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] [2

]
Cap\'{\i }tulo 1.

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[]\OT1/cmr/bx/n/12 Definition 3. []\OT1/cmr/m/it/12 Uma sequ^encia $\OMS/cmsy/m
/n/12 f\OML/cmm/m/it/12 a[]\OMS/cmsy/m/n/12 g$ \OT1/cmr/m/it/12 ^^Se dita \OT1/
cmr/bx/it/12 li-mi-tada su-pe-ri-or-mente \OT1/cmr/m/it/12 quando
 []

[3] [4] [5] [6] [7] [8]
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[]\OT1/cmr/m/n/12 Note que a fun^^Xc~ao $\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OM
L/cmm/m/it/12 x\OT1/cmr/m/n/12 ) = []$ ^^Se tal que $[][] [] = 1$ ent~ao $[][] 
[] =
 []


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\OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 a[]b[] \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12
 lr\OMS/cmsy/m/n/12 j \OML/cmm/m/it/12 < \OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 a[]
b[] \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 a[]r \OT1/cmr/m/n/12 + \OML/cmm/m/it/
12 a[]r \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 lr\OMS/cmsy/m/n/12 j ^^T j\OML/cm
m/m/it/12 a[]\OMS/cmsy/m/n/12 jj\OML/cmm/m/it/12 b[] \OMS/cmsy/m/n/12 ^^@ \OML/
cmm/m/it/12 r\OMS/cmsy/m/n/12 j \OT1/cmr/m/n/12 + \OMS/cmsy/m/n/12 j\OML/cmm/m/
it/12 r\OMS/cmsy/m/n/12 jj\OML/cmm/m/it/12 a[] \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/
it/12 l\OMS/cmsy/m/n/12 j \OML/cmm/m/it/12 < M^^O \OT1/cmr/m/n/12 + \OMS/cmsy/m
/n/12 j\OML/cmm/m/it/12 r\OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 ^^O \OT1/cmr/m/n/12
 = (\OML/cmm/m/it/12 M \OT1/cmr/m/n/12 + \OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 r\O
MS/cmsy/m/n/12 j\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ^^O:
 []

[9]
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[]\OT1/cmr/bx/n/12 Example 27. []\OT1/cmr/m/it/12 Vi-mos que a sequ^encia cujo 
termo ge-ral ^^Se $\OML/cmm/m/it/12 a[] \OT1/cmr/m/n/12 = []$
 []

[10] [11] [12]
Cap\'{\i }tulo 2.
[13

] [14] [15]
Overfull \hbox (0.55138pt too wide) in paragraph at lines 518--519
[]\OT1/cmr/bx/n/12 Example 40. []\OT1/cmr/m/it/12 As s^^Series $[] []$ e $[] []
$ s~ao di-ver-gen-tes e as s^^Series $[] []$
 []


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[]\OT1/cmr/bx/n/12 Theorem 41 \OT1/cmr/m/n/12 (Pro-pri-e-da-des das s^^Series)\
OT1/cmr/bx/n/12 . []\OT1/cmr/m/it/12 Se-jam $[] \OML/cmm/m/it/12 a[]$ \OT1/cmr/
m/it/12 e $[] \OML/cmm/m/it/12 b[]$ \OT1/cmr/m/it/12 s^^Series num^^Sericas
 []

[16] [17]
Overfull \hbox (9.05495pt too wide) in paragraph at lines 571--573
\OT1/cmr/m/n/12 como $[][] []$ di-verge ent~ao pelo teste de com-para^^Xc~ao se
-gue que $[][] []$
 []


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[]\OT1/cmr/bx/n/12 Example 44. []\OT1/cmr/m/it/12 Ana-lise so-bre a con-verg^en
cia ou di-verg^encia da s^^Serie $[][] []$. 
 []


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\OT1/cmr/m/n/12 como $[][] []$ con-verge ent~ao pelo teste de com-para^^Xc~ao a
 s^^Serie $[][] []$
 []

