for the algorithm. Next, the code implementations are discussed and presented along with real-world examples that the author, an experienced software engineer, has used in a variety of commercial applications. Features: Reveals the design methodology behind the code, including design patterns where appropriate, rather than just presenting canned solutions. Implements all methods side by side in both Java and Smalltalk. This contrast can significantly enhance your understanding of the nature of OO programming languages. Provides a step-by-step pathway to new object-oriented techniques for programmers familiar with using procedural languages such as C or Fortran for numerical methods. Includes a chapter on data mining, a key application of numerical methods.

Numerical Methods

Numerical Methods Book
Author : M. K. Jain,Satteluri R. K. Iyengar,Rajinder Kumar Jain
Publisher : New Age International
Release : 2007-01-01
ISBN : 8122415342
Language : En, Es, Fr & De

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Book Description :

Is An Outline Series Containing Brief Text Of Numerical Solution Of Transcendental And Polynomial Equations, System Of Linear Algebraic Equations And Eigenvalue Problems, Interpolation And Approximation, Differentiation And Integration, Ordinary Differential Equations And Complete Solutions To About 300 Problems. Most Of These Problems Are Given As Unsolved Problems In The Authors Earlier Book. User Friendly Turbo Pascal Programs For Commonly Used Numerical Methods Are Given In The Appendix. This Book Can Be Used As A Text/Help Book Both By Teachers And Students.

Numerical Methods that Work

Numerical Methods that Work Book
Author : Forman S. Acton
Publisher : American Mathematical Soc.
Release : 2020-07-31
ISBN : 147045727X
Language : En, Es, Fr & De

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Book Description :

Download Numerical Methods that Work book written by Forman S. Acton, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Numerical Analysis Using MATLAB and Spreadsheets

Numerical Analysis Using MATLAB and Spreadsheets Book
Author : Steven T. Karris
Publisher : Orchard Publications
Release : 2004
ISBN : 0974423912
Language : En, Es, Fr & De

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Book Description :

Annotation This text provides complete, clear, and detailed explanations of the principal numerical analysis methods and well known functions used in science and engineering. These are illustrated with many practical examples. With this text the reader learns numerical analysis with many real-world applications, MATLAB, and spreadsheets simultaneously. This text includes the following chapters:? Introduction to MATLAB? Root Approximations? Sinusoids and Complex Numbers? Matrices and Determinants? Review of Differential Equations? Fourier, Taylor, and Maclaurin Series? Finite Differences and Interpolation? Linear and Parabolic Regression? Solution of Differential Equations by Numerical Methods? Integration by Numerical Methods? Difference Equations? Partial Fraction Expansion? The Gamma and Beta Functions? Orthogonal Functions and Matrix Factorizations? Bessel, Legendre, and Chebyshev Polynomials? Optimization MethodsEach chapter contains numerous practical applications supplemented with detailed instructionsfor using MATLAB and/or Microsoft Excel? to obtain quick solutions.

An Introduction to Numerical Methods and Analysis

An Introduction to Numerical Methods and Analysis Book
Author : James F. Epperson
Publisher : John Wiley & Sons
Release : 2013-10-07
ISBN : 1118367596
Language : En, Es, Fr & De

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Book Description :

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."—Zentralblatt MATH ". . . carefully structured with many detailed worked examples."—The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB An appendix that contains proofs of various theorems and other material The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

Theory Of Difference Equations Numerical Methods And Applications

Theory Of Difference Equations Numerical Methods And Applications Book
Author : V. Lakshmikantham,Donato Trigiante
Publisher : CRC Press
Release : 2002-06-12
ISBN : 0824744241
Language : En, Es, Fr & De

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Book Description :

"Provides a clear and comprehensive overview of the fundamental theories, numerical methods, and iterative processes encountered in difference calculus. Explores classical problems such as orthological polynomials, the Euclidean algorithm, roots of polynomials, and well-conditioning."

The Theory of Matrices in Numerical Analysis

The Theory of Matrices in Numerical Analysis Book
Author : Alston S. Householder
Publisher : Courier Corporation
Release : 2013-06-18
ISBN : 0486145638
Language : En, Es, Fr & De

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Book Description :

This text presents selected aspects of matrix theory that are most useful in developing computational methods for solving linear equations and finding characteristic roots. Topics include norms, bounds and convergence; localization theorems; more. 1964 edition.

