The uncertainty in physical measurements: an introduction to data analysis in the physics laboratory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer
2008
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 289 S. Ill., graph. Darst. |
| ISBN: | 9780387786490 9780387786506 |
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| 100 | 1 | |a Fornasini, Paolo |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The uncertainty in physical measurements |b an introduction to data analysis in the physics laboratory |c Paolo Fornasini |
| 264 | 1 | |a New York, NY |b Springer |c 2008 | |
| 300 | |a XII, 289 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Measurement | |
| 650 | 4 | |a Physical measurements | |
| 650 | 4 | |a Physics |x Data processing | |
| 650 | 4 | |a Statistical physics | |
| 650 | 4 | |a Uncertainty | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface....................................................... VII
Part I Measurements and Uncertainty
1 Physical Quantities....................................... 3
1.1 Methods of Observation and Measurement................. 3
1.2 Physical Quantities..................................... 5
1.3 Direct and Indirect Measurement......................... 6
1.4 Time Dependence of Physical Quantities .................. 8
1.5 Counting of Random Events............................. 10
1.6 Operative Definition of Physical Quantities................ 11
1.7 The Experimental Method............................... 12
2 Measurement Units....................................... 13
2.1 Base and Derived Quantities............................. 13
2.2 Measurement Standards................................. 14
2.3 The International System of Units (SI).................... 15
2.4 Other Systems of Units ................................. 18
2.5 Dimensional Analysis................................... 20
Problems .................................................. 24
3 Measuring Instruments................................... 27
3.1 Functional Elements.................................... 27
3.2 Classifications of Instruments............................ 29
3.3 Static Characteristics of Instruments...................... 31
3.4 Accuracy of an Instrument .............................. 35
3.5 Dynamical Behavior of Instruments....................... 37
3.6 Counters.............................................. 43
4 Uncertainty in Direct Measurements ..................... 45
4.1 Causes of Uncertainty................................... 45
4.2 Measurement Resolution ................................ 46
4.3 Random Fluctuations................................... 48
4.4 Systematic Errors ...................................... 61
X Contents
4.5 Summary and Comparisons.............................. 68
Problems .................................................. 74
Part II Probability and Statistics
5 Basic Probability Concepts............................... 79
5.1 Random Phenomena.................................... 79
5.2 Sample Space. Events................................... 81
5.3 Probability of an Event ................................. 82
5.4 Addition and Multiplication of Events..................... 87
5.5 Probability of the Sum of Events......................... 89
5.6 Probability of the Product of Events...................... 91
5.7 Combinatorial Calculus ................................. 94
Problems .................................................. 96
6 Distributions of Random Variables ....................... 99
6.1 Binomial Distribution................................... 99
6.2 Random Variables and Distribution Laws..................104
6.3 Numerical Characteristics of Distributions.................108
6.4 Poisson Distribution....................................115
6.5 Normal Distribution....................................121
6.6 Meaning of the Normal Distribution......................126
6.7 The Cauchy-Lorentz Distribution ........................130
6.8 Multivariate Distributions...............................132
Problems ..................................................136
7 Statistical Tools ..........................................139
7.1 Parent and Sample Populations ..........................139
7.2 Sample Means and Sample Variances .....................143
7.3 Estimation of Parameters................................147
Problems ..................................................152
Part III Data Analysis
8 Uncertainty in Indirect Measurements.................... 155
8.1 Introduction to the Problem............................. 155
8.2 Independent Quantities, Linear Functions ................. 156
8.3 Independent Quantities. Nonlinear Functions............... 159
8.4 Nonindependent Quantities.............................. 163
8.5 Summary.............................................. 167
Problems .................................................. 168
Contents XI
9 Confidence Levels ........................................169
9.1 Probability and Confidence.............................. 169
9.2 The Student Distribution................................173
9.3 Applications of the Confidence Level......................174
Problems ..................................................176
10 Correlation of Physical Quantities........................ 177
10.1 Relations Between Physical Quantities....................177
10.2 Linear Correlation Coefficient............................179
10.3 Linear Relations Between Two Quantities .................181
10.4 The Least Squares Method ..............................186
Problems ..................................................192
11 The Chi Square Test......................................193
11.1 Meaning of the Chi Square Test.......................... 193
11.2 Definition of Chi Square................................. 194
11.3 The Chi Square Distribution............................. 198
11.4 Interpretation of the Chi Square.......................... 202
Problems .................................................. 203
Part IV Appendices
A Presentation of Experimental Data.......................207
A.I Significant Digits and Rounding..........................207
A.2 Tables ................................................210
A.3 Graphs................................................212
A.4 Histograms............................................216
B Systems of Units .........................................219
B.I The International System of Units (SI)....................219
B.2 Units Not Accepted by the SI............................223
B.3 British Units...........................................224
B.4 Non-SI Units Currently Used in Physics...................225
B.5 Gauss egs Units........................................226
C Tables.................................................... 227
C.I Greek Alphabet........................................ 227
C.2 Some Fundamental Constants of Physics .................. 227
C.3 Integrals of the Standard Normal Distribution.............. 229
C.4 Integrals of the Student Distribution...................... 233
C.5 Integrals of the Chi Square Distribution................... 23.
