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Numerical analysis: with emphasis on the application of numerical techniques to problems of infinitesimal calculus in single variable

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Bibliographische Detailangaben
Beteilige Person:	Kopal, Zdeněk 1914-1993 (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	London Chapman & Hall 1961
Ausgabe:	2. ed.
Schlagwörter:	Numerieke wiskunde Calculus Numerical analysis Numerical calculations Numerische Mathematik
Links:	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
Umfang:	XVI, 594 S.

Internformat

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Datensatz im Suchindex

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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
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language	English
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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
work_keys_str_mv	AT kopalzdenek numericalanalysiswithemphasisontheapplicationofnumericaltechniquestoproblemsofinfinitesimalcalculusinsinglevariable

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