[18]
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[]$\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ) = []$
 \OT1/cmr/m/it/12 atende ^^Ras condi^^Xc~oes ex-pos-tas mas $[][] [] \OT1/cmr/m
/n/12 = [][][[]([] \OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ))][] =
 []

[19] [20]
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[]\OT1/cmr/bx/n/12 Example 54. []\OT1/cmr/m/it/12 A s^^Serie $[] []$ con-verge,
 pois o $[][] [] \OT1/cmr/m/n/12 = 0$ \OT1/cmr/m/it/12 e $[] \OML/cmm/m/it/12 >
 [];    \OMS/cmsy/m/n/12 8\OML/cmm/m/it/12 n$\OT1/cmr/m/it/12 . 
 []


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[]\OT1/cmr/bx/n/12 Theorem 57. []\OT1/cmr/m/it/12 O erro que se co-mete ao se a
pro-xi-mar a soma da s^^Serie $[]\OT1/cmr/m/n/12 (\OMS/cmsy/m/n/12 ^^@\OT1/cmr/
m/n/12 1)[]\OML/cmm/m/it/12 a[]$
 []

[21]
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[]\OT1/cmr/m/n/12 Suponha que $[] \OML/cmm/m/it/12 a[]$ \OT1/cmr/m/n/12 con-ver
ge ab-so-lu-ta-mente ent~ao $[] \OMS/cmsy/m/n/12 j\OML/cmm/m/it/12 a[]\OMS/cmsy
/m/n/12 j$ \OT1/cmr/m/n/12 con-
 []

[22]
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[] \OMS/cmsy/m/n/12 j[]j \OT1/cmr/m/n/12 = [] [] = [] []([]) = [] \OML/cmm/m/it
/12 < \OT1/cmr/m/n/12 1
 []


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[]\OT1/cmr/bx/n/12 Theorem 64 \OT1/cmr/m/n/12 (Teste da Ra^^S^^Pz)\OT1/cmr/bx/n
/12 . []\OT1/cmr/m/it/12 Seja $[] \OML/cmm/m/it/12 a[]$ \OT1/cmr/m/it/12 uma s^
^Serie num^^Serica. Seja $[][] [] \OT1/cmr/m/n/12 =
 []

[23]
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[]\OT1/cmr/bx/n/12 Example 65. []\OT1/cmr/m/it/12 Con-si-dere a s^^Serie $[][] 
[]$. Pelo teste da ra^^S^^Pz: $[][] [] \OT1/cmr/m/n/12 =
 []


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[]\OT1/cmr/bx/n/12 Example 67. []\OT1/cmr/m/it/12 A s^^Serie $[] []$ di-verge e
 a s^^Serie $[] []$ con-ver-gente mas $[][] [] \OT1/cmr/m/n/12 =
 []

[24]
Cap\'{\i }tulo 3.
[25

] [26] [27] [28] [29] [30]
Overfull \hbox (39.27092pt too wide) detected at line 1069
\OML/cmm/m/it/12 P[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ) = \OML
/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 a\OT1/cmr/m/n/12 ) + \OML/cmm/m
/it/12 f[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 a\OT1/cmr/m/n/12 )(\OML/cmm/m/it/12
 x \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 a\OT1/cmr/m/n/12 ) + [](\OML/cmm/m/it/
12 x \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 a\OT1/cmr/m/n/12 )[] + [] + [](\OML/
cmm/m/it/12 x \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 a\OT1/cmr/m/n/12 )[] = [] [
](\OML/cmm/m/it/12 x \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 a\OT1/cmr/m/n/12 )[]

 []

