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Numerical mathematics / (Record no. 467)

MARC details
000 -LEADER
fixed length control field 09392cam a2200229 a 4500
001 - CONTROL NUMBER
control field 1693
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20200701115626.0
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 070307s2008 maua b 001 0 eng
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9780763737672
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 0763737674
040 ## - CATALOGING SOURCE
Transcribing agency DLC
082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 518
Edition number 22
Item number G768
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Grasselli, Matheus.
245 10 - TITLE STATEMENT
Title Numerical mathematics /
Statement of responsibility, etc Matheus Grasselli, Dmitry Pelinovsky.
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc Sudbury, Mass. :
Name of publisher, distributor, etc Jones and Bartlett Publishers,
Date of publication, distribution, etc c2008.
300 ## - PHYSICAL DESCRIPTION
Extent xiv, 668 p.
Other physical details ill. ;
Dimensions 24 cm.
500 ## - GENERAL NOTE
General note Includes bibliographical references (p. 653-654) and indexes.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Numerical analysis.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Pelinovsky, Dmitry.
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Koha item type Books
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Contents<br/>1 Elements of the Laboratory 13<br/>1.1 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14<br/>1.2 Scalars, Vectors and Matrices . . . . . . . . . . . . . . . . . . . . . . . 16<br/>1.3 Matrix Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24<br/>1.4 Built-in Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30<br/>1.5 Programming with MATLAB . . . . . . . . . . . . . . . . . . . . . . . 35<br/>1.6 Graphics and Data Files . . . . . . . . . . . . . . . . . . . . . . . . . . 43<br/>1.7 Floating¿Point Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . 49<br/>1.8 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54<br/>1.9 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56<br/>1.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58<br/>2 Linear Systems 59<br/>2.1 Vector Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60<br/>2.2 Linear Maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70<br/>2.3 Systems of Linear Equations . . . . . . . . . . . . . . . . . . . . . . . . 82<br/>2.4 Vector and Matrix Norms . . . . . . . . . . . . . . . . . . . . . . . . . 87<br/>2.5 Direct Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96<br/>2.6 Iterative Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112<br/>2.7 Cholesky Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . 119<br/>2.8 Determinants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125<br/>2.9 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131<br/>2.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133<br/>3 Orthogonality 135<br/>3.1 Inner Product Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136<br/>3.2 Orthogonal Projections . . . . . . . . . . . . . . . . . . . . . . . . . . 145<br/>3.3 QR Factorization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155<br/>3<br/>3.4 The Least¿Squares Method . . . . . . . . . . . . . . . . . . . . . . . . 166<br/>3.5 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175<br/>3.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176<br/>4 Eigenvalues and Eigenvectors 177<br/>4.1 Matrix Eigenvalue Problems . . . . . . . . . . . . . . . . . . . . . . . . 178<br/>4.2 Properties of Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . 182<br/>4.3 Properties of Eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . 192<br/>4.4 Normal Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198<br/>4.5 Sensitivity of Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . 202<br/>4.6 Power Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209<br/>4.7 Simultaneous Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . 222<br/>4.8 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . 231<br/>4.9 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243<br/>4.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245<br/>5 Polynomial Functions 247<br/>5.1 Properties of Polynomials . . . . . . . . . . . . . . . . . . . . . . . . . 247<br/>5.2 Vandermonde Interpolation . . . . . . . . . . . . . . . . . . . . . . . . 256<br/>5.3 Lagrange Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 263<br/>5.4 Newton Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266<br/>5.5 Errors of Polynomial Interpolation . . . . . . . . . . . . . . . . . . . . 271<br/>5.6 Least Square Approximation . . . . . . . . . . . . . . . . . . . . . . . 