An introduction to numerical methods: a MATLAB approach
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall / CRC
2006
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 608 S. graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 1584885572 9781584885573 |
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Record in the Search Index
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| adam_text | SECOND EDITION AN INTRODUCTION TO NUMERICAL METHODS A MATLAB APPROACH
ABDELWAHAB KHARAB KINGFAHD UNIVERSITY OF PETROLEUM AND MINERALS RONALD
B. GUENTHER OREGON STATE UNIVERSITY ^IJCHAPMAN & HALL/CRC ^ 1 1 TAYLOR
& FRANCIS GROUP BOCA RATON LONDON NEW YORK SINGAPORE CONTENTS 1
INTRODUCTION 1 1.1 ABOUT THE SOFTWARE MATLAB 1 1.2 AN INTRODUCTION TO
MATLAB 2 1.2.1 MATRICES AND MATRIX COMPUTATION 2 1.2.2 POLYNOMIALS 7
1.2.3 OUTPUT FORMAT 8 1.2.4 PLANAR PLOTS 9 1.2.5 3-D MESH PLOTS 10 1.2.6
FUNCTION FILES 11 1.2.7 DEFINING FUNCTIONS 12 1.2.8 RELATIONS AND LOOPS
13 1.3 TAYLOR SERIES 17 2 NUMBER SYSTEM AND ERRORS 25 2.1 FLOATING-POINT
ARITHMETIC . 25 2.2 ROUND-OFF ERRORS 30 2.3 TRUNCATION ERROR 36 2.4
INTERVAL ARITHMETIC 38 3 ROOTS OF EQUATIONS 45 3.1 THE BISECTION METHOD
47 3.2 THE METHOD OF FALSE POSITION 55 3.3 FIXED-POINT ITERATION 62 3.4
THE SECANT METHOD 70 3.5 NEWTON S METHOD 76 3.6 CONVERGENCE OF THE
NEWTON AND SECANT METHODS 87 3.7 MULTIPLE ROOTS AND THE MODIFIED NEWTON
METHOD 90 3.8 NEWTON S METHOD FOR NONLINEAR SYSTEMS 97 APPLIED PROBLEMS
103 4 SYSTEM OF LINEAR EQUATIONS 111 4.1 MATRICES AND MATRIX OPERATIONS
112 4.2 NAIVE GAUSSIAN ELIMINATION 116 4.3 GAUSSIAN ELIMINATION WITH
SCALED PARTIAL PIVOTING 124 4.4 LU DECOMPOSITION 139 4.4.1 CROUT S AND
CHOLESKI S METHODS 140 4.4.2 GAUSSIAN ELIMINATION METHOD 144 4.5
ITERATIVE METHODS 155 4.5.1 JACOBI ITERATIVE METHOD 156 4.5.2
GAUSS-SEIDEL ITERATIVE METHOD 159 4.5.3 CONVERGENCE 160 APPLIED PROBLEMS
170 5 INTERPOLATION 179 5.1 POLYNOMIAL INTERPOLATION THEORY 180 5.2
NEWTON S DIVIDED DIFFERENCE INTERPOLAT- ING POLYNOMIAL 183 5.3 THE ERROR
OF THE INTERPOLATING POLYNOMIAL 195 5.4 LAGRANGE INTERPOLATING
POLYNOMIAL ... 201 APPLIED PROBLEMS 207 6 INTERPOLATION WITH SPLINE
FUNCTIONS 211 6.1 PIECEWISE LINEAR INTERPOLATION 212 6.2 QUADRATIC
SPLINE 219 6.3 NATURAL CUBIC SPLINES 224 APPLIED PROBLEMS 240 7 THE
METHOD OF LEAST SQUARES 243 7.1 LINEAR LEAST SQUARES 244 7.2 LEAST
SQUARES POLYNOMIAL 251 7.3 NONLINEAR LEAST SQUARES 260 7.3.1 EXPONENTIAL
FORM 260 7.3.2 HYPERBOLIC FORM 262 7.4 TRIGONOMETRIC LEAST SQUARES
POLYNOMIAL 269 APPLIED PROBLEMS 272 8 NUMERICAL OPTIMIZATION 275 8.1
ANALYSIS OF SINGLE-VARIABLE FUNCTIONS . . 276 8.2 LINE SEARCH METHODS