Introduction to Precise Numerical Methods

Introduction to Precise Numerical Methods Book
Author : Oliver Aberth
Publisher : Elsevier
Release : 2007-04-11
ISBN : 9780080471204
Language : En, Es, Fr & De

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Book Description :

Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. · Clearer, simpler descriptions and explanations of the various numerical methods · Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane.

Numerical Analysis for Engineers and Scientists

Numerical Analysis for Engineers and Scientists Book
Author : G. Miller
Publisher : Cambridge University Press
Release : 2014-05-29
ISBN : 1107021081
Language : En, Es, Fr & De

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Book Description :

Graduate-level introduction balancing theory and application. Provides full coverage of classical methods with many practical examples and demonstration programs.

Numerical Methods for Engineers

Numerical Methods for Engineers Book
Author : Steven C. Chapra,Raymond P. Canale
Publisher : Unknown
Release : 2002
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

The fourth edition of this book continues the tradition of excellence it established as the winner of the ASEE Meriam/Wiley award for best textbook. Instructors love it because it is a comprehensive text that is easy to teach from. Students love it because of its clear explanations and examples. This edition features an even broader array of applications, including all engineering disciplines. The authors' unique approach opens each part of the text with sections called Motivation, Mathematical Background and Orientation, preparing the student for what is to come in a motivating and engaging manner. Each part closes with an Epilogue containing sections called Trade-Offs, Important Relationships and Formulas, and Advanced Methods and Additional References. Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a preview of more advanced methods. What's new in this edition? A shift in orientation toward more use of software packages, specifically MATLAB and Excel with VBA, includeing material on developing MATLAB m-files and VBA macros. Also, the text has been updated to reflect improvements in MATLAB and Excel since the last edition.

Numerical Methods for the Personal Computer

Numerical Methods for the Personal Computer Book
Author : Terry E. Shoup
Publisher : Prentice Hall
Release : 1983
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Numerical Methods for the Personal Computer book written by Terry E. Shoup, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Numerical Analysis

Numerical Analysis Book
Author : Walter Gautschi
Publisher : Springer Science & Business Media
Release : 1997-08-19
ISBN : 9780817638955
Language : En, Es, Fr & De

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Book Description :

