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020    9780080471204|q(electronic bk.) 
020    |z9780123738592 
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035    (Au-PeEL)EBL287933 
035    (CaPaEBR)ebr10166992 
035    (CaONFJC)MIL96233 
035    (OCoLC)137284559 
040    MiAaPQ|beng|erda|epn|cMiAaPQ|dMiAaPQ 
050  4 QA76.9.M35A24 2007 
082 0  518 
100 1  Aberth, Oliver 
245 10 Introduction to Precise Numerical Methods 
250    2nd ed 
264  1 Burlington :|bElsevier Science & Technology,|c2007 
264  4 |c©2007 
300    1 online resource (267 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
505 0  Front Cover -- Introduction to Precise Numerical Methods -
       - Copyright Page -- Table of Contents -- Preface -- 
       Acknowledgments -- Chapter 1 Introduction -- 1.1 Open-
       source software -- 1.2 Calling up a program -- 1.3 Log 
       files and print files -- 1.4 More on log files -- 1.5 The 
       tilde notation for printed answers -- Chapter 2 Computer 
       Arithmetics -- 2.1 Floating-point arithmetic -- 2.2 
       Variable precision floating-point arithmetic -- 2.3 
       Interval arithmetic -- 2.4 Range arithmetic -- 2.5 
       Practical range arithmetic -- 2.6 Interval arithmetic 
       notation -- 2.7 Computing standard functions in range 
       arithmetic -- 2.8 Rational arithmetic -- Software 
       Exercises A -- Notes and References -- Chapter 3 
       Classification of Numerical Computation Problems -- 3.1 A 
       knotty problem -- 3.2 The impossibility of untying the 
       knot -- 3.3 Repercussions from nonsolvable problem 3.1 -- 
       3.4 Some solvable and nonsolvable decimal place problems -
       - 3.5 The solvable problems handled by calc -- 3.6 Another
       nonsolvable problem -- 3.7 The trouble with discontinuous 
       functions -- Notes and References -- Chapter 4 Real-Valued
       Functions -- 4.1 Elementary functions -- Software 
       Exercises B -- Chapter 5 Computing Derivatives -- 5.1 
       Power series of elementary functions -- 5.2 An example of 
       series evaluation -- 5.3 Power series for elementary 
       functions of several variables -- 5.4 A more general 
       method of generating power series -- 5.5 The demo program 
       deriv -- Software Exercises C -- Notes and References -- 
       Chapter 6 Computing Integrals -- 6.1 Computing a definite 
       integral -- 6.2 Formal interval arithmetic -- 6.3 The demo
       program integ for computing ordinary definite integrals --
       6.4 Taylor's remainder formula generalized -- 6.5 The demo
       program mulint for higher dimensional integrals -- 6.6 The
       demo program impint for computing improper integrals -- 
       Software Exercises D -- Notes and References 
505 8  Chapter 7 Finding Where a Function f(x) is Zero -- 7.1 
       Obtaining a solvable problem -- 7.2 Using interval 
       arithmetic for the problem -- 7.3 Newton's method -- 7.4 
       Order of convergence -- Software Exercises E -- Chapter 8 
       Finding Roots of Polynomials -- 8.1 Polynomials -- 8.2 A 
       bound for the roots of a polynomial -- 8.3 The Bairstow 
       method for finding roots of a real polynomial -- 8.4 
       Bounding the error of a rational polynomial's root 
       approximations -- 8.5 Finding accurate roots for a 
       rational or a real polynomial -- 8.6 The demo program 
       roots -- Software Exercises F -- Notes and References -- 
       Chapter 9 Solving n Linear Equations in n Unknowns -- 9.1 
       Notation -- 9.2 Computation problems -- 9.3 A method for 
       solving linear equations -- 9.4 Computing determinants -- 
       9.5 Finding the inverse of a square matrix -- 9.6 The demo
       programs equat, r_equat, and c_equat -- Software Exercises
       G -- Notes and References -- Chapter 10 Eigenvalue and 
       Eigenvector Problems -- 10.1 Finding a solution to Ax=0 
       when det A=0 -- 10.2 Eigenvalues and eigenvectors -- 10.3 
       Companion matrices and Vandermonde matrices -- 10.4 
       Finding eigenvalues and eigenvectors by Danilevsky's 