278 8.2.1 BRACKETING THE MINIMUM 278 8.2.2 GOLDEN SECTION SEARCH 279
8.2.3 FIBONACCI SEARCH 283 8.2.4 PARABOLIC INTERPOLATION 286 8.3
MINIMIZATION USING DERIVATIVES 294 8.3.1 NEWTON S METHOD 294 8.3.2
SECANT METHOD 295 APPLIED PROBLEMS 298 9 NUMERICAL DIFFERENTIATION 301
9.1 NUMERICAL DIFFERENTIATION 301 9.2 RICHARDSON S FORMULA 309 APPLIED
PROBLEMS 316 10 NUMERICAL INTEGRATION 321 10.1 TRAPEZOIDAL RULE 322 10.2
SIMPSON S RULE 333 10.3 ROMBERG ALGORITHM 344 10.4 GAUSSIAN QUADRATURE
353 APPLIED PROBLEMS 365 11 NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS
371 11.1 EULER S METHOD 372 11.2 ERROR ANALYSIS 380 11.3 HIGHER ORDER
TAYLOR SERIES METHODS ... 385 11.4 RUNGE-KUTTA METHODS 390 11.5
MULTISTEP METHODS 406 11.6 ADAMS-BASHFORTH METHODS 406 11.7
PREDICTOR-CORRECTOR METHODS 417 11.8 ADAMS-MOULTON METHODS 418 11.9
NUMERICAL STABILITY 427 11.10 HIGHER ORDER EQUATIONS AND SYSTEMS OF
DIFFERENTIAL EQUATIONS 431 11.11 IMPLICIT METHODS AND STIFF SYSTEMS ....
438 11.12 PHASE PLANE ANALYSIS: CHAOTIC DIFFERENTIAL EQUATIONS 441
APPLIED PROBLEMS 447 12 BOUNDARY-VALUE PROBLEMS 457 12.1
FINITE-DIFFERENCE METHODS 458 12.2 SHOOTING METHODS 467 12.2.1 THE
NONLINEAR CASE 467 12.2.2 THE LINEAR CASE 472 APPLIED PROBLEMS 480 13
EIGENVALUES AND EIGENVECTORS 485 13.1 BASIC THEORY 485 13.2 THE POWER
METHOD 490 13.3 THE QUADRATIC METHOD 494 13.4 EIGENVALUES FOR
BOUNDARY-VALUE PROBLEMS 505 13.5 BIFURCATIONS IN DIFFERENTIAL EQUATIONS
508 APPLIED PROBLEMS 513 14 PARTIAL DIFFERENTIAL EQUATIONS 515 14.1
PARABOLIC EQUATIONS 516 14.1.1 EXPLICIT METHODS 516 14.1.2 IMPLICIT
METHODS 521 14.2 HYPERBOLIC EQUATIONS 529 14.3 ELLIPTIC EQUATIONS 536
14.4 INTRODUCTION TO FINITE-ELEMENT METHOD . 543 14.4.1 THEORY 543
14.4.2 THE FINITE ELEMENT METHOD 551 APPLIED PROBLEMS 557 BIBLIOGRAPHY
AND REFERENCES 559 APPENDIX 565 A CALCULUS REVIEW 565 A.L LIMITS AND
CONTINUITY 565 A.2 DIFFERENTIATION 566 A.3 INTEGRATION 567 B MATLAB
BUILT-IN FUNCTIONS 569 C TEXT MATLAB FUNCTIONS 573 ANSWERS TO SELECTED
EXERCISES 575 INDEX 603
|
| adam_txt |
SECOND EDITION AN INTRODUCTION TO NUMERICAL METHODS A MATLAB APPROACH
ABDELWAHAB KHARAB KINGFAHD UNIVERSITY OF PETROLEUM AND MINERALS RONALD
B. GUENTHER OREGON STATE UNIVERSITY ^IJCHAPMAN & HALL/CRC ^ 1 1 TAYLOR
& FRANCIS GROUP BOCA RATON LONDON NEW YORK SINGAPORE CONTENTS 1
INTRODUCTION 1 1.1 ABOUT THE SOFTWARE MATLAB 1 1.2 AN INTRODUCTION TO
MATLAB 2 1.2.1 MATRICES AND MATRIX COMPUTATION 2 1.2.2 POLYNOMIALS 7
1.2.3 OUTPUT FORMAT 8 1.2.4 PLANAR PLOTS 9 1.2.5 3-D MESH PLOTS 10 1.2.6
FUNCTION FILES 11 1.2.7 DEFINING FUNCTIONS 12 1.2.8 RELATIONS AND LOOPS