[31]
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\OML/cmm/m/it/12 G\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 t\OT1/cmr/m/n/12 ) = \OML/c
mm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 ) \OMS/cmsy/m/n/
12 ^^@ \OT1/cmr/m/n/12 [\OML/cmm/m/it/12 f\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 t\O
T1/cmr/m/n/12 ) + \OML/cmm/m/it/12 f[]\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 t\OT1/c
mr/m/n/12 )(\OML/cmm/m/it/12 x \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 t\OT1/cmr/
m/n/12 ) + [](\OML/cmm/m/it/12 x \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 t\OT1/cm
r/m/n/12 )[] + [] + [](\OML/cmm/m/it/12 x \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12
 t\OT1/cmr/m/n/12 )[]] \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 R[]\OT1/cmr/m/n/12
 (\OML/cmm/m/it/12 x\OT1/cmr/m/n/12 )[]
 []

[32] [33]

Package amsmath Warning: Foreign command \atopwithdelims;
(amsmath)                \frac or \genfrac should be used instead
(amsmath)                 on input line 1185.

[34] [35] [36]
Cap\'{\i }tulo 4.

Overfull \hbox (9.94447pt too wide) in paragraph at lines 1246--1254
\OT1/cmr/m/n/12 As s^^Series de Fou-rier s~ao fer-ra-men-tas muito im-por-tante
 na re-solu^^Xc~ao de Equa^^Xc~oes
 []


Overfull \hbox (9.3542pt too wide) in paragraph at lines 1260--1262
[]\OT1/cmr/bx/n/12 Definition 85. []\OT1/cmr/m/it/12 Uma fun^^Xc~ao $\OML/cmm/m
/it/12 f \OT1/cmr/m/n/12 : []$ \OT1/cmr/m/it/12 ^^Se peri^^Sodica de per^^S^^Po
do $\OML/cmm/m/it/12 T$ \OT1/cmr/m/it/12 se $\OML/cmm/m/it/12 f [] \OT1/cmr/m/n
/12 =
 []

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<Figura16.eps>
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 <Figura13.eps> [37

] [38] [39] [40] [41] [42] [43]

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Overfull \hbox (2.32191pt too wide) in paragraph at lines 1767--1775
\OT1/cmr/m/it/12 pois nos pon-tos onde $\OML/cmm/m/it/12 f[]$ \OT1/cmr/m/it/12 
^^Se des-cont^^S^^Pnua, a des-con-ti-nui-dade ^^Se de se-gunda esp^^Secie,
 []

[44] [45]
File: Figura26.eps Graphic file (type eps)
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Overfull \hbox (17.04185pt too wide) in paragraph at lines 1939--1939
[]\OT1/cmr/bx/n/17.28 S^^Series de Fou-rier de fun^^Xc~oes pa-res e ^^S^^Pmpare
s 
 []

[47]
Overfull \hbox (0.62378pt too wide) in paragraph at lines 2045--2053
[]\OT1/cmss/m/n/12 Demonstra^^Xc~ao:\OT1/cmr/m/n/12 Seja $\OML/cmm/m/it/12 f$ \
OT1/cmr/m/n/12 uma fun^^Xc~ao par e con-si-dere a in-te-gral $[]\OML/cmm/m/it/1
2 f \OT1/cmr/m/n/12 = []\OML/cmm/m/it/12 f \OT1/cmr/m/n/12 +
 []

[48] [49]
File: Figura24.eps Graphic file (type eps)
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File: Figura12.eps Graphic file (type eps)
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[54] [55] [56

]
Cap\'{\i }tulo 5.
[57] [58] [59] [60] [61] [62]
Overfull \hbox (18.6118pt too wide) in paragraph at lines 2806--2806
[]\OT1/cmr/bx/n/17.28 Equa^^Xc~oes di-fe-ren-ci-ais com co-e-fi-ci-en-tes cons-

 []

[63]
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\OT1/cmr/m/n/12 A equa^^Xc~ao (5.20[]) ^^Se co-nhe-cida como equa^^Xc~ao ca-rac
-ter^^S^^Pstica as-so-ci-ada ^^Ra equa^^Xc~ao
 []

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\OT1/cmr/m/sl/12 5.5.  EQUA[][]OES DIFERENCIAIS COM COEFICIENTES CONSTANTES \OT
1/cmr/m/n/12 65
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