E-Book, Englisch, 254 Seiten, Web PDF
Todd / Blanc / Ghizzetti Numerical Analysis
1. Auflage 2014
ISBN: 978-1-4832-6891-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 254 Seiten, Web PDF
ISBN: 978-1-4832-6891-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Basic Numerical Mathematics, Volume 1: Numerical Analysis focuses on numerical analysis, with emphasis on the ideas of 'controlled computational experiments' and 'bad examples'. The concepts of convergence and continuity are discussed, along with the rate of convergence, acceleration, and asymptotic series. The more traditional topics of interpolation, quadrature, and differential equations are also explored. Comprised of 10 chapters, this volume begins with an analysis of the algorithms of Gauss, Borchardt, and Carlson in relation to the rate of convergence. The reader is then introduced to orders of magnitude and rates of convergence; recurrence relations for powers; and the solution of equations. Subsequent chapters deal with uniform convergence and approximation; the acceleration processes of Aitken and Euler; asymptotic series; interpolation; and quadrature. The final chapter is devoted to linear difference equations with constant coefficients, along with differentiation and differential equations. This book will be of interest to mathematicians and students of mathematics.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Numerical Analysis;4
3;Copyright Page;5
4;Table of Contents;8
5;Notations and Abbreviations;9
6;Preface;11
7;CHAPTER 1. The Algorithms of Gauss, Borchardt and Carlson;14
7.1;1. THE ARITHMETIC-GEOMETRIC MEAN OF GAUSS;14
7.2;2. THE ALGORITHM OF BORCHARDT;16
7.3;3. THE CARLSON ALGORITHM;17
7.4;4. HISTORICAL REMARKS;18
7.5;Chapter 1, Problems;20
8;CHAPTER 2. Orders of Magnitude and Rates of Convergence;25
8.1;1. ORDERS OF MAGNITUDE;25
8.2;2. RATES OF CONVERGENCE;30
8.3;Chapter 2, Problems;31
9;CHAPTER 3. Recurrence Relations for Powers;34
9.1;1. RECIPROCALS;34
9.2;2. SQUARE ROOTS;38
9.3;3. ...R.TIO.;39
9.4;4. ORIGIN OF THE RECURRENCE RELATIONS;40
9.5;5. PRACTICAL COMPUTATION AND THEORETICAL ARITHMETIC;43
9.6;Chapter 3, Problems;44
10;CHAPTER 4. The Solution of Equations;47
10.1;1. QUADRATIC EQUATIONS;47
10.2;2. BAD EXAMPLES;48
10.3;3. NEWTON'S PROCESS;49
10.4;4. NEWTON'S PROCESS FOR POLYNOMIAL EQUATIONS;53
10.5;Chapter 4, Problems;54
11;CHAPTER 5. Uniform Convergence and Approximations;56
11.1;1. UNIFORM CONVERGENCE;56
11.2;2. WEIERSTRASS THEOREM. BERNSTEIN PROOF;59
11.3;3. BEST APPROXIMATION: CHEBYSHEV POLYNOMIALS;61
11.4;Chapter 5, Problems;63
12;CHAPTER 6. The Acceleration Processes of Aitken and Euler;67
12.1;1. THE AITKEN TRANSFORM OF A SEQUENCE;67
12.2;2. THE EULER TRANSFORM OF AN ALTERNATING SERIES;69
12.3;Chapter 6, Problems;71
13;CHAPTER 7. Asymptotic Series;74
13.1;1. A CLASSICAL EXAMPLE;74
13.2;2. THE FRESNEL INTEGRALS;77
13.3;3. THE ERROR FUNCTIONS;78
13.4;4. THE GAMMA FUNCTION;80
13.5;5. THE COMPUTATION OF FUNCTIONS;80
13.6;6. THE TABULATION OF FUNCTIONS;82
13.7;Chapter 7, Problems;83
14;CHAPTER 8. Interpolation;85
14.1;1. LAGRANGIAN INTERPOLATION;85
14.2;2. AlTKEN'S ALGORITHM;87
14.3;3. INVERSE INTERPOLATION;89
14.4;4. ERRORS IN INTERPOLATION;90
14.5;5. HERMITE INTERPOLATION;91
14.6;Chapter 8, Problems;94
15;CHAPTER 9. Quadrature;98
15.1;1. TRAPEZOIDAL QUADRATURE;98
15.2;2. RICHARDSON – EXTRAPOLATION – ROMBERG QUADRATURE;101
15.3;3. GAUSSIAN QUADRATURE;104
15.4;4. GAUSS – CHEBYSHEV QUADRATURE;106
15.5;5. THE LEMNISCATE CONSTANTS;110
15.6;6. STIRLING's FORMULA;112
15.7;Chapter 9, Problems;114
16;CHAPTER 10. Difference Equations, Differentiation and Differential Equations;119
16.1;1. DIFFERENCE EQUATIONS;119
16.2;2. DIFFERENCING;122
16.3;3. DIFFERENTIATION;123
16.4;4. DIFFERENTIAL EQUATIONS – TYPES OF PROBLEMS;124
16.5;5. NUMERICAL SOLUTION: PICARD, EULER, HEUN;126
16.6;6. MILNE–SIMPSON PREDICTOR-CORRECTOR;128
16.7;7. LOCAL TAYLOR SERIES;130
16.8;8. INSTABILFTY;131
16.9;9. TWO POINT PROBLEMS;132
16.10;Chapter 10, Problems;134
17;APPENDIX: Bessel Functions;142
18;Solutions to Selected Problems;160
19;Bibliographical Remarks;248
20;Contents Vol. 2, Numerical Algebra;251
21;INDEX;252
