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Bestseller
BestsellerE-book
Author Heister, Timo, author.

Title Introduction to scientific computing : for scientists and engineers / Timo Heister, Leo G. Rebholz.

Publication Info. Berlin ; Boston : De Gruyter, [2015]

Item Status

Description 1 online resource (xi, 138 pages) : illustrations (some color).
text file
Series De Gruyter textbook
De Gruyter textbook.
Contents 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.
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.
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.
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.
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.
Summary 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?
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject Engineering -- Data processing.
Engineering -- Data processing.
Science -- Data processing.
Science -- Data processing.
Numerical analysis.
Numerical analysis.
Numerical analysis -- Data processing.
Numerical analysis -- Data processing.
Genre/Form Electronic books.
Added Author Rebholz, Leo G., author.
Other Form: Print version: Heister, Timo. Introduction to scientific computing. Berlin ; Boston : De Gruyter, [2015] 9783110359404 (DLC) 2015026895 (OCoLC)913572856
ISBN 3110359421 (electronic book)
9783110359428 (electronic book)
9783110386806 (electronic book)
3110386801 (electronic book)
9783110359404 (paperback)
3110359405 (paperback)