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Mathematica hat sich in den vergangenen Jahren als unentbehrliches Werkzeug \
im Ingenieurwesen etabliert. Es bietet dem professionellen Anwender, durch \
seinen m\[ADoubleDot]chtigen und fortschrittlichen Funktionsumfang, eine \
unerreichte Flexibilit\[ADoubleDot]t bei der Analyse, Modellierung und \
Visualisierung der w\[ADoubleDot]hrend der t\[ADoubleDot]glichen \
Ingenieurarbeit anfallenden Daten. Im Sommer 1994 startete Wolfram Research \
die Ver\[ODoubleDot]ffentlichung der Mathematica Anwendungs-Pakete, die dem \
Benutzer sofort einsetzbare Funktionen aus speziellen Anwendungsbereichen \
bieten. Dem Anwender wird durch diese Pakete der schrittweise Einstieg in die \
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wurde seit dieser Zeit auf \[UDoubleDot]ber 30 Zusatzpakete erweitert.\
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Ein \[CapitalUDoubleDot]bersicht zu den Zusatzpaketen ist aktuell im INTERNET \
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Chapter 2
Importing and Exporting Data
2.1 Importing Data from an ASCII File 23
2.1.1 Introduction 23
2.1.2 A Real-World Example 29
2.1.3 Summary of ImportData 34
2.2 Exporting Data to an ASCII File 37
2.2.1 Introduction 37
2.2.2 Summary of ExportData 41
2.3 Importing Data from a Binary File 43
2.4 Getting Data from a Scanned Plot 46 \
\>", "Subsubtitle",
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"Chapter 3\nExperimental Errors and Error Analysis\n3.1 Introduction \
51\n3.1.1 The Purpose of \
Error Analysis 51\n3.1.2 Different Types of Errors \
53\n3.1.3 References \
53\n3.2 Determining the Precision \
54\n3.2.1 The Standard Deviation \
54\n3.2.2 The Reading Error \
59\n3.2.3 \"THE\" Error \
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Propagation of Errors of Precision",
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Calibration, Accuracy, and Systematic Errors 74\n3.5 Summary of the \
Error Propagation Routines 77"
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Background Discussion 81\n4.1.1 Linear \
Fits 81\n4.1.2 \
Least-Squares Techniques 83\n4.1.3 Fitting to \
Data with Experimental Errors 85\n4.1.4 Evaluating the Goodness of \
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Chapter 7
Robust Fitting
7.1 Introduction \
283
7.1.1 Using the Median \
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7.1.2 Using Weighting Techniques 289
7.2 Details \
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7.2.1 RobustCurveFit \
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7.2.2 RobustLineFit \
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7.2.3 Comparing RobustCurveFit and RobustLineFit 300
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Chapter 8
Exploration and Transformation of Data\
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Chapter 1
Introduction to
Experimental Data Analyst\
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Experimental Data Analyst (EDA) is a collection of tools and tutorials \
designed specifically for the needs of the physical scientist and engineer \
and the students of science and engineering. Included are over 30 functions, \
tutorials in using the functions, tutorials in using Mathematica built-in \
commands and standard Mathematica packages, and discussions of the underlying \
theory of data analysis at a variety of levels from beginning undergraduate \
to practicing researcher. The tutorials make use of a variety of real \
experimental data drawn from many different fields, and the data is also \
included in the package.\
\>", "Text",
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Cell["\<\
The material is divided into eight chapters, beginning with this chapter \
which provides an overview of the contents. The chapters can be accessed as \
the hard-copy version, or read on line as Mathematica notebooks. The \
notebooks can be read with the front end included with Mathematica or with \
the free MathReader program available from the MathSource archive; in the \
former case, the notebooks can be interactive, and the reader is encouraged \
to experiment with the commands and supplied data sets.\
\>", "Text",
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Cell["\<\
If you are reading this chapter with the Mathematica front end, when you open \
the notebook a dialog box inquires if you wish to initialize the notebook. If \
you reply \"Yes\", the following initialization command is executed.\
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If the command is executed, and produces any error messages, you should \
consult your installation document for the package or see Section 1.1.2 \
\"Using EDA\"; if no error messages are produced, then this notebook is \
\"live\" and all Mathematica commands in the notebook may be executed, \
changed, reexecuted, etc.\
\>", "Text",
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The chapters do not all have to be read in order. In general, we recommend \
that you look over this chapter in its entirety before going on to the \
others. Section 1.1.1 gives further recommendations of which chapters and \
sections are probably prerequisites for succeeding ones.\
\>", "Text",
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Cell["\<\
If you are reading this chapter on line, the following sections are \
\"closed\". A solid triangle on the bottom of the cell bracket identifies a \
closed group. To open a closed group, point at the cell bracket with the \
mouse or trackball and double click; alternatively, point at the bracket, \
click once, and choose the Open/Close Group command from the Cell menu at the \
top of this window.\
\>", "Text",
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Chapter 2 deals with methods of getting data into Mathematica so that it may \
be analyzed. This chapter is independent of all other chapters supplied with \
EDA. It discusses techniques to read and write files containing data sets; \
and also introduces the EDA programs ImportData and ExportData.\
\>", "Text",
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Cell["\<\
Chapter 3 discusses a topic which pervades data analysis in the physical \
sciences and engineering: error analysis. Here a tutorial is supplied. \
Although the level is suitable for an undergraduate student in the sciences, \
we are also aware of many professional researchers whose education and \
training have managed to miss some of the material discussed here. In \