       method -- 10.5 Error bounds for Danilevsky's method -- 
       10.6 Rational matrices -- 10.7 The demo programs eigen, 
       c_eigen, and r_eigen -- Software Exercises H -- Chapter 11
       Problems of Linear Programming -- 11.1 Linear algebra 
       using rational arithmetic -- 11.2 A more efficient method 
       for solving rational linear equations -- 11.3 Introduction
       to linear programming -- 11.4 Making the simplex process 
       foolproof -- 11.5 Solving n linear interval equations in n
       unknowns -- 11.6 Solving linear interval equations via 
       linear programming -- 11.7 The program linpro for linear 
       programming problems -- 11.8 The program i_equat for 
       interval linear equations -- Software Exercises I -- Notes
       and References 
505 8  Chapter 12 Finding Where Several Functions are Zero -- 
       12.1 The general problem for real elementary functions -- 
       12.2 Finding a suitable solvable problem -- 12.3 Extending
       the f(x) solution method to the general problem -- 12.4 
       The crossing parity -- 12.5 The crossing number and the 
       topological degree -- 12.6 Properties of the crossing 
       number -- 12.7 Computation of the crossing number -- 12.8 
       Newton's method for the general problem -- 12.9 Searching 
       a more general region for zeros -- Software Exercises J --
       Notes and References -- Chapter 13 Optimization Problems -
       - 13.1 Finding a function's extreme values -- 13.2 Finding
       where a function's gradient is zero -- 13.3 The demo 
       program extrema -- Software Exercises K -- Notes and 
       References -- Chapter 14 Ordinary Differential Equations -
       - 14.1 Introduction -- 14.2 Two standard problems of 
       ordinary differential equations -- 14.3 Difficulties with 
       the initial value problem -- 14.4 Linear differential 
       equations -- 14.5 Solving the initial value problem by 
       power series -- 14.6 Degree 1 interval arithmetic -- 14.7 
       An improved global error -- 14.8 Solvable two-point 
       boundary-value problems -- 14.9 Solving the boundary-value
       problem by power series -- 14.10 The linear boundary-value
       problem -- Software Exercises L -- Notes and References --
       Chapter 15 Partial Differential Equations -- 15.1 Partial 
       differential equation terminology -- 15.2 ODE and PDE 
       initial value problems -- 15.3 A power series method for 
       the ODE problem -- 15.4 The first PDE solution method -- 
       15.5 A simple PDE problem as an example -- 15.6 A defect 
       of the first PDE method -- 15.7 The revised PDE method 
       with comparison computation -- 15.8 Higher dimensional 
       spaces -- 15.9 Satisfying boundary conditions -- Software 
       Exercises M -- Notes and References -- Chapter 16 
       Numerical Methods with Complex Functions -- 16.1 
       Elementary complex functions 
505 8  16.2 The demo program c_deriv -- 16.3 Computing line 
       integrals in the complex plane -- 16.4 Computing the roots
       of a complex polynomial -- 16.5 Finding a zero of an 
       elementary complex function f(z) -- 16.6 The general zero 
       problem for elementary complex functions -- Software 
       Exercises N -- Notes and References -- The Precise 
       Numerical Methods Program PNM -- Index 
520    Helps students understand that numerical analysis is not 
       purely a mathematical discipline, but only comes to life 
       when implemented 
588    Description based on publisher supplied metadata and other
       sources 
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
       may be limited to ProQuest Ebook Central affiliated 
       libraries 
650  0 Computer science -- Mathematics.;Numerical analysis -- 
       Data processing 
655  4 Electronic books 
776 08 |iPrint version:|aAberth, Oliver|tIntroduction to Precise 
       Numerical Methods|dBurlington : Elsevier Science & 
       Technology,c2007|z9780123738592 
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