13 1.3 TAYLOR SERIES 17 2 NUMBER SYSTEM AND ERRORS 25 2.1 FLOATING-POINT
ARITHMETIC . 25 2.2 ROUND-OFF ERRORS 30 2.3 TRUNCATION ERROR 36 2.4
INTERVAL ARITHMETIC 38 3 ROOTS OF EQUATIONS 45 3.1 THE BISECTION METHOD
47 3.2 THE METHOD OF FALSE POSITION 55 3.3 FIXED-POINT ITERATION 62 3.4
THE SECANT METHOD 70 3.5 NEWTON'S METHOD 76 3.6 CONVERGENCE OF THE
NEWTON AND SECANT METHODS 87 3.7 MULTIPLE ROOTS AND THE MODIFIED NEWTON
METHOD 90 3.8 NEWTON'S METHOD FOR NONLINEAR SYSTEMS 97 APPLIED PROBLEMS
103 4 SYSTEM OF LINEAR EQUATIONS 111 4.1 MATRICES AND MATRIX OPERATIONS
112 4.2 NAIVE GAUSSIAN ELIMINATION 116 4.3 GAUSSIAN ELIMINATION WITH
SCALED PARTIAL PIVOTING 124 4.4 LU DECOMPOSITION 139 4.4.1 CROUT'S AND
CHOLESKI'S METHODS 140 4.4.2 GAUSSIAN ELIMINATION METHOD 144 4.5
ITERATIVE METHODS 155 4.5.1 JACOBI ITERATIVE METHOD 156 4.5.2
GAUSS-SEIDEL ITERATIVE METHOD 159 4.5.3 CONVERGENCE 160 APPLIED PROBLEMS
170 5 INTERPOLATION 179 5.1 POLYNOMIAL INTERPOLATION THEORY 180 5.2
NEWTON'S DIVIDED DIFFERENCE INTERPOLAT- ING POLYNOMIAL 183 5.3 THE ERROR
OF THE INTERPOLATING POLYNOMIAL 195 5.4 LAGRANGE INTERPOLATING
POLYNOMIAL . 201 APPLIED PROBLEMS 207 6 INTERPOLATION WITH SPLINE
FUNCTIONS 211 6.1 PIECEWISE LINEAR INTERPOLATION 212 6.2 QUADRATIC
SPLINE 219 6.3 NATURAL CUBIC SPLINES 224 APPLIED PROBLEMS 240 7 THE
METHOD OF LEAST SQUARES 243 7.1 LINEAR LEAST SQUARES 244 7.2 LEAST
SQUARES POLYNOMIAL 251 7.3 NONLINEAR LEAST SQUARES 260 7.3.1 EXPONENTIAL
FORM 260 7.3.2 HYPERBOLIC FORM 262 7.4 TRIGONOMETRIC LEAST SQUARES
POLYNOMIAL 269 APPLIED PROBLEMS 272 8 NUMERICAL OPTIMIZATION 275 8.1
ANALYSIS OF SINGLE-VARIABLE FUNCTIONS . . 276 8.2 LINE SEARCH METHODS
278 8.2.1 BRACKETING THE MINIMUM 278 8.2.2 GOLDEN SECTION SEARCH 279
8.2.3 FIBONACCI SEARCH 283 8.2.4 PARABOLIC INTERPOLATION 286 8.3
MINIMIZATION USING DERIVATIVES 294 8.3.1 NEWTON'S METHOD 294 8.3.2
SECANT METHOD 295 APPLIED PROBLEMS 298 9 NUMERICAL DIFFERENTIATION 301
9.1 NUMERICAL DIFFERENTIATION 301 9.2 RICHARDSON'S FORMULA 309 APPLIED
PROBLEMS 316 10 NUMERICAL INTEGRATION 321 10.1 TRAPEZOIDAL RULE 322 10.2
SIMPSON'S RULE 333 10.3 ROMBERG ALGORITHM 344 10.4 GAUSSIAN QUADRATURE
353 APPLIED PROBLEMS 365 11 NUMERICAL METHODS FOR DIFFERENTIAL EQUATIONS
371 11.1 EULER'S METHOD 372 11.2 ERROR ANALYSIS 380 11.3 HIGHER ORDER
TAYLOR SERIES METHODS . 385 11.4 RUNGE-KUTTA METHODS 390 11.5
MULTISTEP METHODS 406 11.6 ADAMS-BASHFORTH METHODS 406 11.7
PREDICTOR-CORRECTOR METHODS 417 11.8 ADAMS-MOULTON METHODS 418 11.9
NUMERICAL STABILITY 427 11.10 HIGHER ORDER EQUATIONS AND SYSTEMS OF
DIFFERENTIAL EQUATIONS 431 11.11 IMPLICIT METHODS AND STIFF SYSTEMS .
