RE: variable definition help
- To: mathgroup at smc.vnet.net
- Subject: [mg42391] RE: [mg42379] variable definition help
- From: "David Park" <djmp at earthlink.net>
- Date: Fri, 4 Jul 2003 01:33:10 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Jay, You might want to look at Section 2.3.1 on patterns in The Mathematica Book. Generally you will want to use f[x_] as in f[x_]:= x + Sin[x] x_ is a pattern that can stand for anything. After you make the definition you could write f[x], f[y], f[t], f[x+y] or f[anything] and obtain the expected result. You could also use f'[t] to obtain the derivative. If instead you used f[x]:= x + Sin[x] then the definition would only work for f[x]. f[y], f[t], f[x+y] would be left unevaluated. Using f = x + Sin[x] loses the variable information and does not really define a function. You could use a pure function definition: f = Function[x, x + Sin[x]] or f = # + Sin[#]& but this would just be the long method for the first definition. If you have a function with parameters you could use the following form f[a_, b_][x_]:= a Sin[x] + b Cos[x] Then you could obtain the derivative for a specific case by writing f[3, 2]'[x] This form is generally more convenient than f[x_]:= a Sin[x] + b Cos[x] and then using a = 3; b = 2; f[x] or f'[x] because it avoids having to set values for a and b. David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: seferiad [mailto:seferiad at pacbell.net] To: mathgroup at smc.vnet.net When defining functions, any of the following seem to be commonly used (assuming the function is of one variable, x): f or f[x] or f[x_]. Can someone point me to an explanation that defines the pros/cons of using one approach over the other. In particular, when I should use f[x] vs. f[x_]. Thanks, Jay