Numerical methods for scientists and engineers:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston ; Basel ; Berlin
Birkhäuser
2002
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXII, 842 S. 1 CD-ROM (12 cm) |
| ISBN: | 3764367156 |
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Record in the Search Index
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| adam_text | H. M. ANTIA NUMERICAL METHODS FOR SCIENTISTS AND ENGINEERS SECOND
EDITION BIRKHAUSERVERLAG BASEL * BOSTON * BERLIN CONTENTS PREFACE XI
NOTATION XV LIST OF COMPUTER PROGRAMS XVI 1 INTRODUCTION 1 1.1 ERRORS IN
NUMERICAL COMPUTATION 2 1.2 TRUNCATION ERROR 4 1.3 PROGRAMMING 7
BIBLIOGRAPHY 14 EXERCISES 15 2 ROUNDOFF ERROR 17 2.1 NUMBER
REPRESENTATION 17 2.2 ROUNDOFF ERROR 25 2.3 ERROR ANALYSIS 35 2.4
CONDITION AND STABILITY 45 BIBLIOGRAPHY 53 EXERCISES 54 3 LINEAR
ALGEBRAIC EQUATIONS 63 3.1 INTRODUCTION 64 3.2 GAUSSIAN ELIMINATION 67
3.3 DIRECT TRIANGULAR DECOMPOSITION 74 3.4 ERROR ANALYSIS 81 3.5 MATRIX
INVERSION 90 3.6 SINGULAR VALUE DECOMPOSITION 91 3.7 ITERATIVE METHODS
100 BIBLIOGRAPHY 104 EXERCISES 105 4 INTERPOLATION 114 4.1 POLYNOMIAL
INTERPOLATION 115 4.2 DIVIDED DIFFERENCE INTERPOLATION FORMULA 120 VI
CONTENTS 4.3 HERMITE INTERPOLATION 130 4.4 CUBIC SPLINE INTERPOLATION
132 4.5 B-SPLINES 137 4.6 RATIONAL FUNCTION INTERPOLATION 142 4.7
INTERPOLATION IN TWO OR MORE DIMENSIONS 148 4.8 SPLINE INTERPOLATION IN
TWO OR MORE DIMENSIONS 150 BIBLIOGRAPHY 153 EXERCISES 153 5
DIFFERENTIATION 160 5.1 DIFFERENTIATION OF INTERPOLATING POLYNOMIALS 160
5.2 METHOD OF UNDETERMINED COEFFICIENTS 164 5.3 EXTRAPOLATION METHOD 168
BIBLIOGRAPHY 172 EXERCISES 173 6 INTEGRATION 175 6.1 NEWTON-COTES
QUADRATURE FORMULAS 176 6.2 EXTRAPOLATION METHODS 186 6.3 GAUSSIAN
QUADRATURE 193 6.4 ROUNDOFF ERROR 198 6.5 WEIGHT FUNCTION 201 6.6
IMPROPER INTEGRALS 209 6.7 INTEGRATION OVER INFINITE INTERVAL 220 6.8
AUTOMATIC INTEGRATION 224 6.9 SUMMATION 235 6.10 MULTIPLE INTEGRALS 242
6.11 RULES EXACT FOR MONOMIALS 247 6.12 MONTE CARLO METHOD 253 6.13
EQUIDISTRIBUTED SEQUENCES 259 BIBLIOGRAPHY 264 EXERCISES ; 265 7
NONLINEAR ALGEBRAIC EQUATIONS 277 7.1 REAL ROOTS 278 7.2 FIXED-POINT
ITERATION 282 7.3 METHOD OF FALSE POSITION 284 7.4 SECANT METHOD 289 7.5
NEWTON-RAPHSON METHOD 293 7.6 BRENT S METHOD 297 7.7 COMPLEX ROOTS 302
7.8 MULLER S METHOD 305 7.9 QUADRATURE BASED METHOD 309 CONTENTS VII
7.10 REAL ROOTS OF POLYNOMIALS 313 7.11 LAGUERRE S METHOD 316 7.12
ROUNDOFF ERROR 320 7.13 CRITERION FOR ACCEPTANCE OF A ROOT 323 7.14
ILL-CONDITIONING 326 7.15 SYSTEM OF NONLINEAR EQUATIONS 330 7.16
NEWTON S METHOD 335 7.17 BROYDEN S METHOD 340 BIBLIOGRAPHY 342 EXERCISES
343 8 OPTIMISATION 354 8.1 GOLDEN SECTION SEARCH 356 8.2 BRENT S METHOD
362 8.3 METHODS USING DERIVATIVE 365 8.4 MINIMISATION IN SEVERAL
DIMENSIONS 369 8.5 QUASI-NEWTON METHODS 373 8.6 DIRECTION SET METHODS
380 8.7 LINEAR PROGRAMMING 387 8.8 SIMULATED ANNEALING 398 BIBLIOGRAPHY
403 EXERCISES 404 9 FUNCTIONAL APPROXIMATIONS 409 9.1 CHOICE OF NORM AND
MODEL 410 9.2 LINEAR LEAST SQUARES 415 9.3 NONLINEAR LEAST SQUARES 431
9.4 LEAST SQUARES APPROXIMATION IN TWO DIMENSIONS 436 9.5 DISCRETE
FOURIER TRANSFORM 438 9.6 FAST FOURIER TRANSFORM 443 9.7 FFT IN TWO OR
MORE DIMENSIONS 452 9.8 INVERSION OF LAPLACE TRANSFORM 454 9.9 PADE
APPROXIMATIONS 457 9.10 CHEBYSHEV EXPANSIONS 463 9.11 MINIMAX
APPROXIMATIONS 472 9.12 DISCRETE MINIMAX APPROXIMATIONS 481 9.13
LI-APPROXIMATIONS 486 BIBLIOGRAPHY 488 EXERCISES 490 10 ALGEBRAIC
EIGENVALUE PROBLEM 502 10.1 INTRODUCTION 503 10.2 POWER METHOD 507 VIII
CONTENTS 10.3 INVERSE ITERATION 513 10.4 EIGENVALUES OF A REAL SYMMETRIC
