HW2, EECS 203A. UCI, FALL 2004
by Nasser Abbasi


Part(a).
Given s=T(r)=^(-αr^2)
To solve, note that s=A/2when r=L_0

<<Utilities`Notation`

In[27]:=

Clear["Global`*"] ; Symbolize[L_0] ;

Symbolize :: bsymbexs : Warning: The box structure attempting to be symbolized has a similar or identical symbol already defined, possibly overriding previously symbolized box structure.

In[141]:=

RowBox[{, RowBox[{s[A_, L_0 : _, r_] := ^((Log[A/2]/L_0^2) r^2), , s[2, 3, 4], , RowBox[{RowBox[{Log, [, 0.05, ]}], //, N}]}]}]

Out[142]=

1

Out[143]=

RowBox[{-, 2.99573}]

In[89]:=

? Log

Log[z] gives the natural logarithm of z (logarithm to base e). Log[b, z] gives the logarithm to base b. More…

In[158]:=

data = Table[s[A, L_0, r], {A, 0, 1, .5}, {L_0, .1, 1, .2}] ; Plot[Evaluate[data], {r, 0, 1}, PlotRange {0, 1}] ;

[Graphics:HTMLFiles/index_13.gif]

Clear["Global`*"] ss[A_, (L_0) _, r_] := ^((Ln[A/2]/L_0^2) r^2) ss[A_, L_, r_] := Cos[A] ; RowBox[{RowBox[{ss, [, RowBox[{0.1, ,, 0.1, ,, 1}], ]}], //, N}]

0.995004

Information[s]

Global`s

s[A_, {0, _, 2 _, 3 _, 4 _, 5 _, 6 _, 7 _, 8 _, 9 _, 10 _, 11 _, 12 _, 13 _, 14 _, 15 _, 16 _, ... 93 _, 94 _, 95 _, 96 _, 97 _, 98 _, 99 _, 100 _}, r_] := ^(Ln[A/2] r^2)/Subscript[L, 0]^2

foo[a_] := a^2 foo[4]

16

<<Utilities`Notation`

In[14]:=

Symbolize[L_0]

Symbolize :: noboxtag : The Symbolize boxes L do not have an embedded NotationBoxTag TagBox. ... 0 0

Out[14]=

$Failed

In[60]:=

Clear["Global`*"] Symbolize[X] Information[X] foo[X : _] := X^2

Symbolize :: bsymbexs : Warning: The box structure attempting to be symbolized has a similar or identical symbol already defined, possibly overriding previously symbolized box structure.

Global`X

In[64]:=

foo[4]

Out[64]=

X^2

In[15]:=

? Symbolize

Symbolize[ℴℯ] forces any box structure matching &# ... 5; to be treated internally as a single symbol anywhere it appears in an input expression.

In[16]:=

Symbolize[L_0]

Created by Mathematica  (October 17, 2004)