C.6 Integrals of the Linear Correlation Coefficient Distribution. . . 237
XII Contents
D Mathematical Complements..............................239
D.I Response of Instruments: Differential Equations............239
D.2 Transformed Functions of Distributions ...................243
D.3 Moments of the Binomial Distribution ....................245
D.4 Moments of the Uniform Distribution.....................246
D.5 Moments of the Poisson Distribution......................247
D.6 Moments of the Normal Distribution......................248
D.7 Parameters of the Cauchy Distribution....................252
D.8 Theorems on Means and Variances .......................253
E Experiments..............................................255
E.I Caliper and Micrometer.................................255
E.2 Simple Pendulum: Measurement of Period.................258
E.3 Helicoidal Spring: Elastic Constant .......................261
E.4 Helicoidal Spring: Oscillations............................266
E.5 Simple Pendulum: Dependence of Period on Length.........269
E.6 Simple Pendulum: Influence of Mass and Amplitude ........274
E.7 Time Response of a Thermometer........................277
Suggested Reading ...........................................283
Index.........................................................285
|
| adam_txt |
Contents
Preface. VII
Part I Measurements and Uncertainty
1 Physical Quantities. 3
1.1 Methods of Observation and Measurement. 3
1.2 Physical Quantities. 5
1.3 Direct and Indirect Measurement. 6
1.4 Time Dependence of Physical Quantities . 8
1.5 Counting of Random Events. 10
1.6 Operative Definition of Physical Quantities. 11
1.7 The Experimental Method. 12
2 Measurement Units. 13
2.1 Base and Derived Quantities. 13
2.2 Measurement Standards. 14
2.3 The International System of Units (SI). 15
2.4 Other Systems of Units . 18
2.5 Dimensional Analysis. 20
Problems . 24
3 Measuring Instruments. 27
3.1 Functional Elements. 27
3.2 Classifications of Instruments. 29
3.3 Static Characteristics of Instruments. 31
3.4 Accuracy of an Instrument . 35
3.5 Dynamical Behavior of Instruments. 37
3.6 Counters. 43
4 Uncertainty in Direct Measurements . 45
4.1 Causes of Uncertainty. 45
4.2 Measurement Resolution . 46
4.3 Random Fluctuations. 48
4.4 Systematic Errors . 61
X Contents
4.5 Summary and Comparisons. 68
Problems . 74
Part II Probability and Statistics
5 Basic Probability Concepts. 79
5.1 Random Phenomena. 79
5.2 Sample Space. Events. 81
5.3 Probability of an Event . 82
5.4 Addition and Multiplication of Events. 87
5.5 Probability of the Sum of Events. 89
5.6 Probability of the Product of Events. 91
5.7 Combinatorial Calculus . 94
Problems . 96
6 Distributions of Random Variables . 99
6.1 Binomial Distribution. 99
6.2 Random Variables and Distribution Laws.104
6.3 Numerical Characteristics of Distributions.108
6.4 Poisson Distribution.115
6.5 Normal Distribution.121
6.6 Meaning of the Normal Distribution.126
6.7 The Cauchy-Lorentz Distribution .130
6.8 Multivariate Distributions.132
Problems .136
7 Statistical Tools .139
7.1 Parent and Sample Populations .139
7.2 Sample Means and Sample Variances .143
7.3 Estimation of Parameters.147
Problems .152
Part III Data Analysis
8 Uncertainty in Indirect Measurements. 155
8.1 Introduction to the Problem. 155
8.2 Independent Quantities, Linear Functions . 156
8.3 Independent Quantities. Nonlinear Functions. 159
8.4 Nonindependent Quantities. 163
8.5 Summary. 167
Problems . 168
Contents XI
9 Confidence Levels .169
9.1 Probability and Confidence. 169
9.2 The Student Distribution.173
9.3 Applications of the Confidence Level.174
Problems .176
10 Correlation of Physical Quantities. 177
10.1 Relations Between Physical Quantities.177
10.2 Linear Correlation Coefficient.179
10.3 Linear Relations Between Two Quantities .181
10.4 The Least Squares Method .186
Problems .192
11 The Chi Square Test.193
11.1 Meaning of the Chi Square Test. 193
11.2 Definition of Chi Square. 194
11.3 The Chi Square Distribution. 198
11.4 Interpretation of the Chi Square. 202
Problems . 203
Part IV Appendices
A Presentation of Experimental Data.207
A.I Significant Digits and Rounding.207
A.2 Tables .210
A.3 Graphs.212
A.4 Histograms.216
B Systems of Units .219
B.I The International System of Units (SI).219
B.2 Units Not Accepted by the SI.223
B.3 British Units.224
B.4 Non-SI Units Currently Used in Physics.225
B.5 Gauss egs Units.226
C Tables. 227
C.I Greek Alphabet. 227
C.2 Some Fundamental Constants of Physics . 227
C.3 Integrals of the Standard Normal Distribution. 229
C.4 Integrals of the Student Distribution. 233
C.5 Integrals of the Chi Square Distribution. 23."
