{VERSION 3 0 "IBM INTEL NT" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 0 0 1 0 0 0 0 0 0 } {CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "2 D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 }{CSTYLE "Help Heading" -1 26 "" 1 14 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 7 "Advice:" }{TEXT -1 20 " D efining functions" }}{PARA 0 "" 0 "" {TEXT -1 16 " " }} {PARA 0 "" 0 "" {TEXT -1 45 "Here is a correct way of defining a funct ion:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:= x -> x^2 + 1;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrow GF(,&*$)9$\"\"#\"\"\"\"\"\"F2F2F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 75 "You can then evaluate such a function with a constant or variable arg ument:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(u);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&*$%\"uG\"\"#\"\"\"F'F'" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 5 "f(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}{PARA 0 "" 0 "" {TEXT -1 70 "Similarly, for a function of several v ariables (note the parentheses):" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "g:= (x,y) -> x+y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGR 6$%\"xG%\"yG6\"6$%)operatorG%&arrowGF),&9$\"\"\"*$)9%\"\"#\"\"\"F/F)F) F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(u,v);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#,&%\"uG\"\"\"*$)%\"vG\"\"#\"\"\"F%" }}}{PARA 0 " " 0 "" {TEXT -1 78 "On the other hand, the following defines an expres sion rather than a function:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "h:= x^2 + 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG,&*$)%\"xG\" \"#\"\"\"\"\"\"F+F+" }}}{PARA 0 "" 0 "" {TEXT -1 176 "This is no probl em if that's what you wanted, but functions and expressions are used i n different ways. In particular, you get a strange-looking result if \+ you try to evaluate " }{MPLTEXT 0 21 1 "h" }{TEXT -1 25 " as you would a function:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h(u);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)-%\"xG6#%\"uG\"\"#\"\"\"\"\"\"F,F ," }}}{PARA 0 "" 0 "" {TEXT -1 21 "In order to evaluate " }{MPLTEXT 0 21 1 "h" }{TEXT -1 19 " for some value of " }{MPLTEXT 0 21 1 "x" } {TEXT -1 15 ", you must use " }{MPLTEXT 0 21 4 "subs" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(x=u, h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"uG\"\"#\"\"\"\"\"\"F)F)" }}}{PARA 0 "" 0 "" {TEXT -1 62 "Since in ordinary mathematics we often speak of \"th e function " }{XPPEDIT 18 0 "f(x) = x^2 + 1" "6#/-%\"fG6#%\"xG,&*$F'\" \"#\"\"\"\"\"\"F+" }{TEXT -1 44 "\", a common beginner's mistake is to define " }{MPLTEXT 0 21 4 "f(x)" }{TEXT -1 21 " instead of defining \+ " }{MPLTEXT 0 21 1 "f" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "F(x):= x^2 + 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>- %\"FG6#%\"xG,&*$)F'\"\"#\"\"\"\"\"\"F-F-" }}}{PARA 0 "" 0 "" {TEXT -1 56 "Beware! Everything seems fine, as long as you use only " } {MPLTEXT 0 21 4 "F(x)" }{TEXT -1 27 ". But when you try to use " } {MPLTEXT 0 21 1 "F" }{TEXT -1 54 " with some other argument, it appear s to be undefined:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "F(u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"FG6#%\"uG" }}}{PARA 0 "" 0 "" {TEXT -1 49 "This is not surprising, since in fact it is only " } {MPLTEXT 0 21 4 "F(x)" }{TEXT -1 10 ", and not " }{MPLTEXT 0 21 1 "F" }{TEXT -1 43 " of anything else, that you have defined. " }}{PARA 0 " " 0 "" {TEXT -1 93 "There is a legitimate use of such a construction ( it places a value in the remember table of " }{MPLTEXT 0 21 1 "F" } {TEXT -1 4 "). " }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 9 "See also:" } {TEXT -1 1 " " }{HYPERLNK 17 "function" 2 "function" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "remember" 2 "remember" "" }{TEXT -1 2 ", " } {HYPERLNK 17 "subs" 2 "subs" "" }}}{SECT 0 {PARA 0 "" 0 "" {TEXT 26 23 "Maple Advisor Database " }{TEXT -1 16 " R. Israel, 1997" }}}} {MARK "0 18 4" 54 }{VIEWOPTS 1 1 0 1 1 1803 }