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 +  = 16 ;   (x2 + x3)dx ;  
 ________ 
x = -b ±  b2 - ac ;
(1) (2) (3)
G(x) = 

0		 tx-1 e-t dt ; 
kr =  kBT
h		  e DS/R  · e -E*/RT ;
  
(4) (5)
f(x)   def 
   		  f(x) ;
xA   xA
x0
2U(x,y,z) =  2U
x2		  +  2U
y2		  +  2U
z2		 ;
 
 
(6) (7)
a b
 
e f








;
c d g h
0
i j
k l
    
det c0 c1 c2 ··· cn
> 0 ;
c1 c2 c3 ···  cn+1
c2 c3 c4 ···  cn+2
 
cn   cn+1 cn+2 ···  c2n
(8) (9)

(1) 
<SUB><IMG SRC="frac12.gif"></SUB> +
<SUB><IMG SRC="frac23.gif"></SUB> =
1<IMG SRC="1over.gif"><FONT SIZE="-1"><SUB>6</SUB></FONT> ;

(2) 
<SUB><IMG SRC="integral.gif"></SUB>(<SUB><IMG SRC="frac14.gif"
></SUB>x<SUP>2</SUP> + x<IMG SRC="sqrt.gif">3)dx ;

(3) 
<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
<TR><TD>&nbsp;</TD>
    <TD>________</TD>
    <TD>&nbsp;</TD>
    </TR>
<TR><TD>x =
        <FONT FACE=SYMBOL>-</FONT><SUB
        ><IMG SRC="frac12.gif"></SUB>b &plusmn;
        <SUB><IMG SRC="S_qrt.gif"></SUB></TD>
    <TD><SUB><IMG SRC="frac14.gif"></SUB>b<SUP>2</SUP>
        <FONT FACE=SYMBOL>-</FONT> ac</TD>
    <TD> ;</TD>
    </TR>
</TABLE>
And this is how it is set together: 
  ________  
x = -b ±  b2 - ac ;

P.S. The black line is made up of 8 consecutive underbars (_).

(4) 
<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
<TR><TD VALIGN=MIDDLE><FONT FACE=SYMBOL>
            <B>G</B></FONT>(x)&nbsp;=<SUB>&nbsp;</SUB></TD>
    <TD VALIGN=MIDDLE ALIGN=CENTER>
            <IMG SRC="infty.gif"><BR>
            <IMG SRC="INT_gral.gif"><BR>
            <FONT SIZE="-1">0</FONT></TD>
    <TD VALIGN=MIDDLE NOWRAP>
            t<SUP>x<FONT FACE=SYMBOL>-</FONT>1</SUP>
            e<SUP><FONT FACE=SYMBOL>-</FONT>t<SUP>
            dt ;<SUB>&nbsp;</SUB></TD>
    </TR>
</TABLE>
And this is how it is set together: 
G(x) = 



0		 tx-1 e-t dt ; 

(5) 
<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
<TR><TD ROWSPAN=2 VALIGN=MIDDLE>
        k<SUB>r</SUB>&nbsp;=<SUP><SUP>&nbsp;</SUP></SUP></TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE ALIGN=CENTER>
        k<FONT SIZE=-1><SUB>B</SUB></FONT>T
        <HR SIZE=1>
        h</TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE>&nbsp;e</TD>
    <TD VALIGN=MIDDLE NOWRAP>
        <SUP><FONT FACE=SYMBOL>D</FONT>S<SUP><IMG
        SRC="thrmd.gif"></SUP><SUB><FONT
        SIZE=+1>/</FONT>R</SUB></TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE>&nbsp;&middot;&nbsp;e</TD>
    <TD VALIGN=MIDDLE NOWRAP>
        <SUP><FONT FACE=SYMBOL>-</FONT>E<SUP>*</SUP><SUB><FONT
        SIZE=+1>/</FONT>RT</SUB></TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE>;</TD>
    </TR>
<TR><TD>&nbsp;</TD>
    <TD>&nbsp;</TD>
    </TR>
</TABLE>
And this is how it is set together: 
kr =  kBT
h		  e DS/R  · e -E*/RT ;
   

P.S. The black line is the <HR> horizontal line.