'The book reads like an unfolding story... Topics are motivated with great care and ingenuity that might be given to establishing the drive behind characters in a good novel... Clarity is never sacrificed for elegance. Above all, the pace is always lively and brisk, the writing concise, and the author never lets the exposition bog down... Both the theoretical problems and machine assignments are a great resource... This is a stylish, lucid, and engaging book... [It] successfully conveys the author's interest and experience in the subject to the reader. ' -- SIAM Review, 1998 'This book is well written... Every teacher should look at this textbook to see how this material has been presented by a numerical analyst with many years of teaching experience and a high reputation.' -- Computing Reviews (March 1998) The term 'Numerical Analysis,' in this text, means the branch of mathematics that develops and analyzes computational methods dealing with problems arising in classical analysis, approximation theory, the theory of equations, and ordinary differential equations. The topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible. In this sense, the text is an introduction. Topics that, even though important, require a level of technicality that goes beyond the standards of simplicity imposed, are referenced in detailed bibliographic notes at the end of each chapter. In this way, the reader is given guidance and an opportunity to pursue advanced modern topics in more depth. Contrary to tradition, the text does not include numerical linear algebra, which is felt by the author to have matured into an autonomous discipline having an identity of its own and therefore deserving treatment in separate books and separate courses on the graduate level. For similar reasons, the numerical solution of partial differential equations is not covered either. The text is geared to a one- or two-semester graduate course in numerical analysis for students who have a good background in calculus and advanced calculus and some knowledge of linear algebra, complex analysis, and differential equations. Previous exposure to numerical methods in an undergraduate course is desirable but not absolutely necessary. A significant feature of the book is a large collection of exercises, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. A list of corrections can be obtained at http://www.cs.purdue.edu/homes/wxg/CS514/text.html the author's website. Contents PREFACE CHAPTER 0. PROLOGUE 0.1 Overview 0.2 Numerical analysis software 0.3 Textbooks and monographs 0.4 Journals CHAPTER 1. MACHINE ARITHMETIC AND RELATED MATTERS 1. Real Numbers, Machine Numbers, and Rounding 1.1 Real numbers 1.2 Machine numbers 1.3 Rounding 2. Machine Arithmetic 2.1 A model of machine arithmetic 2.2 Error propagation in arithmetric operations; cancellation error 3. The Condition of a Problem 3.1 Condition numbers 3.2 Examples 4. The Condition of an Algorithm 5. Computer Solution of a Problem; Overall Error Notes to Chapter 1 Exercises and Machine Assignments to Chapter 1 CHAPTER 2. APPROXIMATION AND INTERPOLATION 1. Least Squares Approximation 1.1 Inner products 1.2 The normal equations 1.3 Least squares error; convergence 1.4 Examples of orthogonal systems 2. Polynomial Interpolation 2.1 Lagrange interpolation formula; interpolation operator 2.2 Interpolation error 2.3 Convergence 2.4 Chebyshev polynomials and nodes 2.5 Barycentric formula 2.6 Newton's formula 2.7 Hermite interpolation 2.8 Inverse interpolation 3. Approximation and Interpolation by Spline Functions 3.1 Interpolation by piecewise linear functions 3.2 A basis for S 0 1(Delta) 3.3 Least squares approximation 3.4 Interpolation by cubic splines 3.5 Minimality properties of cubic spline interpolants Notes to Chapter 2 Exercises and Machine Assignments to Chapter 2 CHAPTER 3. NUMERICAL DIFFERENTIATION AND INTEGRATION 1. Numerical Differentiation 1.1 A general differentiation formula for unequally spaced points 1.2 Examples 1.3 Numerical differentiation with perturbed data 2. Numerical Integration 2.1 The composite trapezoidal and Simpson's rules 2.2 (Weighted) Newton-Cotes and Gauss formulae 2.3 Properties of Gaussian quadrature rules 2.4 Some applications of the Gauss quadrature rule 2.5 Approximation of linear functionals: method of interpolation vs. method of undermined coefficients 2.6 Peano representation of linear functionals 2.7 Extrapolation methods Notes to Chapter 3 Exercises and Machine Assignments to Chapter 3 CHAPTER 4. NONLINEAR EQUATIONS 1. Examples 1.1 A transcendental equation 1.2 A two-point boundary value problem 1.3 A nonlinear integral equation 1.4 s- Orthogonal polynomials 2. Iteration, Convergence, and Efficiency 3. The Methods of Bisection and Sturm Sequences 3.1 Bisection method 3.2 Method of Sturm sequences 4. Method of False Position 5. Secant Method 6. Newton's Method 7. Fixed Iteration 8. Algebraic Equations 8.1 Newton's method applied to an algebraic equation 8.2 An accelerated Newton method for equations with real roots 9. Systems of Nonlinear Equations 9.1 Contraction mapping principle 9.2 Newton's method for systems of equations Notes to Chapter 4 Exercises and Machine Assignments to Chapter 4 CHAPTER 5. INITIAL VALUE PROBLEMS FOR ODEs - ONE-STEP METHODS 0.1 Examples 0.2 Types of diffential equations 0.3 Existence and uniqueness 0.4 Numerical Methods 1. Local Description of One-Step Methods 2. Examples of One-Step Methods 2.1 Euler's method 2.2 Method of Taylor expansion 2.3 Improved Euler methods 2.4 Second-order two-stage methods 2.5 Runge-Kutta methods 3. Global Description of One-Step Methods 3.1 Stability 3.2 Convergence 3.3 Asymptotics of global error 4. Error Monitoring and Step Control 4.1 Estimation of global error 4.2 Truncation error estimates 4.3 Step control 5. Stiff Problems 5.1 A-stability 5.2 Pade approximation 5.3 Examples of A-stable one-step methods 5.4 Regions of absolute stability Notes to Chapter 5 Exercises and Machine Assignments to Chapter 5 CHAPTER 6. INITIAL VALUE PROBLEMS FOR ODEs - MULTISTEP METHODS 1. Local Description of Multistep Methods 1.1 Explicit and implicit methods 1.2 Local accuracy 1.3 Polynomial degree vs. order 2. Examples of Multistep Methods 2.1 Adams-Bashforth method 2.2 Adams-Moulton method 2.3 Predictor-corrector methods 3. Global Description of Multistep Methods 3.1 Linear difference equations 3.2 Stability and root condition 3.3 Convergence 3.4 Asymptotics of global error 3.5 Estimation of global error 4. Analytic Theory of Order and Stability 4.1 Analytic characterization of order 4.2 Stable methods of maximum order 4.3 Applications 5. Stiff Problems 5.1 A-stability 5.2 A(alpha)-stability Notes to Chapter 6 Exercises and Machine Assignments to Chapter 6 CHAPTER 7. TWO-POINT BOUNDARY VALUE PROBLEMS FOR ODEs 1. Existence and Uniqueness 1.1 Examples 1.2 A scalar boundary value problem 1.3 General linear and nonlinear systems 2. Initial Value Techniques 2.1 Shooting method for a scalar boundary value problem 2.2 Linear and nonlinear systems 2.3 Parallel shooting 3. Finite Difference Methods 3.1 Linear second-order equations 3.2 Nonlinear second-order equations 4. Variational Methods 4.1 Variational formualtion 4.2 The extremal problem 4.3 Approximate solution of the extremal problem Notes to Chapter 7 Exercises and Machine Assignments to Chapter 7 References Subject Index