438 11.12 PHASE PLANE ANALYSIS: CHAOTIC DIFFERENTIAL EQUATIONS 441
APPLIED PROBLEMS 447 12 BOUNDARY-VALUE PROBLEMS 457 12.1
FINITE-DIFFERENCE METHODS 458 12.2 SHOOTING METHODS 467 12.2.1 THE
NONLINEAR CASE 467 12.2.2 THE LINEAR CASE 472 APPLIED PROBLEMS 480 13
EIGENVALUES AND EIGENVECTORS 485 13.1 BASIC THEORY 485 13.2 THE POWER
METHOD 490 13.3 THE QUADRATIC METHOD 494 13.4 EIGENVALUES FOR
BOUNDARY-VALUE PROBLEMS 505 13.5 BIFURCATIONS IN DIFFERENTIAL EQUATIONS
508 APPLIED PROBLEMS 513 14 PARTIAL DIFFERENTIAL EQUATIONS 515 14.1
PARABOLIC EQUATIONS 516 14.1.1 EXPLICIT METHODS 516 14.1.2 IMPLICIT
METHODS 521 14.2 HYPERBOLIC EQUATIONS 529 14.3 ELLIPTIC EQUATIONS 536
14.4 INTRODUCTION TO FINITE-ELEMENT METHOD . 543 14.4.1 THEORY 543
14.4.2 THE FINITE ELEMENT METHOD 551 APPLIED PROBLEMS 557 BIBLIOGRAPHY
AND REFERENCES 559 APPENDIX 565 A CALCULUS REVIEW 565 A.L LIMITS AND
CONTINUITY 565 A.2 DIFFERENTIATION 566 A.3 INTEGRATION 567 B MATLAB
BUILT-IN FUNCTIONS 569 C TEXT MATLAB FUNCTIONS 573 ANSWERS TO SELECTED
EXERCISES 575 INDEX 603 |
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| index_date | 2024-07-02T13:57:06Z |
| indexdate | 2024-07-09T20:35:27Z |
| institution | BVB |
| isbn | 1584885572 9781584885573 |
| language | English |
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| physical | 608 S. graph. Darst. 1 CD-ROM (12 cm) |
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| publisher | Chapman & Hall / CRC |
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| spelling | Kharab, Abdelwahab Verfasser aut An introduction to numerical methods a MATLAB approach Abdelwahab Kharab ; Ronald B. Guenther A MATLAB approach 2. ed. Boca Raton [u.a.] Chapman & Hall / CRC 2006 608 S. graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier MATLAB Analyse numérique - Informatique Analyse numérique - Informatique ram MATLAB (logiciel) ram Datenverarbeitung Numerical analysis Data processing MATLAB (DE-588)4329066-8 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s MATLAB (DE-588)4329066-8 s DE-604 Guenther, Ronald B. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014635295&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kharab, Abdelwahab Guenther, Ronald B. An introduction to numerical methods a MATLAB approach MATLAB Analyse numérique - Informatique Analyse numérique - Informatique ram MATLAB (logiciel) ram Datenverarbeitung Numerical analysis Data processing MATLAB (DE-588)4329066-8 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4329066-8 (DE-588)4042805-9 |
| title | An introduction to numerical methods a MATLAB approach |
| title_alt | A MATLAB approach |
| title_auth | An introduction to numerical methods a MATLAB approach |
| title_exact_search | An introduction to numerical methods a MATLAB approach |
| title_exact_search_txtP | An introduction to numerical methods a MATLAB approach |
| title_full | An introduction to numerical methods a MATLAB approach Abdelwahab Kharab ; Ronald B. Guenther |
| title_fullStr | An introduction to numerical methods a MATLAB approach Abdelwahab Kharab ; Ronald B. Guenther |
| title_full_unstemmed | An introduction to numerical methods a MATLAB approach Abdelwahab Kharab ; Ronald B. Guenther |
| title_short | An introduction to numerical methods |
| title_sort | an introduction to numerical methods a matlab approach |
| title_sub | a MATLAB approach |
| topic | MATLAB Analyse numérique - Informatique Analyse numérique - Informatique ram MATLAB (logiciel) ram Datenverarbeitung Numerical analysis Data processing MATLAB (DE-588)4329066-8 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | MATLAB Analyse numérique - Informatique MATLAB (logiciel) Datenverarbeitung Numerical analysis Data processing Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014635295&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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