(6) 
<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
<TR><TD VALIGN=BOTTOM>
        <IMG SRC="S_UM.gif"></TD>
    <TD VALIGN=MIDDLE>
        <SUP><SUP><IMG SRC="Prime.gif" HEIGHT=6></SUP></SUP></TD>
    <TD VALIGN=BOTTOM ALIGN=CENTER>
        f(x)<SUB>&nbsp;</SUB></TD>
    <TD VALIGN=BOTTOM ALIGN=CENTER>
        <FONT SIZE="-1">&nbsp;def&nbsp;</FONT><BR>
         <IMG SRC="eq.gif"><SUB>  </SUB></TD>
    <TD VALIGN=BOTTOM>
        <IMG SRC="S_UM.gif"></TD>
    <TD VALIGN=BOTTOM ALIGN=CENTER>
        &nbsp;f(x)<SUB>&nbsp;</SUB>;</TD>
    </TR>
<TR><TD COLSPAN=2 VALIGN=TOP>
        x<IMG SRC="in.gif">A</TD>
    <TD COLSPAN=2>&nbsp;</TD>
    <TD COLSPAN=2 VALIGN=TOP>
        x<IMG SRC="in.gif">A<BR>
        x<IMG SRC="neq.gif">0</TD>
    </TR>
</TABLE>
And this is how it is set together: 
f(x)   def 
   		  f(x) ;
xA   xA
x0

(7) 
<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
<TR><TD VALIGN=MIDDLE><SUB>
        <IMG SRC="nabla.gif"></SUB><SUP>2</SUP>U(x,y,z) = </TD>
    <TD VALIGN=MIDDLE ALIGN=CENTER>
        <IMG SRC="pardif.gif"><SUP>2</SUP>U
        <HR SIZE=1>
        <IMG SRC="pardif.gif">x<SUP>2</SUP></TD>
    <TD VALIGN=MIDDLE>&nbsp;+&nbsp;</TD>
    <TD VALIGN=MIDDLE ALIGN=CENTER>
        <IMG SRC="pardif.gif"><SUP>2</SUP>U
        <HR SIZE=1>
        <IMG SRC="pardif.gif">y<SUP>2</SUP></TD>
    <TD VALIGN=MIDDLE>&nbsp;+&nbsp;</TD>
    <TD VALIGN=MIDDLE ALIGN=CENTER>
        <IMG SRC="pardif.gif"><SUP>2</SUP>U
        <HR SIZE=1>
        <IMG SRC="pardif.gif">z<SUP>2</SUP></TD>
    <TD VALIGN=MIDDLE>;</TD>
    </TR>
</TABLE>
And this is how it is set together: 
2U(x,y,z) = 2U
x2		  +  2U
y2		  +  2U
z2		 ;

P.S. The black lines are <HR> horizontal lines.

(8) 
<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
<TR><TD ROWSPAN=4 VALIGN=MIDDLE>
        <IMG SRC="LA_PAR.gif"><BR
       ><IMG SRC="LSTRUT.gif"><BR
       ><IMG SRC="LSTRUT.gif"><BR
       ><IMG SRC="LSTRUT.gif"><BR
       ><IMG SRC="LSTRUT.gif"><BR
       ><IMG SRC="LSTRUT.gif"><BR
       ><IMG SRC="LSTRUT.gif"><BR
       ><IMG SRC="LV_PAR.gif"><BR>
        </TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE>
        <IMG SRC="L_PAR.gif"><BR></TD>
    <TD ALIGN=CENTER>a&nbsp;b</TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE>
        <IMG SRC="R_PAR.gif"><BR></TD>
    <TD ROWSPAN=4>&nbsp;</TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE>
        <IMG SRC="L_PAR.gif"><BR></TD>
    <TD ALIGN=CENTER>e&nbsp;f</TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE>
        <IMG SRC="R_PAR.gif"><BR></TD>
    <TD ROWSPAN=4 VALIGN=MIDDLE>
        <IMG SRC="RA_PAR.gif"><BR
       ><IMG SRC="RSTRUT.gif"><BR
       ><IMG SRC="RSTRUT.gif"><BR
       ><IMG SRC="RSTRUT.gif"><BR
       ><IMG SRC="RSTRUT.gif"><BR
       ><IMG SRC="RSTRUT.gif"><BR
       ><IMG SRC="RSTRUT.gif"><BR
       ><IMG SRC="RV_PAR.gif"><BR>
        </TD>
    <TD ROWSPAN=4 VALIGN=MIDDLE>
        ; </TD></TR>
<TR><TD ALIGN=CENTER>c&nbsp;d</TD>
    <TD ALIGN=CENTER>g&nbsp;h</TD></TR>
<TR><TD ROWSPAN=2 COLSPAN=3 ALIGN=CENTER VALIGN=MIDDLE>0</TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE>
        <IMG SRC="L_PAR.gif"><BR>
    </TD>
    <TD ALIGN=CENTER>i&nbsp;j</TD>
    <TD ROWSPAN=2 VALIGN=MIDDLE>
        <IMG SRC="R_PAR.gif"><BR>
    </TD></TR>
<TR><TD ALIGN=CENTER>k&nbsp;l</TD></TR>
</TABLE>
And this is how it is set together: 

