Numerical analysis: with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Chapman & Hall
1961
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 594 S. |
Internformat
MARC
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| 245 | 1 | 0 | |a Numerical analysis |b with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable |c Zdeněk Kopal |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a London |b Chapman & Hall |c 1961 | |
| 300 | |a XVI, 594 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Numerieke wiskunde |2 gtt | |
| 650 | 4 | |a Calculus | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 4 | |a Numerical calculations | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-001363792 | ||
Datensatz im Suchindex
| _version_ | 1804116534515204096 |
|---|---|
| adam_text | CONTENTS
Preface to the Second Edition vii
Preface i*
I. Introduction 1
II. Polynomial Interpolation
A. Statement of the Problem. Weierstrass s Theorem
on Polynomial Approximation 18
B. Lagrangian Interpolation 20
C. Remainder Term 22
D. Divided Differences. Newton s Interpolation
Formula 26
E. Other Approaches to Interpolation. Hemrite s
Formula 31
F. Interpolation by Iteration. Aitken s and Neville s
Processes 36
G. Interpolation with Equal Intervals. Tabular Dif¬
ferences. Newton s Forward and Backward
Formulae 39
H. Interpolation Formulae of Gauss, Stirling, and
Bessel 43
J. Fraser Diagram and its Use 47
K. Interpolation Formulae of Everett and Steffensen 50
*L. Throwback, and Construction of Tables 54
M. Inverse Interpolation 64
N. Round off Errors. Propagation and Detection of
Errors in Tabular Differences 69
Bibliographical Notes 78
Problems 83
III. Numerical Differentiation
A. Introduction. Differentiation of the Formulae of
Lagrange, Hermite, and Newton 87
B. Differentiation of the Remainder Term. Errors of
the Formulae for Numerical Differentiation 92
C. Derivatives in Terms of Tabular Differences 97
D. Tabular Differences in Terms of the Derivatives 102
*E. Optimum Interval for Numerical Differentiation 104
F. Applications of Numerical Differentiation, Curve
Fitting 111
Bibliographical Notes 114
Problems 115
xiii
jSTUMEBICAL ANALYSIS
IV. Integration of Ordinary Differential Equations
A. Statement of the Problem 119
B. Quadratures in Terms of Tabular Differences 122
C. Differential Equations of First Order 128
D. Differential Equations of Second and Higher Orders 135
E. Start of a Solution. Method of Taylor Series 140
P. Picard s Approximations 145
*G. Expansion in Power Series 153
*H. Differential Equations of Functions defined by
Power Series 163 I
J. Solution of Differential Equations by Successive
Extrapolation 169
*K. Successive Extrapolation. Application to Practical
Cases 178
L. Solution of Differential Equations by Successive
Substitutions 195
M. Propagation of Errors in Numerical Solutions of
Differential Equations 219
Bibliographical Notes 231
Problems 234
V. Boundary Value Problems: Algebraic Methods
A. Introduction 240
B. Use of Lagrangian Three Point Formulae 243
C. Deferred Approach to the Limit 250
D. Use of Three Point Extrapolation Formulae 255
E. Use of Five Point Formulae 263
F. Use of Five Point Extrapolation Formulae 269
*G. Use of Seven Point Extrapolation Formulae 272
H. Miscellaneous Boundary Value Problems 277
J. Construction of the Characteristic Functions. Non
homogeneous Problems 283
K. Methods Employing Finite Differences 287
Bibliographical Notes 295
Problems 296
VI. Boundary Value Problems: Variational, Iterative,
and other Methods
A. Introduction. Rayleigh s Principle 299
B. Rayleigh Bitz Method 303
C. Bayleigh Bitz Method: Particular Cases 309
D. Iterative Methods: Introduction 319
E. Schwarz s Method: Fundamental Mode 322
*F. Schwarz s Method: Higher Modes 331
xiv
CONTENTS
G. interpolation ( Collocation ) Method 335
H. Least Squares Method 340
Bibliographical Notes 343
Problems 345
VII. Mechanical Quadratures
A. Introduction 347
B. Gaussian Quadratures: Algebraic Approach 349
C. Gaussian Quadratures: Geometric Approach 352
D. Gaussian Quadratures: Analytical Approach 354
E. Gaussian Quadratures: Infinite Intervals 359
F. Some General Properties of Gaussian Abscissae and
Weight Coefficients 362
G. Particular Types of Gaussian Quadrature Formulae 367
H. Weight Functions: General 373
*J. Christoffel s Weight Functions 376
*K. Mehler s and Other Weight Functions 381
