Mathematics and statistics for scientists and engineers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
van Nostrand
1966
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 299 S. graph. Darst. |
Internformat
MARC
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| 100 | 1 | |a MacDonald, Peter |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Mathematics and statistics for scientists and engineers |c P. Macdonald |
| 264 | 1 | |a London [u.a.] |b van Nostrand |c 1966 | |
| 300 | |a XII, 299 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathématiques | |
| 650 | 4 | |a Statistique mathématique | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematical statistics | |
| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
| _version_ | 1804121217668481024 |
|---|---|
| adam_text | Contents
Preface v
Notation xi
Chapter 1. Rates of Change
1.1 Introduction 1
1.2 Standard Results in Differentiation 4
1.3 Standard Rules for Differentiation 7
Exercises 1.1 11
1.4 Important Additional Results 11
Exercises 1.2 15
Solutions to Exercises 1.1 16
Solutions to Exercises 1.2 17
References and Bibliography 18
Chapter 2. Integration
2.1 Introduction 19
2.2 Techniques of Integration 20
2.3 Integration by Substitution 21
2.4 Integration by Parts 22
2.5 The Integration of Special Types of Integrand 23
Exercises 2.1 24
Exercises 2.2 28
Solutions to Exercises 2.1 28
Solutions to Exercises 2.2 29
Chapter 3. The Differentiation of Functions of More than One
Variable
3.1 Introduction and Techniques of Differentiation 32
Exercises 3.1 40
3.2 The Calculation of Small Changes in Functions 40
3.3 Total Derivatives 42
3.4 Implicit Functions 42
3.5 The Condition for a Complete Differential 43
Exercises 3.2 45
Solutions to Exercises 3.1 45
Solutions to Exercises 3.2 46
References and Bibliography 47
Chapter 4. Further Techniques in Integration
4.1 Rational Algebraic Functions 48
vii
yiii CONTENTS
4.2 Algebraic Functions with Irrational Denominators 55
Exercises 4.1 56
4.3 Special Trigonometrical Integrands 57
4.4 General Remarks on Integration 60
Exercises 4.2 60
Solutions to Exercises 4.1 61
Solutions to Exercises 4.2 62
Chapter 5. Applications of Differentiation
5.1 The Calculation of Errors and Approximate Changes 63
5.2 The Expansion of Functions in Series 63
Exercises 5.1 69
5.3 The Determination of Maximum and Minimum Values of a
Function 69
Exercises 5.2 74
5.4 The Numerical Solution of Algebraic Equations 74
Exercises 5.3 77
Solutions to Exercises 5.1 77
Solutions to Exercises 5.2 79
Solutions to Exercises 5.3 80
References and Bibliography 81
Chapter 6. Differential Equations
6.1 Introduction 82
6.2 Differential Equations of the First Order 83
Exercises 6.1 87
6.3 Differential Equations of the Second Order 88
Exercises 6.2 92
Solutions to Exercises 6.1 99
Solutions to Exercises 6.2 100
References and Bibliography 103
Chapter 7. Applications of Integration
7.1 Introduction 104
7.2 Integration as a Summation 104
7.3 Applications of Summation to Plane Areas, Volumes and Mean
Values 106
7.4 Applications of Summation to First and Second Moments 113
7.5 The Calculation of Arc Lengths and Surface Areas 123
7.6 Two Theorems of Pappus 126
7.7 A Comprehensive Example 127
7.8 Simpson s Rule 128
Exercises 7.1 130
Solutions to Exercises 7.1 131
References and Bibliography 134
Chapter 8. Applications of Second Order Linear Differential
Equations
8.1 Importance of Second Order Equations 135
8.2 Undamped Oscillations 135
8.3 Damped Oscillations 136
CONTENTS IX
8.4 Application to Electrical Circuits 138
Exercises 8.1 140
Solutions to Exercises 8.1 141
References and Bibliography 144
Chapter 9. Important Geometrical Shapes
9.1 Introduction 145
9.2 Linear Functions 145
9.3 Quadratic Functions 148
9.4 The Curvature of Plane Curves 153
9.5 Cubic Functions 155
9.6 Functions of Polar Coordinates 156
9.7 The Catenary 159
9.8 Other Curves 159
Exercises 9.1 160
Solutions to Exercises 9.1 160
References and Bibliography 164
Chapter 10. Simultaneous Linear Equations
10.1 Introduction 165
10.2 The Algebraic Solution of Simultaneous Equations 166
10.3 Matrix Notation 167
10.4 Matrix Terminology 172
Exercises 10.1 175
10.5 The Use of Matrix Theory in the Solution of Linear Equations 176
Exercises 10.2 184
Solutions to Exercises 10.1 185
Solutions to Exercises 10.2 186
