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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Set 13.1" }{MPLTEXT 1 0 0 "
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Q20:   add these" }{MPLTEXT 
1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "z:=I*t:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "int(Re(z^2)*diff(z,t),t=0..1
);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^##!\"\"\"\"$" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "z:=I+t:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
30 "int(Re(z^2)*diff(z,t),t=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
#!\"#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "z:=1+I-t*I:" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "int(Re(z^2)*diff(z,t),t=0..1);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#^##!\"#\"\"$" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "z:=1-t:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "int
(Re(z^2)*diff(z,t),t=0..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##!\"\"
\"\"$" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q24:" }{MPLTEXT 1 0 0 "" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "evalc(exp(4*(8-3*I-Pi*I))
/4-exp(4*(8-3*I))/4);  " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Set 13.3" }{MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Q14:  Singularities at z =0 and" }
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evalc(l
n(2*I))+2*Pi*k;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(-%#lnG6#\"\"#\"\"
\"*&^##F(F'F(%#PiGF(F(*(F'F(F,F(%\"kGF(F(" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 104 "None of these are inside. The  z = 0 residue is  exp(0)/
(exp(0)-2i) = (1+2i)/5.  Answer:  2 Pi /5 *(i-2)" }{MPLTEXT 1 0 1 " " 
}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "Q16:  The only singularity insi
de is at  z = 2i.  The corresponding residue is  sin(2i)/4/(2i)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "evalc(2*Pi*I*sin(2*I)/8/I); \+
evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(^##\"\"\"\"\"%F&%#PiGF&
-%%sinhG6#\"\"#F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^#$\"+-&H&[G!\"*
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Set 15.3" }{MPLTEXT 1 0 0 "" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 67 "Q20:    There are 3 singularitie
s inside, at z = 0 and + and - Pi/4" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 57 "restart:  eval(diff(z*exp(-z^2),z)/diff(sin(4*z),z),z
=0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"\"\"\"%" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 126 "simplify(eval(diff((z+Pi/4)*exp(-z^2),z)
/diff(sin(4*z),z),z=-Pi/4)\n+eval(diff((z-Pi/4)*exp(-z^2),z)/diff(sin(
4*z),z),z=Pi/4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&#\"\"\"\"\"#F
&-%$expG6#,$*&\"#;!\"\"%#PiGF'F.F&F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 58 "Answer:       Pi*I/2 - Pi*I*exp(-Pi^2/16)               or" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "evalf(Pi/2-Pi*exp(-Pi^2/16))
*I;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#^#$!*+u`C\"!\"*" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 8 "Sec 15.4" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 3 "Q8:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 44 "f:=simplify((1+2*(z+1/z))/(17-4*(z+1/z))/z)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,$*(,(%\"zG\"\"\"*&\"\"#F))
F(F+F)F)F+F)F)F(!\"\",(*&\"#<F)F(F)F-*&\"\"%F)F,F)F)F2F)F-F-" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "solve(4*z^2-17*z+4,z);  # we
 know how to do this by hand" }}{PARA 11 "" 1 "" {XPPMATH 20 "6$\"\"%#
\"\"\"F#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "eval(-(z+2*z^2+
2)/z/4/(z-4),z=1/4) + eval(-(z+2*z^2+2)/(4*z^2+4-17*z),z=0);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6##\"\"#\"#:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 19 "Answer:     4*Pi/15" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 4 "Q14:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "solve(x^2-2*x+5,x);  # do by hand" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6$^$\"\"\"\"\"#^$F$!\"#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "eval(diff(1/(z-1+2*I)^2,z),z=1+2*I);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#^##!\"\"\"#K" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
15 "Answer:   Pi/16" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 4 "Q20:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 37 "eval(diff(exp(2*z*I)/(z+I)^2,z),z=I);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#*&^##!\"$\"\"%\"\"\"-%$expG6#!\"#F(" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 26 "Answer:   Pi*(3/2*exp(-2))" }{MPLTEXT 1 
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