a b
 
e f
;
c d g h
0
i j
k l

(9) 
<TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0>
<TR><TD ROWSPAN=5 VALIGN=MIDDLE>
        det</TD>
    <TD ROWSPAN=5 VALIGN=MIDDLE>
        <IMG SRC="CSTRUT.gif" HEIGHT=95 WIDTH=8></TD>
    <TD>c<SUB>0</SUB></TD>
    <TD>c<SUB>1</SUB></TD>
    <TD>c<SUB>2</SUB></TD>
    <TD>&middot;&middot;&middot;&nbsp;</TD>
    <TD>c<SUB>n</SUB></TD>
    <TD ROWSPAN=5 VALIGN=MIDDLE>
        <IMG SRC="CSTRUT.gif" HEIGHT=95 WIDTH=8><BR></TD>
    <TD ROWSPAN=5 VALIGN=MIDDLE>
       &gt; 0 ;</TD>
    </TR>
<TR><TD>c<SUB>1</SUB></TD>
    <TD>c<SUB>2</SUB></TD>
    <TD>c<SUB>3</SUB></TD>
    <TD>&middot;&middot;&middot;&nbsp;</TD>
    <TD>c<SUB>n+1</SUB></TD>
    </TR>
<TR><TD>c<SUB>2</SUB></TD>
    <TD>c<SUB>3</SUB></TD>
    <TD>c<SUB>4</SUB></TD>
    <TD>&middot;&middot;&middot;&nbsp;</TD>
    <TD>c<SUB>n+2</SUB></TD>
    </TR>
<TR><TD><IMG SRC="v3d.gif"></TD>
    <TD><IMG SRC="v3d.gif"></TD>
    <TD><IMG SRC="v3d.gif"></TD>
    <TD>&nbsp;</TD>
    </TR>
    <TD><IMG SRC="v3d.gif"></TD>
<TR><TD>c<SUB>n&nbsp;&nbsp;</SUB></TD>
    <TD>c<SUB>n+1</SUB></TD>
    <TD>c<SUB>n+2</SUB></TD>
    <TD>&middot;&middot;&middot;&nbsp;</TD>
    <TD>c<SUB>2n</SUB></TD>
    </TR>
</TABLE>
And this is how it is set together: 
det c0 c1 c2 ···  cn
> 0 ;
c1 c2 c3 ···  cn+1
c2 c3 c4 ···  cn+2
 
cn   cn+1 cn+2 ···  c2n

NOTICE: if you entered this page from outside, note that the above examples involve the use of symbol GIFs, and will only lead to the desired results when these are located in the same directory (folder). When this is not the case, you will have to indicate the path to the directory (folder) in which you keep the GIF in each <IMG SRC="...">.
Do not under any circumstances place such paths to the GIFs of this site, but download the GIFs you need to your site first. To find them, click here.
http://w3.rz-berlin.mpg.de/~wm/SYM/SYM-Q1.html 
© Fritz-Haber-Institut der MPG, 2001
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