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class16 - PHYS 5900 Class 16 Zi-Wei Lin Two-Dimensional...

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PHYS 5900 Class 16 (9/30/2009) Zi-Wei Lin Two-Dimensional Forms with Built-in Meanings include x y power x y division x square root x n nth root i = i1 i2 f i sum i = i1 i2 f i product f x or a b f x integral x f or x , y f partial derivative Using Two-Dimensional Notations Example 2.5.1 In[1]:= v_ : = ¶ x v * i + ¶ y v * j + ¶ z v * k In[2]:= Φ @ x_, y_, z_ D : = k q x 2 + y 2 + z 2 In[3]:= - Φ @ x, y, z D Out[3]= kqxi I x 2 + y 2 + z 2 M 3 2 + kqyj I x 2 + y 2 + z 2 M 3 2 + kqzk I x 2 + y 2 + z 2 M 3 2 In[4]:= % Factor Out[4]= kq J xi + yj + zk N I x 2 + y 2 + z 2 M 3 2 In[5]:= Clear @ Φ , Del D
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Input and Output Forms include InputForm OutputForm StandardForm TraditionalForm Global settings can be done at Edit/Preferences/Evaluation (on Windows) or Mathamatica/Preferences/Evaluation (on Mac). Local settings can be done by Cell/ConvertTo or using the commands: Example: x 3 Sin @ x D 2 + 2 + f @ x D x In[6]:= myExpr = x^3 H Sin @ x D ^2 + 2 L + Integrate @ f @ x D , x D Out[6]= f @ x D x + x 3 2 + Sin @ x D 2 In[7]:= myExpr InputForm Out[7]//InputForm= Integrate[f[x], x] + x^3/(2 + Sin[x]^2) In[8]:= myExpr OutputForm Out[8]//OutputForm= 3 x Integrate[f[x], x] + ----------- ---------- 2 2 + Sin[x] In[9]:= myExpr StandardForm Out[9]//StandardForm= f @ x D x + x 3 2 + Sin @ x D 2 In[10]:= myExpr TraditionalForm Out[10]//TraditionalForm= f H x L x + x 3 sin 2 H x L + 2 In[11]:= Clear @ myExpr D 2 class16.nb
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StandardForm includes whatever can be entered in InputForm . It's easier to debug in InputForm than StandardForm . Warning: TraditionalForm gives the traditional mathematical notation but often lacks the necessary precision for input. Example: In[12]:= 8 S @ 1 + Α D , FresnelS @ 1 + Α D , S * H 1 + Α L< StandardForm Out[12]//StandardForm= 8 S @ 1 + Α D , FresnelS @ 1 + Α D , S H 1 + Α L< In[13]:= 8 S @ 1 + Α D , FresnelS @ 1 + Α D , S * H 1 + Α L< TraditionalForm Out[13]//TraditionalForm= 8 S H Α + 1 L , S H Α + 1 L , S H Α + 1 L< The above three different expressions look too similar in TraditionalForm .
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