Numerical Analysis

Numerical Analysis Book
Author : Vithal A. Patel
Publisher : Harcourt College Pub
Release : 1994
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Numerical Analysis book written by Vithal A. Patel, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Numerical Methods with MATLAB

Numerical Methods with MATLAB Book
Author : Gerald W. Recktenwald
Publisher : Pearson College Division
Release : 2000
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This thorough, modern exposition of classic numerical methods using MATLAB briefly develops the fundamental theory of each method. Rather than providing a detailed numerical analysis, the behavior of the methods is exposed by carefully designed numerical experiments. The methods are then exercised on several nontrivial example problems from engineering practice. KEY TOPICS: This structured, concise, and efficient book contains a large number of examples of two basic types--One type of example demonstrates a principle or numerical method in the simplest possible terms. Another type of example demonstrates how a particular method can be used to solve a more complex practical problem. The material in each chapter is organized as a progression from the simple to the complex. Contains an extensive reference to using MATLAB. This includes interactive (command line) use of MATLAB, MATLAB programming, plotting, file input and output. MARKET: For a practical and rigorous introduction to the fundamentals of numerical computation.

Computer Oriented Numerical Methods

Computer Oriented Numerical Methods Book
Author : N Datta
Publisher : Vikas Publishing House
Release : 2004
ISBN : 9788125914242
Language : En, Es, Fr & De

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Book Description :

This book clearly presents the algorithms required for easy implementation of numerical methods in computer programming. The book deals with the important topics of numerical methods, including errors in numerical computation, in a lucid style. Chapter-end short questions with answers and appendices with theory questions and ‘C’ programs are student-friendly feature of the book.

Fundamental Numerical Methods for Electrical Engineering

Fundamental Numerical Methods for Electrical Engineering Book
Author : Stanislaw Rosloniec
Publisher : Springer Science & Business Media
Release : 2008-07-17
ISBN : 3540795197
Language : En, Es, Fr & De

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Book Description :

Stormy development of electronic computation techniques (computer systems and software), observed during the last decades, has made possible automation of data processing in many important human activity areas, such as science, technology, economics and labor organization. In a broadly understood technology area, this developmentledtoseparationofspecializedformsofusingcomputersforthedesign and manufacturing processes, that is: – computer-aided design (CAD) – computer-aided manufacture (CAM) In order to show the role of computer in the rst of the two applications m- tioned above, let us consider basic stages of the design process for a standard piece of electronic system, or equipment: – formulation of requirements concerning user properties (characteristics, para- ters) of the designed equipment, – elaboration of the initial, possibly general electric structure, – determination of mathematical model of the system on the basis of the adopted electric structure, – determination of basic responses (frequency- or time-domain) of the system, on the base of previously established mathematical model, – repeated modi cation of the adopted diagram (changing its structure or element values) in case, when it does not satisfy the adopted requirements, – preparation of design and technological documentation, – manufacturing of model (prototype) series, according to the prepared docum- tation, – testing the prototype under the aspect of its electric properties, mechanical du- bility and sensitivity to environment conditions, – modi cation of prototype documentation, if necessary, and handing over the documentation to series production. The most important stages of the process under discussion are illustrated in Fig. I. 1. xi xii Introduction Fig. I.