References and Bibliography 189
Chapter 11. Introduction to Statistics
11.1 Measurements 190
11.2 The Normal Distribution 191
11.3 Probability 196
Exercises 11.1 200
11.4 Applications of Statistics 201
Solutions to Exercises 11.1 202
References and Bibliography 203
Chapter 12. The Binomial and Poisson Distributions
12.1 Introduction 204
12.2 Permutations and Combinations 204
12.3 The Binomial Distribution 205
12.4 Applications of the Binomial Distribution 210
12.5 The Poisson Distribution 212
12.6 Applications of the Poisson Distribution 214
Exercises 12.1 216
Solutions to Exercises 12.1 217
X CONTENTS
Chapter 13. Continuous Distributions
13.1 Introduction 218
13.2 The Derivation of the Normal Distribution 218
13.3 The Interpretation of the Normal Distribution 220
Exercises 13.1 222
13.4 Moments of a Distribution 222
13.5 General Normal Distributions 232
13.6 Rapid Methods for the Normal Distribution 234
Exercises 13.2 237
Solutions to Exercises 13.1 238
Solutions to Exercises 13.2 238
References and Bibliography 241
Chapter 14. Significance Tests
14.1 Standard Error of a Sample Mean 242
14.2 Confidence Limits for the Mean 244
14.3 The t Distribution 246
14.4 The Significance of Deviations from a Mean 248
14.5 Testing a Difference in Means 251
14.6 The Paired Comparison Test 254
14.7 The x2 Test 255
Exercises 14.1 259
Solutions to Exercises 14.1 261
References and Bibliography 264
Chapter 15. Curve Fitting
15.1 Introduction 265
15.2 The Method of Least Squares 266
15.3 Correlation 270
15.4 Rank Correlation 272
15.5 Non Linear Functions 274
Exercises 15.1 276
Solutions to Exercises 15.1 277
References and Bibliography 278
Chapter 16. Quality Control
16.1 Introduction 279
16.2 Control Chart for the Range 279
16.3 Control Chart for the Mean 282
16.4 Control Charts for Discrete Variables 283
16.5 The Detection of Trends and Jumps 285
Exercises 16.1 289
Solutions to Exercises 16.1 290
References and Bibliography 291
Table Al The Normal Probability Integral D(x) 292
Table A2 The Integral of the ^ Distribution 294
Table A3 The Integral of the ^ Distribution 295
Table A4 The Distribution of the Range 295
Index 297
|
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| indexdate | 2024-07-09T16:54:28Z |
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| language | English |
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| physical | XII, 299 S. graph. Darst. |
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| spelling | MacDonald, Peter Verfasser aut Mathematics and statistics for scientists and engineers P. Macdonald London [u.a.] van Nostrand 1966 XII, 299 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques Statistique mathématique Mathematik Mathematical statistics Mathematics Statistics (Mathematics) Mathematik (DE-588)4037944-9 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Mathematik (DE-588)4037944-9 s Statistik (DE-588)4056995-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004471957&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | MacDonald, Peter Mathematics and statistics for scientists and engineers Mathématiques Statistique mathématique Mathematik Mathematical statistics Mathematics Statistics (Mathematics) Mathematik (DE-588)4037944-9 gnd Statistik (DE-588)4056995-0 gnd |
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| title | Mathematics and statistics for scientists and engineers |
| title_auth | Mathematics and statistics for scientists and engineers |
| title_exact_search | Mathematics and statistics for scientists and engineers |
| title_full | Mathematics and statistics for scientists and engineers P. Macdonald |
| title_fullStr | Mathematics and statistics for scientists and engineers P. Macdonald |
| title_full_unstemmed | Mathematics and statistics for scientists and engineers P. Macdonald |
| title_short | Mathematics and statistics for scientists and engineers |
| title_sort | mathematics and statistics for scientists and engineers |
| topic | Mathématiques Statistique mathématique Mathematik Mathematical statistics Mathematics Statistics (Mathematics) Mathematik (DE-588)4037944-9 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathématiques Statistique mathématique Mathematik Mathematical statistics Mathematics Statistics (Mathematics) Statistik |
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