--- loncom/html/adm/help/tex/Math_Response_Problems.tex 2007/01/22 21:49:26 1.1 +++ loncom/html/adm/help/tex/Math_Response_Problems.tex 2007/05/22 00:55:09 1.2 @@ -11,47 +11,74 @@ The answerdisplay is what is displayed w The following example illustrates this. \begin{verbatim} - +$example=&xmlparse('An example would be $(sin($n1\cdot x)+cos($n2\cdot x))/\sqrt{2}$'); + + -Give an example of a function -
    -
  1. which is orthogonal to $function with respect to the -scalar product -\[ = -\frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\] -
    2. -
  2. whose norm is 1.
    3. -
+ Give an example of a function +
    +
  1. + which is orthogonal to $function with respect to the + scalar product + + \[ = + \frac{1}{\pi} \int_{-\pi}^{\pi}dx g(x) \cdot h(x)\] + +
    2. +
  2. + whose norm is 1. +
    3. +
+ + -overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi; + +overlap:integrate((RESPONSE[1])*(LONCAPALIST[1]),x,-%pi,%pi)/%pi; norm:integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi; -is(overlap=0 and norm=1); - - - -overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi; -is(not overlap = 0); - - -norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi; -is(not norm = 1); - - -The function you have provided does not have a norm of one. - - - -The function you have provided is not orthogonal. - - +is(overlap=0 and norm=1); + + + + + +overlap: integrate((LONCAPALIST[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi; +is(not overlap = 0); + + + + +norm: integrate((RESPONSE[1])*(RESPONSE[1]),x,-%pi,%pi)/%pi; +is(not norm = 1); + + + + +The function you have provided does not have a norm of one. + + + + +The function you have provided is not orthogonal. + + + -

Note that with respect to the above norm, $\cos(nx)$ is perpendicular to $\sin(nx)$ and perpendicular to $\cos(mx)$ for $n\ne m$.

+ + + + +

+Note that with respect to the above norm, $\cos(nx)$ is perpendicular +to $\sin(nx)$ and perpendicular to $\cos(mx)$ for +$n\ne m$. +

+ \end{verbatim}