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

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

Label
Introduction to scientific computing : for scientists and engineers
Title
Introduction to scientific computing
Title remainder
for scientists and engineers
Statement of responsibility
Timo Heister, Leo G. Rebholz
Creator
Contributor
Author
Subject
Language
eng
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?
Member of
Cataloging source
CN3GA
Dewey number
518
Illustrations
illustrations
Index
no index present
LC call number
QA297
LC item number
.H45 2015
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
De Gruyter textbook
Label
Introduction to scientific computing : for scientists and engineers, Timo Heister, Leo G. Rebholz
Publication
Bibliography note
Includes bibliographical references
http://library.link/vocab/branchCode
  • net
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
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
  • 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
  • 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
Control code
ocn913335694
Dimensions
unknown
Extent
1 online resource (xi, 138 pages)
Form of item
online
Isbn
9783110359404
Media category
computer
Media MARC source
rdamedia
Media type code
c
Other control number
9783110359404
Other physical details
illustrations (some color)
http://library.link/vocab/ext/overdrive/overdriveId
788192
http://library.link/vocab/recordID
.b36386042
Specific material designation
remote
System control number
  • (OCoLC)913335694
  • pebcs3110359405

Library Locations

    • Deakin University Library - Geelong Waurn Ponds CampusBorrow it
      75 Pigdons Road, Waurn Ponds, Victoria, 3216, AU
      -38.195656 144.304955
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