What's the difference between Gnuplot, MuPAD, and my calculator?

Gnuplot is a general purpose graphing and plotting application. Like a graphical scientific calculator, it plots equations. Like others, it can also solve for single or multiple variables, can do numerical integration and find the values of derivatives. Unlike most calculators, it can plot 3D equations, use data files, output to numerous devices, etc.. In other words, it's a lot more flexible than your TI85.

MuPAD is a symbolic mathematics package. It does not (necessarily) rely on numerical methods to solve integrals or other equations. For example, whereas a calculator may give you the (x,y) coordinates as an "answer" to a derivative, MuPAD can give the equation of the derivative.

R is the powerful statistics package modeled after S.

Why should you use one of these packages instead of your calculator? Well, that's what the entire math section is for! It's still very much beta, but the next section (complete except for pretty graphics) will try to answer this question. I'm finishing off the gnuplot/limits portion now, and move into the fun calculus portion in a few weeks.

• Gnuplot
  
• MuPAD
  
• R
  
• Octave
  
• Scientific Applications on Linux
  

History of Unix in Academia
 
Types of Mathematics Software
  Basic Calculators
    Native Calc
    Emulated (TI85, HP, Casio)

  Plotting Software
    GnuPLOT

  Symbolic Mathematics
    MuPAD
    Octave
    Mathematica

  Statistics
    R

GnuPLOT
  Not Open Source, only coincidentally related by name to GNU 
  Is *free*, as in beer
  Download from gnuplot website

  Can run in batch or interactive mode
    Batch mode very useful for autogeneration of graphs
    Interactive mode useful to see how changes affect graph
      E.g., vary the slope, coefficients, x/y offset

  First plots
    A line!
    Quadratics
    Zooming in and out
    Change grid density

  3D plots
    The splot command
    Hidden line removal

  Extras
    Changing the default terminal
    Setting output file
    Importing data from file
    
  Applications
    Graphing system load

MuPAD
  Solving linear equations
  Solving quadratics
  Finding the derivate
  Computing integrals

Octave
  Defining a matrix
  Computing determinants
  Solving systems of equations
  
R
  Basic statistics
     mean, median, etc..
  Regression
  Pretty graphic demo