T;;,$A+N
0-E !"#$%"&'(#$"#)
.D7)+7'K#H,L/2&8'8"7<'#8'%<,'K #H,L/2&8' +$' %<,' !"#$%"&'
/$)D'L,#%"2,'8+$,'K#H,8'+$' +$%,B,2'L2,Z",$7D'2#%+/8'%/'%<,'
L"$A#&,$ %# )')+[ ,' A/ " W ),' L2, Z" , $ 7D a'%2+; ), 'L2, Z " ,$ 7 D' #$ A '8 /'
/$4'*</8,';#2%+#)8'#2,'7#)),A' G7BJ*834-' W,7#"8,' %<,+2'L2,Y
Z",$7D'+8'#'<#2&/$+7'&")%+;),'/L'%<,'L"$A#&,$%#)4'
./$L"8+$Bu'F,%`8'B,$,2#)+],'+%'%/'7D7)+7'K #H,L/2&8e'#'7D7)+7'
K#H,L/2&' ^' )+[,' 8#K %/ /% <a' 8Z"#2,a' ,%74' ^' /$)D' 7/$8+8%8' /L'
<#2&/$+7' ;#2%+#)84' *<,' <#2&/$+7' K+%<' %<,' )/K,8%' L2,Y
Z",$7D'+8'A/&+$#$%'#$A'%<,2,L/2,'7#)),A'%<,'L"$A#&,$%# )4'
T))'/%<,2'<#2&/$+78'#2,'7#)),A'/H,2%/$,84'
The Sawtooth Wave
*<,':#K%//%<'>#H,'+8' %<,'&/8%' ;/;")#2'8D$%<,8+],2'K#H,Y
L/2&4'P%'7/$8+8%8'/ L'#))'< #2&/$+78'+$'K<+7< '%< ,'&#B$+%"A,'/L'
,#7<'<#2& /$+7'A,87,$A8'WD'%<,'L#7%/2'/L'+%8';/8+%+/$4'*<+8'
&,#$8' %<#%' %<,' L+28%' <#2&/$+7' O%<,' L"$A#&,$%#)R' <#8' L"))'
&#B$+%"A,a' %<,' 8,7/$A' <#2&/$+7' <#8' <#)L' &#B$+%"A,a' %<,'
%<+2A' <#2&/$+7' <#8' #' %<+2A' &#B$+%"A,a' #$A' 8/' /$ 4' *<,'
L/))/K+$B' ;+7%"2,' 8</K8' </K' %<,' +$A+H+A"#)' <#2&/ $+7 8'
W"+)A'";'%<,'8#K%//%<'K#H,e'
&
'II3+3N,&4*J?*8,8+-&*/&+G,&>7]+**+G&]7N,&
*<,' 8#K%//%<' K#H,' K#8' %</"B<%' #8' #$' #W8%2#7%+/$' /L' %<,'
%+&W2,' /L' 8%2+$B' #$A' W2#88' +$8%2"&,$%84' \/"' 7#$' , #8+)D'
"$A,28%#$A'%<#%'K<,$'D/"'%<+$['/L'#'H+/)+$4' P&#B+$,'#'W/K'