# How to interpolate data in mathematica

## Mathematica

### What is Mathematica?

This question is answered in great detail in:*Stephen Wolfram, Mathematica - A System for Doing Mathematics by Computer, 2nd edition, 1991, Addison-Wesley*.

This book contains a detailed description of the syntax and hundreds of examples and is both an introduction to the handling and capabilities of the program and a reference work. At X-Terminals one can access the lexicon-like appendix of this book via the program "mathbook".

### Mathematica is suitable ...

### Possible forms of use:

- interactive ()
- via the Mathematica notebook ()
- as a programming language
- via program packages
- linked to other programs

### A first attempt (comments indented and in brackets):

- prompt> math
- (Mathematica is usually called with ''. The following lines then appear :)
- Mathematica 2.2 for SGI Copyright 1988-93 Wolfram Research, Inc. - Motif graphics initialized -
- (Mathematica is now started and ready to receive commands.)
- In [1]: =
- (This is what the 'prompt' of Mathematica looks like. All entries are automatically numbered from 1 upwards by Mathematica. You can later access old entries using these numbers. Type a command after the equal sign and finish the entry by pressing Enter Key. After that, this line could look something like this :)
- In [1]: = 2 * 2
- (Mathematica will now print the following :)
- Out [1] = 4
- (And be ready again for the next input. The outputs are also numbered exactly like the inputs and they can also be accessed later at any time.)
- In [2]: = Plot [Sin [x], {x, 0.2 Pi}] Out [2] = -Graphics-
- (Mathematica reports a graphical output and a new window appears showing the sine function from 0 to 2 Pi. And are functions that are available to the user immediately after starting Mathematica. Function names usually begin with an uppercase letter ; The arguments are enclosed in square brackets and separated by commas. Curly brackets, on the other hand, enclose lists of objects. Some mathematical constants such as Pi = 3.14159 ... are available to the user at the start; their names also begin with capital letters. Between ' 2 'and' Pi 'in curly brackets, the mal point () is omitted and replaced by a space, which is allowed in Mathematica.)
- In [3]: =? Plot Plot [f, {x, xmin, xmax}] generates a plot of f as a function of x from xmin to xmax. Plot [{f1, f2, ...}, {x, xmin, xmax}] plots several functions fi. In [3]: =
- (You can get information about functions by using "" followed by the name of the function. Such a command is not counted, which is why "" appears as prompt.)
- In [3]: = ?? Plot Plot [f, {x, xmin, xmax}] generates a plot of f as a function of x from xmin to xmax. Plot [{f1, f2, ...}, {x, xmin, xmax}] plots several functions fi. Attributes [Plot] = {HoldAll, Protected} Options [Plot] = {AspectRatio -> GoldenRatio ^ (- 1), Axes -> Automatic, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> Automatic, Background -> Automatic , ColorOutput -> Automatic, Compiled -> True, DefaultColor -> Automatic, Epilog -> {}, Frame -> False, FrameLabel -> None, FrameStyle -> Automatic, FrameTicks -> Automatic, GridLines -> None, MaxBend -> 10., PlotDivision -> 20., PlotLabel -> None, PlotPoints -> 25, PlotRange -> Automatic, PlotRegion -> Automatic, PlotStyle -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, DefaultFont:> $ DefaultFont, DisplayFunction:> $ DisplayFunction} In [3]: =
- (If you enter '' followed by the function name, you get even more detailed information in which, among other things, all options with which the function can be called are listed. The arrows behind the option name ('') refer to the current value of this Option. If you are looking for related functions or if you do not know the name of the function exactly, the use of wildcards ('') is recommended; the names of the commands that match the pattern '' then appear.)
- In [3]: =? Plot * Plot PlotJoined PlotRange Plot3D PlotColor PlotLabel PlotRegion Plot3Matrix PlotDivision PlotPoints PlotStyle In [3]: = (You leave Mathematica with the command.) In [3]: = Quit

### Examples of the use of Mathematica in numerical and symbolic calculations

- In [1]: = N [Log [4 Pi]] Out [1] = 2.53102
- (The function specifies the numerical value of the expression in brackets. The number of digits output can be changed using an option from :)
- In [2]: = N [Log [4 Pi], 12] Out [2] = 2.53102424697
- (An example of symbolic computing :)
- In [3]: = Integrate [1 / x, x] Out [3] = Log [x]
- (The indefinite integral of was calculated; the second argument of Integrate specifies the name of the variable to be used for integration. The function can be used to integrate numerically :)
- In [4]: = NIntegrate [1 / x, {x, 1.4 Pi}] Out [4] = 2.53102
- (Mathematica has solutions for many common math problems; e.g. integration, differentiation, sums, series, solving equations of various kinds, solving systems of equations, and differential equations.)
(You can also define your own functions, for example :)

- In [5]: = myfunction [x _]: = Log [x] * Sin [x]
- (Here a new function with name has been defined. The underscore behind the x denotes a so-called function in Mathematica.
*'Pattern'*; it means something like*"Any expression can be used at this point"*.) - In [6]: = myfunction [1] Out [6] = 0 In [7]: = myfunction [2] Out [7] = Log [2] Sin [2] In [8]: = N [myfunction [2 ]] Out [8] = 0.630277
- (Lists are an important type of object Mathematica works with. There are many commands for reading, creating, editing, and outputting lists. Example :)
- In [9]: = Table [N [myfunction [v]], {v, 1,2,0.1}] Out [9] = {0, 0.0849411, 0.169931, 0.252803, 0.331576, 0.404449, 0.469803, 0.526205, 0.572415, 0.607386, 0.630277}
- (With a list of values of the function at the positions 1.0, 1.1, 1.2, ..., 2.0 was created. With you can display this table graphically :)
- In [10]: = ListPlot [%, PlotJoined-> True] Out [10] = -Graphics-

### Representation of functions and data

- (Mathematica has many options for outputting functions and data; for example, in the form of lists and tables, 1, 2 or 3-dimensional graphics, which can also be colored and animated. Acoustic representations are also possible. Furthermore, codes can be output that are processed by other programs or compilers after minor additions (C, Fortran, TeX, PostScript). Here are some examples :)

### Modeling and analysis of data

You can use Mathematica to analyze and model data:- how is the data distributed?
- how well can you describe them with a model?

#### It is planned to create further texts with tips and examples. However, this costs the authors a lot of (free) time. Therefore patience (or cooperation) is requested.

Content: Daniel Hoffmann, HTML formatting: Heiko Schlichting, February 7, 1994

- What is California Corporations Code Section 1505
- What's chicken wor mine
- How many nanoseconds old am I?
- So what a field mob zippyshare
- What does it mean to see 20 magpies
- Eso, where to start with Elden Root Quests
- Dummies, what do tin foil hats donation
- Msza ojca daniela czatachowa uzdrowienia
- Cgewho mohali phase III water
- Ya dil ko howa kya
- What does Stall Urban Dictionary
- Agustin to stop period how many mg
- X Factor Gamu, what happened to Bob
- Typo3 link validator howto
- Jennifer Rukavina how old
- Anna grygierczyk stomatolog czechowice dziedzice mapa
- Tully's kids pay what they weigh
- Android WhatsApp source code
- Khayari rachid chow eko
- Tove vigeland sling earrings wholesale
- What makes green double arrow Snapchat history
- What do the Alta tennis levels mean
- Brilux candle labels wholesale
- What does lukewarm growth mean