addition, EDA supplies programs and constructs to simplify error analysis, \
and they are introduced in this chapter. The EDA functions discussed are \
AdjustSignificantFigures, CombineWithError, DivideWithError, PlusWithError, \
PowerWithError, Quadrature, SubtractWithError, and TimesWithError. Also, EDA \
defines Data and Datum constructs for doing propagation of errors; these \
constructs are introduced in this chapter. The functions and constructs \
discussed here are used in later chapters.\
\>", "Text",
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Chapters 4 through 8 are the \"heart\" of the analysis tools provided by EDA.\
\
\>", "Text",
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Cell["\<\
Chapter 4 introduces one of the most commonly performed tasks in data \
analysis: fitting data to linear models, especially straight lines and \
curves. Section 4.1 provides background discussions of a linear fit, \
least-squares techniques, evaluation of the quality of the fit, etc.; some \
familiarity with this material is assumed in all later sections. The \
remainder of Chapter 4 discusses the EDA function LinearFit that performs \
linear least-squares fits to data; included is a discussion of the related \
EDA functions ShowLinearFit and ToLinearFunction. The LinearFit function is \
used in all subsequent chapters. Also, many other EDA functions have similar \
syntax. Thus, some familiarity with its syntax and options is recommended.\
\>", "Text",
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Chapter 5 extends the materials of Chapter 4 to arbitrary models. It \
introduces the EDA function FindFit and the related functions ShowFitFunction \
and ToFitFunction. Also discussed are some convenience functions that define \
peak shapes; these are BreitWigner, Galatry, Gaussian, Lorentzian, \
PearsonVII, RelativisticBrietWigner, and Voigt. Little in the chapter is used \
in later discussions, although the FindPeaks function discussed in Chapter 8 \
is primarily intended as a companion to FindFit.\
\>", "Text",
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Chapter 6 discusses techniques to eliminate noise in data and to fill in \
missing values. It also discusses the related topic of fitting data when a \
model is not available or \
\>", "Text",
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appropriate. The chapter introduces the EDA functions SmoothData, LoessFit, \
and FillData. There is also a tutorial on using built-in Mathematica \
functions to smooth data, and the algorithm used by the FindPeaks program \
discussed in Chapter 8 is introduced here. With the exception of the \
algorithm of FindPeaks, nothing in later chapters depends on anything \
appearing here. \
\>", "Text",
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Cell["\<\
Chapter 7 discusses techniques to fit data to lines and curves when one or \
more of the data points may be \"wild\", i.e.,the data contains \"outliers.\" \
Alternatives to least-squares techniques should be considered in this case \
since an outlier can have a significant effect on the least-squares fit. The \
chapter introduces the EDA functions RobustCurveFit and RobustLineFit. \
Nothing in the chapter is required for Chapter 8.\
\>", "Text",
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Cell["\<\
Chapter 8 discusses what to do when the relations in a data set are not \
known. Graphical techniques are explored in Section 8.1. The discussion \
includes the EDA function EDAListPlot, which is briefly introduced in Section \
1.3; the EDA functions Histogram and BoxPlot are also discussed. Section 8.2 \
is a tutorial on using Mathematica built-in functions to transform the data; \
the discussion is one of the more advanced in EDA. Nonetheless, Section 8.2 \
only \"scratches the surface\" of this topic. Finally, Section 8.3 gives a \
full discussion of the FindPeaks function; this function was briefly \
introduced in Chapter 5, and its algorithm was discussed in Section 6.1.5.\
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Cell["\<\
Although EDA notebooks include general purpose tutorials, EDA is also a \
collection of software tools, and this subsection discusses using the \
software. The software consists of 12 Mathematica packages, which are files \
written in the Mathematica language. These are the files that define EDA's \
functions, options, etc.\
\>", "Text",
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Cell["\<\
The easiest way to access an EDA function is to load the EDA`Master` file. \
This file knows which package file contains which programs, symbols, etc. \
Then when you invoke a specific function, the Mathematica kernel loads the \
appropriate package. The Master file can be loaded with the following. \
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If Mathematica cannot find the Master package, verify that the $Path variable \
includes the directory where applications such as Experimental Data Analyst \
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Once the EDA`Master` file has successfully loaded, you can use Mathematica \
just as if all the packages of EDA were loaded, except for a few differences. \
The three main differences are the following.\
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First, since all of the packages are loaded only when needed, the size of the \
Mathematica kernel is over a megabyte smaller than if they were actually \
loaded.\
\>", "Text",
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Second, the first time you invoke an EDA function, the package containing the \
function has to be loaded. Often, other packages are used by the package \
containing the definition of the function you have invoked, and they must be \
loaded, too. For example, the package containing the definition of LinearFit \
loads six other packages; some of these load yet other packages. For this \
example, invoking LinearFit loads 10 other packages besides the one \
containing the definition for LinearFit itself. Therefore, the first time you \
invoke some EDA functions, it may take a few moments before everything is \
loaded and the program begins its work. Second and subsequent invocations \
will begin their work almost immediately.\
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]
*)
(***********************************************************************
End of Mathematica Notebook file.
***********************************************************************)