MATRIX 520 10.5 THE QL ALGORITHM 527 10.6 REDUCTION OF A MATRIX TO
HESSENBERG FORM 531 10.7 LANCZOS METHOD 535 10.8 QR ALGORITHM FOR A REAL
HESSENBERG MATRIX 537 10.9 ROUNDOFF ERRORS 543 BIBLIOGRAPHY 545
EXERCISES 545 11 ORDINARY DIFFERENTIAL EQUATIONS 552 11.1 INITIAL VALUE
PROBLEM 553 11.2 STABILITY OF NUMERICAL INTEGRATION METHODS 557 11.3
PREDICTOR-CORRECTOR METHODS 565 11.4 RUNGE-KUTTA METHODS 579 11.5
EXTRAPOLATION METHODS 587 11.6 STIFF DIFFERENTIAL EQUATIONS 589 11.7
BOUNDARY VALUE PROBLEM 598 11.8 FINITE DIFFERENCE METHODS 605 11.9
EIGENVALUE PROBLEM 613 11.10 EXPANSION METHODS 620 11.11 SOME SPECIAL
TECHNIQUES 623 BIBLIOGRAPHY 627 EXERCISES 628 12 INTEGRAL EQUATIONS 638
12.1 INTRODUCTION 639 12.2 FREDHOLM EQUATIONS OF THE SECOND KIND 642
12.3 EXPANSION METHODS 649 12.4 EIGENVALUE PROBLEM 653 12.5 FREDHOLM
EQUATIONS OF THE FIRST KIND 657 12.6 INVERSE PROBLEMS ...- 661 12.7
VOLTERRA EQUATIONS OF THE SECOND KIND 666 12.8 VOLTERRA EQUATIONS OF THE
FIRST KIND 672 BIBLIOGRAPHY 675 EXERCISES 676 13 PARTIAL DIFFERENTIAL
EQUATIONS 682 13.1 INTRODUCTION 683 13.2 DIFFUSION EQUATION IN TWO
DIMENSIONS 687 13.3 GENERAL PARABOLIC EQUATION IN TWO DIMENSIONS 697
13.4 PARABOLIC EQUATIONS IN SEVERAL SPACE VARIABLES 704 13.5 WAVE
EQUATION IN TWO DIMENSIONS 708 CONTENTS IX 13.6 GENERAL HYPERBOLIC
EQUATIONS 714 13.7 ELLIPTIC EQUATIONS 720 13.8 SUCCESSIVE
OVER-RELAXATION METHOD 727 13.9 ALTERNATING DIRECTION METHOD 731 13.10
FOURIER TRANSFORM METHOD 734 13.11 FINITE ELEMENT METHODS 736
BIBLIOGRAPHY 742 EXERCISES 743 APPENDIX A: ANSWERS AND HINTS 751 A.I
INTRODUCTION 751 A.2 ROUNDOFF ERROR 752 A.3 LINEAR ALGEBRAIC EQUATIONS
758 A.4 INTERPOLATION 763 A.5 DIFFERENTIATION 767 A.6 INTEGRATION 769
A.7 NONLINEAR ALGEBRAIC EQUATIONS 775 A.8 OPTIMISATION 782 A.9
FUNCTIONAL APPROXIMATIONS 784 A. 10 ALGEBRAIC EIGENVALUE PROBLEM 792 A.
11 ORDINARY DIFFERENTIAL EQUATIONS 796 A.12 INTEGRAL EQUATIONS 800 A.13
PARTIAL DIFFERENTIAL EQUATIONS 802 BIBLIOGRAPHY 805 INDEX 806
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| bvnumber | BV014129061 |
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| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV014129061 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:58:12Z |
| institution | BVB |
| isbn | 3764367156 |
| language | English |
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| physical | XXII, 842 S. 1 CD-ROM (12 cm) |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Birkhäuser |
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| spelling | Antia, H. M. Verfasser (DE-588)123485886 aut Numerical methods for scientists and engineers H. M. Antia 2. ed. Boston ; Basel ; Berlin Birkhäuser 2002 XXII, 842 S. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009683425&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Antia, H. M. Numerical methods for scientists and engineers Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Numerical methods for scientists and engineers |
| title_auth | Numerical methods for scientists and engineers |
| title_exact_search | Numerical methods for scientists and engineers |
| title_full | Numerical methods for scientists and engineers H. M. Antia |
| title_fullStr | Numerical methods for scientists and engineers H. M. Antia |
| title_full_unstemmed | Numerical methods for scientists and engineers H. M. Antia |
| title_short | Numerical methods for scientists and engineers |
| title_sort | numerical methods for scientists and engineers |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009683425&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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