279<br/>5.7 Approximation with Orthogonal Polynomials . . . . . . . . . . . . . . 288<br/>5.8 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297<br/>5.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299<br/>6 Differential and Integral Calculus 303<br/>6.1 Derivatives and Finite Differences . . . . . . . . . . . . . . . . . . . . . 304<br/>6.2 Higher¿Order Numerical Derivatives . . . . . . . . . . . . . . . . . . . 309<br/>6.3 Multi¿Point First¿Order Numerical Derivatives . . . . . . . . . . . . . 316<br/>6.4 Richardson Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . 321<br/>6.5 Integrals and Finite Sums . . . . . . . . . . . . . . . . . . . . . . . . . 327<br/>6.6 Newton-Cotes Integration Rules . . . . . . . . . . . . . . . . . . . . . . 339<br/>6.7 Romberg Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349<br/>6.8 Gaussian Quadrature Rules . . . . . . . . . . . . . . . . . . . . . . . . 353<br/>6.9 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363<br/>4<br/>6.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364<br/>7 Vector Calculus 369<br/>7.1 Scalar Functions of Several Variables . . . . . . . . . . . . . . . . . . . 370<br/>7.2 Partial Derivatives and Differentiability . . . . . . . . . . . . . . . . . 378<br/>7.3 The Gradient Vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384<br/>7.4 Paths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 388<br/>7.5 Vector Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391<br/>7.6 Line Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398<br/>7.7 Surface Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402<br/>7.8 Integral Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409<br/>7.9 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415<br/>7.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417<br/>8 Zeros and Extrema of Functions 419<br/>8.1 One¿dimensional root finding . . . . . . . . . . . . . . . . . . . . . . . 420<br/>8.2 Multidimensional root finding . . . . . . . . . . . . . . . . . . . . . . . 439<br/>8.3 One¿dimensional minimization . . . . . . . . . . . . . . . . . . . . . . 447<br/>8.4 Multidimensional Minimization . . . . . . . . . . . . . . . . . . . . . . 454<br/>8.5 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461<br/>8.6 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462<br/>9 Initial¿Value Problems for ODEs 463<br/>9.1 Approximations of Solutions . . . . . . . . . . . . . . . . . . . . . . . . 463<br/>9.2 Single¿Step Runge¿Kutta Solvers . . . . . . . . . . . . . . . . . . . . . 472<br/>9.3 Adaptive Single¿Step Solvers . . . . . . . . . . . . . . . . . . . . . . . 485<br/>9.4 Multi¿step Adams Solvers . . . . . . . . . . . . . . . . . . . . . . . . . 495<br/>9.5 Implicit Methods for Stiff Differential Equations . . . . . . . . . . . . 510<br/>9.6 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 518<br/>9.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520<br/>10 Boundary¿Value Problems for ODEs and PDEs 525<br/>10.1 Finite¿Difference Methods for ODEs . . . . . . . . . . . . . . . . . . . 526<br/>10.2 Shooting Methods for ODEs . . . . . . . . . . . . . . . . . . . . . . . . 540<br/>10.3 Finite¿Difference Methods for Parabolic PDEs . . . . . . . . . . . . . 552<br/>10.4 Finite¿Difference Methods for Hyperbolic PDEs . . . . . . . . . . . . . 565<br/>10.5 Finite¿Difference Methods for Elliptic PDEs . . . . . . . . . . . . . . . 575<br/>10.6 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588<br/>5<br/>10.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590<br/>11 Spectral Methods 595<br/>11.1 Trigonometric Approximation and Interpolation . . . . . . . . . . . . . 595<br/>11.2 Errors of Trigonometric Interpolation . . . . . . . . . . . . . . . . . . . 604<br/>11.3 Trigonometric Methods for Differential Equations . . . . . . . . . . . . 612<br/>11.4 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 628<br/>11.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629<br/>12 Finite Element Methods 633<br/>12.1 Spline Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633<br/>12.2 Hermite Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . 648<br/>12.3 Finite Elements for Differential Equations . . . . . . . . . . . . . . . . 658<br/>12.4 Summary and Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668<br/>12.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669<br/>Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678<br/>MATLAB Functions and Commands . . . . . . . . . . . . . . . . . . . . . . 686<br/>Mathematical Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688
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      UE-Central Library UE-Central Library 06.06.2018 U.E. 518 G768 T1693 06.06.2018 06.06.2018 Books
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