C.6 Integrals of the Linear Correlation Coefficient Distribution. . . 237
XII Contents
D Mathematical Complements.239
D.I Response of Instruments: Differential Equations.239
D.2 Transformed Functions of Distributions .243
D.3 Moments of the Binomial Distribution .245
D.4 Moments of the Uniform Distribution.246
D.5 Moments of the Poisson Distribution.247
D.6 Moments of the Normal Distribution.248
D.7 Parameters of the Cauchy Distribution.252
D.8 Theorems on Means and Variances .253
E Experiments.255
E.I Caliper and Micrometer.255
E.2 Simple Pendulum: Measurement of Period.258
E.3 Helicoidal Spring: Elastic Constant .261
E.4 Helicoidal Spring: Oscillations.266
E.5 Simple Pendulum: Dependence of Period on Length.269
E.6 Simple Pendulum: Influence of Mass and Amplitude .274
E.7 Time Response of a Thermometer.277
Suggested Reading .283
Index.285 |
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| spelling | Fornasini, Paolo Verfasser aut The uncertainty in physical measurements an introduction to data analysis in the physics laboratory Paolo Fornasini New York, NY Springer 2008 XII, 289 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Datenverarbeitung Measurement Physical measurements Physics Data processing Statistical physics Uncertainty Datenanalyse (DE-588)4123037-1 gnd rswk-swf Experiment (DE-588)4015999-1 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Datenanalyse (DE-588)4123037-1 s Experiment (DE-588)4015999-1 s Physik (DE-588)4045956-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016570126&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fornasini, Paolo The uncertainty in physical measurements an introduction to data analysis in the physics laboratory Datenverarbeitung Measurement Physical measurements Physics Data processing Statistical physics Uncertainty Datenanalyse (DE-588)4123037-1 gnd Experiment (DE-588)4015999-1 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4123037-1 (DE-588)4015999-1 (DE-588)4045956-1 |
| title | The uncertainty in physical measurements an introduction to data analysis in the physics laboratory |
| title_auth | The uncertainty in physical measurements an introduction to data analysis in the physics laboratory |
| title_exact_search | The uncertainty in physical measurements an introduction to data analysis in the physics laboratory |
| title_exact_search_txtP | The uncertainty in physical measurements an introduction to data analysis in the physics laboratory |
| title_full | The uncertainty in physical measurements an introduction to data analysis in the physics laboratory Paolo Fornasini |
| title_fullStr | The uncertainty in physical measurements an introduction to data analysis in the physics laboratory Paolo Fornasini |
| title_full_unstemmed | The uncertainty in physical measurements an introduction to data analysis in the physics laboratory Paolo Fornasini |
| title_short | The uncertainty in physical measurements |
| title_sort | the uncertainty in physical measurements an introduction to data analysis in the physics laboratory |
| title_sub | an introduction to data analysis in the physics laboratory |
| topic | Datenverarbeitung Measurement Physical measurements Physics Data processing Statistical physics Uncertainty Datenanalyse (DE-588)4123037-1 gnd Experiment (DE-588)4015999-1 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Datenverarbeitung Measurement Physical measurements Physics Data processing Statistical physics Uncertainty Datenanalyse Experiment Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016570126&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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