Mathematica Reference Page


Common Mistakes
Most Mathematica syntax problems are of a very few types:
  1. Parenthesis (), Braces {}, and Brackets [].
    • Parenthesis are for breaking up multiplication and addition e.g. (x+2)^2 is the same as x^2 + 4 x + 4.
    • Braces {} are for grouping things together e.g. {1, 2} is the point or vector with coordinates x=1, and y-2.
    • Brackets [] are for functions e.g. Sin[x].
  2. Capitalization. All Mathematica commands start with a Capital letter.
    • Sin[x] not sin[x].
    • Plot[Cos[x],{x,0,4}] not plot[Cos[x],{x,0,4}]
    • Pi or the pretty version on the Pallete not pi
    • E or the pretty version on the Pallete not e
    • etc.
  3. Missing commas.
    • Plot[Cos[x],{x,0,4}] not Plot[Cos[x]{x,0,4}]
  4. Bad function definitions.
    f[x_] = Cos[x^2]
    defines a function. Common mistakes are:
    • f[x] = Cos[x^2]
      missing underscore.
    • f(x_) = Cos[x^2]
      It needs brackets [] not parens ().
examples of the error messages priduced by these errors are below.

Avoiding Common Mistakes
Avoiding these mistakes is simple:

  1. Parenthesis (), Braces {}, and Brackets []. Remeber the rules:
    • Parenthesis () are for breaking up multiplication and addition
    • Braces {} are for grouping things together
    • Brackets [] are for functions
  2. Capitalization. Remember ll Mathematica commands start with a Capital letter.
    • Paste from the Palette.
    • Always Capitalize
  3. Missing commas.
    • Paste from the palette and fill in the template.
    • Copy carefully from the Help.
  4. Bad function definitions.
    • Remember the underscore.
    • Remember to use brackets [].

Error Messages
These syntax errors produce (once you know how to read them) fairly clear (well compared to Matlab, Maple, Fortran, C++, Java, etc.) error messages. the trick is to only look at the first message.

  1. Parenthesis (), Braces {}, and Brackets [].
    • Plot[Sin(x),{x,0,4}]
      produces the error message
      sin x is not a real number at x=1.66666 x 10^-7
      In other words it thinks sin and x are two seperate things.
    • Plot(Sin[x],{x,0,4})
      produces the message "(" can not be followed by "Sin[x], {x,0,4})".
    • Expand[ (x+2)^2] gives x^2 + 4 x + 4
    • What do you think
      Plot[ {Sin[x], Cos[x]},{x, 0, Pi}]
      will give? Remember the braces group things together.
  2. Capitalization. All Mathematica commands start with a Capital letter.
    • Plot[sin[x],{x,0,4}]
      produces the error message
      sin(x) is not a real number at x=1.66666 x 10^-7
      In other words it does not understand sin[x].
    • plot[Cos[x],{x,0,4}]
      Just parrots back the command. This is what Mathematica does when it does not know what to do. You also get a warning the first time you do this that "plot" is similar to "Plot".
    • Plot[ Cos[x],{x,0,pi}]
      gives the message that
      Limiting value pi in {x,0,pi} is not a real number.
    • Plot[e^x, {x, 0, Pi}]
      gives the messgae that e^x is not a real number at x=1.309 x 10^(-7).
  3. Missing commas.
    • Plot[Cos[x]{x,0,4}]
      produces the message
      Plot called with one argument; 2 or more arguments are expected.
  4. Bad function definitions.
    • After defining f[x_] = Cos[x^2]
      f'[x] gives the derivative -2 x Sin[x^2].
    • After running f[x] = Cos[x^2]
      f'[x] simply parrots.
    • f(x_) = Cos[x^2]
      produces the strange message
      Tag Times in ..... is protected.