Introduction to numerical analysis and applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chicago
Markham
1971
|
| Schriftenreihe: | Markham mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX,182 S.m.Abb. |
| ISBN: | 084101020X |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | CONTENTS
Preface v
Chapter 1. Approximation 1
1.1 Introduction 1
1.2 Discrete Functions 1
1.3 Interpolation 3
1.4 Lagrange Interpolation Formulas 5
1.5 General Theory 9
1.6 Least Squares Interpolation 12
1.7 Selected Theory for Least Squares Interpolation 15
1.8 Remarks 18
Exercises 18
Chapter 2. Approximate Integration and Differentiation 22
2.1 Introduction 22
2.2 Trapezoidal Rule 23
2.3 Theory for the Trapezoidal Rule 25
2.4 Simpson s Rule 29
2.5 Theory for Simpson s Rule 30
2.6 Approximate Integration by Least Squares 32
2.7 Remarks on Approximate Integration 32
2.8 Approximate Differentiation 34
Exercises 40
Chapter 3. Algebraic and Transc endental Systems 42
3.1 Introduction 42
3.2 Matrices and Linear Systems 42
3.3 Tridiagonal Linear Systems 43
vii
viii CONTENTS i
3.4 Direct Solution of Tridiagonal Systems 47
3.5 Iterative Solution of Linear and Nonlinear Systems 53
3.6 Remarks 60
Exercises 60
Chapter 4. Second Order Differential and Difference Equations 65
4.1 Introduction 65
4.2 Linear Differential Equations 67
4.3 Linear Differential Equations with Constant Coefficients 69
4.4 Linear Differential Equations with Nonconstant Coefficients 72
4.5 Initial and Boundary Value Problems 79
4.6 Difference Equations 81
Exercises 85
Chapter 5. Approximate Solution of Boundary Value
Problems for Differential Equations 88
5.1 Introduction 88
5.2 Approximate Solution of Linear Boundary Value Problems 88
5.3 Approximate Solution of Nonlinear Boundary Value
Problems 93
5.4 Convergence 95
5.5 Remarks 99
Exercises 99
Chapter 6. Approximate Solution of Initial Value Problems
for Ordinary Differential Equations 101
6.1 Introduction 101
6.2 First Order Differential Equations 102
6.3 First Order Difference Equations 104
6.4 Euler s Method 105
6.5 Convergence 107
6.6 A Runge Kutta Method 111
6.7 Higher Order Runge Kutta Formulas 113
6.8 Approximate Solution of Initial Value Problems for
Second Order Differential Equations 114
6.9 Nonlinear Pendulum 116
6.10 Instability 119
6.11 Remarks 123
Exercises 123
CONTENTS ix
Chapter 7. Discrete Model Theory 126
7.1 Introduction 126
7.2 Implications of Constraints on Measurement 126
7.3 Special Discrete Functions 127
7.4 Particles, Time, and Motion 129
7.5 Velocity and Acceleration 130
7.6 Law of Motion 133
7.7 Damped Motion in a Nonlinear Force Field 133
7.8 Conservation of Energy 136
7.9 Momentum 139
7.10 Angular Velocity and Acceleration 140
7.11 Remark 144
Exercises 144
Chapter 8. Interval Arithmetic 147
8.1 Introduction 147
8.2 Interval Arithmetic 148
8.3 General Application of Interval Arithmetic 158
8.4 Application to Difference Equations 159
8.5 Remarks 162
Exercises 163
References and Sources for Further Reading 167
Answers to Selected Exercises 173
Index 179
|
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| institution | BVB |
| isbn | 084101020X |
| language | English |
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| physical | IX,182 S.m.Abb. |
| publishDate | 1971 |
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| spelling | Greenspan, Donald 1928- Verfasser (DE-588)130583073 aut Introduction to numerical analysis and applications Chicago Markham 1971 IX,182 S.m.Abb. txt rdacontent n rdamedia nc rdacarrier Markham mathematics series Analyse numérique Analyse numérique - Informatique Numerieke wiskunde gtt Datenverarbeitung Numerical analysis Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content 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=003554230&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Greenspan, Donald 1928- Introduction to numerical analysis and applications Analyse numérique Analyse numérique - Informatique Numerieke wiskunde gtt Datenverarbeitung Numerical analysis Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4151278-9 |
| title | Introduction to numerical analysis and applications |
| title_auth | Introduction to numerical analysis and applications |
| title_exact_search | Introduction to numerical analysis and applications |
| title_full | Introduction to numerical analysis and applications |
| title_fullStr | Introduction to numerical analysis and applications |
| title_full_unstemmed | Introduction to numerical analysis and applications |
| title_short | Introduction to numerical analysis and applications |
| title_sort | introduction to numerical analysis and applications |
| topic | Analyse numérique Analyse numérique - Informatique Numerieke wiskunde gtt Datenverarbeitung Numerical analysis Numerical analysis Data processing Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Analyse numérique Analyse numérique - Informatique Numerieke wiskunde Datenverarbeitung Numerical analysis Numerical analysis Data processing Numerische Mathematik Einführung |
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