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Introduction to scientific computing : for scientists and engineers /
Nowadays most mathematics done in practice is done on a computer. In engineering it is necessary to solve more than 1 million equations simultaneously, and computers can be used to reduce the calculation time from years to minutes or even seconds. This book explains: How can we approximate these imp...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin ; Boston :
De Gruyter,
[2015]
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| Colección: | De Gruyter textbook.
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| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Heister, Timo, |e author. | |
| 245 | 1 | 0 | |a Introduction to scientific computing : |b for scientists and engineers / |c Timo Heister, Leo G. Rebholz. |
| 264 | 1 | |a Berlin ; |a Boston : |b De Gruyter, |c [2015] | |
| 300 | |a 1 online resource (xi, 138 pages) : |b illustrations (some color) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter textbook | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface; Contents; 1 Introduction; 1.1 Why study numerical methods?; 1.2 Terminology; 1.3 Convergence terminology; 1.4 Exercises; 2 Computer representation of numbers and roundoff error; 2.1 Examples of the effects of roundoff error; 2.2 Binary numbers; 2.3 64 bit floating point numbers; 2.3.1 Avoid adding large and small numbers; 2.3.2 Subtracting two nearly equal numbers is bad; 2.4 Exercises; 3 Solving linear systems of equations; 3.1 Linear systems of equations and solvability; 3.2 Solving triangular systems; 3.3 Gaussian elimination; 3.4 The backslash operator; 3.5 LU decomposition. | |
| 505 | 8 | |a 3.6 Exercises4 Finite difference methods; 4.1 Approximating the first derivative; 4.1.1 Forward and backward differences; 4.1.2 Centered difference; 4.1.3 Three point difference formulas; 4.1.4 Further notes; 4.2 Approximating the second derivative; 4.3 Application: Initial value ODE's using the forward Euler method; 4.4 Application: Boundary value ODE's; 4.5 Exercises; 5 Solving nonlinear equations; 5.1 The bisection method; 5.2 Newton's method; 5.3 Secant method; 5.4 Comparing bisection, Newton, secant method; 5.5 Combining secant and bisection and the fzero command. | |
| 505 | 8 | |a 5.6 Equation solving in higher dimensions5.7 Exercises; 6 Accuracy in solving linear systems; 6.1 Gauss-Jordan elimination and finding matrix inverses; 6.2 Matrix and vector norms and condition number; 6.3 Sensitivity in linear system solving; 6.4 Exercises; 7 Eigenvalues and eigenvectors; 7.1 Mathematical definition; 7.2 Power method; 7.3 Application: Population dynamics; 7.4 Exercises; 8 Fitting curves to data; 8.1 Interpolation; 8.1.1 Interpolation by a single polynomial; 8.1.2 Piecewise polynomial interpolation; 8.2 Curve fitting; 8.2.1 Line of best fit; 8.2.2 Curve of best fit. | |
| 505 | 8 | |a 8.3 Exercises9 Numerical integration; 9.1 Newton-Cotes methods; 9.2 Composite rules; 9.3 MATLAB's integral function; 9.4 Gauss quadrature; 9.5 Exercises; 10 Initial value ODEs; 10.1 Reduction of higher order ODEs to first order; 10.2 Common methods and derivation from integration rules; 10.2.1 Backward Euler; 10.2.2 Crank-Nicolson; 10.2.3 Runge-Kutta 4; 10.3 Comparison of speed of implicit versus explicit solvers; 10.4 Stability of ODE solvers; 10.4.1 Stability of forward Euler; 10.4.2 Stability of backward Euler; 10.4.3 Stability of Crank-Nicolson; 10.4.4 Stability of Runge-Kutta 4. | |
| 505 | 8 | |a 10.5 Accuracy of ODE solvers10.5.1 Forward Euler; 10.5.2 Backward Euler; 10.5.3 Crank-Nicolson; 10.5.4 Runge-Kutta 4; 10.6 Summary, general strategy, and MATLAB ODE solvers; 10.7 Exercises; A Getting started with Octave and MATLAB; A.1 Basic operations; A.2 Arrays; A.3 Operating on arrays; A.4 Script files; A.5 Function files; A.5.1 Inline functions; A.5.2 Passing functions to other functions; A.6 Outputting information; A.7 Programming in MATLAB; A.8 Plotting; A.9 Exercises. | |
| 520 | |a Nowadays most mathematics done in practice is done on a computer. In engineering it is necessary to solve more than 1 million equations simultaneously, and computers can be used to reduce the calculation time from years to minutes or even seconds. This book explains: How can we approximate these important mathematical processes? How accurate are our approximations? How efficient are our approximations? | ||
| 504 | |a Includes bibliographical references. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Engineering |x Data processing. | |
| 650 | 0 | |a Science |x Data processing. | |
| 650 | 0 | |a Numerical analysis. | |
| 650 | 0 | |a Numerical analysis |x Data processing. | |
| 650 | 6 | |a Ingénierie |x Informatique. | |
| 650 | 6 | |a Sciences |x Informatique. | |
| 650 | 6 | |a Analyse numérique. | |
| 650 | 6 | |a Analyse numérique |x Informatique. | |
| 650 | 7 | |a MATHEMATICS |x Numerical Analysis. |2 bisacsh | |
| 650 | 7 | |a Engineering |x Data processing |2 fast | |
| 650 | 7 | |a Numerical analysis |2 fast | |
| 650 | 7 | |a Numerical analysis |x Data processing |2 fast | |
| 650 | 7 | |a Science |x Data processing |2 fast | |
| 650 | 7 | |a Numerische Mathematik |2 gnd | |
| 650 | 7 | |a MATLAB |2 gnd | |
| 700 | 1 | |a Rebholz, Leo G., |e author. | |
| 758 | |i has work: |a Introduction to scientific computing (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFRQJpBdTb4bvFWG6CrPBd |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Heister, Timo. |t Introduction to scientific computing. |d Berlin ; Boston : De Gruyter, [2015] |z 9783110359404 |w (DLC) 2015026895 |w (OCoLC)913572856 |
| 830 | 0 | |a De Gruyter textbook. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=2056391 |z Texto completo |
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