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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin ; Boston :
De Gruyter,
[2015]
|
| Series: | De Gruyter textbook.
|
| Subjects: | |
| Online Access: | CONNECT |
MARC
| LEADER | 00000cam a2200000 i 4500 | ||
|---|---|---|---|
| 001 | mig00005468545 | ||
| 006 | m o d | ||
| 007 | cr |n||||||||| | ||
| 008 | 150705s2015 gw a ob 000 0 eng d | ||
| 005 | 20240618145919.6 | ||
| 019 | |a 910281895 |a 910447168 |a 982105136 |a 982140391 |a 982233872 |a 1066463753 | ||
| 020 | |a 3110359421 |q (electronic bk.) | ||
| 020 | |a 9783110359428 |q (electronic bk.) | ||
| 020 | |a 9783110386806 |q (electronic bk.) | ||
| 020 | |a 3110386801 |q (electronic bk.) | ||
| 020 | |a 3110359405 | ||
| 020 | |a 9783110359404 | ||
| 020 | |z 9783110359404 |q (paperback) | ||
| 020 | |z 3110359405 |q (paperback) | ||
| 024 | 3 | |a 9783110359404 | |
| 035 | |a 1WRLDSHRocn913335694 | ||
| 035 | |a (OCoLC)913335694 |z (OCoLC)910281895 |z (OCoLC)910447168 |z (OCoLC)982105136 |z (OCoLC)982140391 |z (OCoLC)982233872 |z (OCoLC)1066463753 | ||
| 037 | |a 788192 |b MIL | ||
| 040 | |a CN3GA |b eng |e pn |c CN3GA |d OCLCO |d YDXCP |d OCLCO |d EBLCP |d IDEBK |d E7B |d OCLCO |d N$T |d CUV |d OCLCO |d OCLCF |d OCLCO |d DEBSZ |d OCLCQ |d OCLCO |d AGLDB |d ICA |d YDX |d OCLCO |d ZCU |d MERUC |d OCLCQ |d IDB |d D6H |d VTS |d ICG |d VT2 |d OCLCQ |d WYU |d STF |d DKC |d OCLCQ |d M8D |d OCLCQ |d RBN |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 049 | |a TXMM | ||
| 050 | 4 | |a QA297 |b .H45 2015 | |
| 082 | 0 | 4 | |a 518 |2 23 |
| 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 | ||
| 347 | |a data file |2 rda | ||
| 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. | ||
| 500 | |a EBSCO eBook Academic Comprehensive Collection North America |5 TMurS | ||
| 500 | |a EBSCO eBook EngineeringCore |5 TMurS | ||
| 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. | |
| 700 | 1 | |a Rebholz, Leo G., |e author. | |
| 730 | 0 | |a WORLDSHARE SUB RECORDS | |
| 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://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=999665&authtype=ip,sso&custid=s4672406 |z CONNECT |3 eBooks on EBSCOhost |t 0 |
| 907 | |a 4746333 |b 05-26-21 |c 07-06-20 | ||
| 949 | |a ho0 | ||
| 994 | |a 92 |b TXM | ||
| 998 | |a wi |d z | ||
| 999 | f | f | |s 05c4b802-d259-4468-99f3-e55d8b5344a8 |i 44235705-7307-49f8-8916-1b363be0917b |t 0 |
| 952 | f | f | |a Middle Tennessee State University |b Main |c James E. Walker Library |d Electronic Resources |t 0 |e QA297 .H45 2015 |h Library of Congress classification |