*L. Repeated Gaussian Quadratures 386
M. Pre assigned Abscissae or Weights. Radau s Quad¬
rature Formulae 390
N. Newton Cotes Quadrature Formulae: General 397
O. Newton Cotes Quadratures: Particular Cases 405
P. Quadrature Formulae obtainable by Combination
of the Newton Cotes Formulae. Weddle s and
Hardy s Rules 410
Q. Accumulation of Errors in Mechanical Quadratures 415
R. Tchebysheff Quadrature Formulae 417
S. Stochastic ( Monte Carlo ) Methods of Quadratures 428
Bibliographical Notes 430
Problems 434
VIII. Numerical Solution of Integral and Integro
Differential Equations
A. Introduction 440
*B. Equivalence of Integral Equations with Initial Value
Problems 441
*C. Equivalence of Integral Equations with Boundary
Value Problems 444
*D. Green s Function and its Construction 447
E. Numerical Solution of Integral Equations: Algebraic 452
Methods
F. Numerical Solution of Integral Equations: Iterative 465
and Other Methods
G. Collocation and Least Squares Methods 471
H. Numerical Solution of Integro Differential Equa¬
tions 474
Bibliographical Notes 481
Problems 483
XV
NUMERICAL ANALYSIS
IX. Operational Methods in Numerical Analysis
A. Introduction 486
B. Operational Methods: Polynomial Approximations 490
C. Operational Methods: Rational Approximations 499
D. Formulae of Integration 506
E. Problems of Stability 513
Bibliographical Notes 520
Problems 521
Appendices
I. Trigonometric Interpolation. Tchebysheff Poly.
nomials and their Use for Optimum Interval
Interpolation 523
II. Rational Approximations to the Integration Opera¬
tors in terms of Central and Diagonal Differences 543
III. Coefficients of the Lagrangian Formulae for
Numerical Differentiation 554
IV. Abscissae and Weight Coefficients of Different
Formulae for Mechanical Quadratures 562
V. Notes on the Resolution of Algebraic Equations,
and of Systems of Linear Equations 582
Name Index 585
Subject Index 589
* See Preface, page x
xvi
|
| any_adam_object | 1 |
| author | Kopal, Zdeněk 1914-1993 |
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| dewey-raw | 519.4 |
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| dewey-sort | 3519.4 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:40:02Z |
| institution | BVB |
| language | English |
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| physical | XVI, 594 S. |
| publishDate | 1961 |
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| publisher | Chapman & Hall |
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| spelling | Kopal, Zdeněk 1914-1993 Verfasser (DE-588)118987844 aut Numerical analysis with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable Zdeněk Kopal 2. ed. London Chapman & Hall 1961 XVI, 594 S. txt rdacontent n rdamedia nc rdacarrier Numerieke wiskunde gtt Calculus Numerical analysis Numerical calculations Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001363792&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kopal, Zdeněk 1914-1993 Numerical analysis with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable Numerieke wiskunde gtt Calculus Numerical analysis Numerical calculations Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Numerical analysis with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable |
| title_auth | Numerical analysis with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable |
| title_exact_search | Numerical analysis with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable |
| title_full | Numerical analysis with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable Zdeněk Kopal |
| title_fullStr | Numerical analysis with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable Zdeněk Kopal |
| title_full_unstemmed | Numerical analysis with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable Zdeněk Kopal |
| title_short | Numerical analysis |
| title_sort | numerical analysis with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable |
| title_sub | with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable |
| topic | Numerieke wiskunde gtt Calculus Numerical analysis Numerical calculations Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerieke wiskunde Calculus Numerical analysis Numerical calculations Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001363792&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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