# [APPM 2360] - Midterm Exam Guide - Comprehensive Notes for the exam (16 pages long!)

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6 Feb 2017
School
Department
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CU-Boulder
APPM 2360
MIDTERM EXAM
STUDY GUIDE
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n'.i.i{. rililt\ I inef\t Atrt?l
Diiferenhol Eq, 1 iTiLrltltrrioiitcrl erpre::infl conrour\nq (ililotrrtcg or u 0c?c.nclcn\ \01iou1e \ t/rg
t
ql1fi tlrdtpefid,liii xttr*, uit t
- de{'i{O\\{C: Sri- -) dtqr}rC.ifii
dt -: \ndtptndrr\t -) \l', q
exotl1pleil 0q = -\-l , 0\$ = -l , t1 = r.1 tcortrl
'd,['cltl
. hl or0tr "0101n0\u si((c1r\$icil eq,nl"
\---.*. t \+.--:-'
hiSht",:l I indtP.
dtrivoli{e vqti0ble
:t -0j
dt,
qrne(ql n6101is\)
tcrrncrt\ \i1 0\dt{ 0QE's il.{ = ftt,rq\**5\s\e funt'1 trnoc,tl {un\$isil'l
cti
' ?nd 0lcltf oDE rlld2x " - q (Ne\N10n1 T(ond 10\A,\
0\'
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. Pqllio\ c\\{f ere\$ierl rqfl, ' s} : }" u
Al dx'
l:2- so\u\tonl \o \:* o1otr 0{}[
frtlCl {Lr.trq.i\tit qtt\ fio\ :.o.ir',iit'; the 00U (}n 0 Qr\tl1 t- o0\nc\i\i
exqmp\e: i\ ut{} '1-t n :ttutron t0 s\ " '3
siq
3" tt't \= :L
dt 1't
e-t - -tet
I-* tf * I nrt r\ lotutisn
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exonlpe 1
exCtl\rPlCr H - -q
\* I
qtt\= ll - t-,\ r' -+ ?o\tlcu\ol
sL tl- t')'/2 = - t
dt [1- gz lrlz
-'la
i t r-t') (-2t) = -t t
'ttr"t.)"'- l - t'\ -'12
t tl- t')-'l2
solu\t\$n r rril\: for ltt I I
- qtnctol lqtLriict) httctltf
o( t\$\t\\i(n)
qrr) . Qt-t I
I'r 0tdtr oDE natt i0\$\r\\t: o( :oturtiotll ---+qfl]tlcli s0\u1i0ns
\f s\$\\e dq '-q und utcl = 5 tnr\io\ {0\e p{o\r\tTn
qi\tn qH\= te-t q,t\$tlet :o\u\ion
vo\litril0T sot\iioii ior 111iii0\ \i0lue \t\$\=3
qto) " (t'o'5
t'5 + gttl\ ' te-o
. Grughrto\ ss\u\\t}nr t D{ttlttii
for q! " {t\-rl\ + -q
dt \-
mnrr(tr t-'q fl0te
I stopt tittqtl\
(sn)ftr oDf , q\\\$ lnt:tqK
l
-L-.. t
.t\
I
I
n (no frt
0
o
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