Geometría Vectorial y Analitica actual.doc

Facultad de Ciencias Exactas y Naturales Departamento de Matemáticas Coordinación de Servicios

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CURSOS DE SERVICIOS PARA LA FACULTAD FACULTAD DE INGENIERIA IMS 120 ó INM INM 171 CODIGO: GEOMETRÍA VECTORIAL Y ANALÍTICA NOMBRE DEL CURSO: REQUISITOS: DURACION DEL SEMESTRE: 16 SEMANAS NUMERO DE CREDITOS: 4

CARACTERIZACIÓN Es un cus! "#$ %$&n "# #s'u"(!s "# (n)#n(#*&+ "#$ c(c$! ,-s(c!+ c$&s(.(c&,$#+ /&$("&,$#  &,($('&,$#

OBJETIVOS OBJETIVOS GENERALES PARA LOS CURSOS DE MATEMÁTICA EN INGENIERÍA C!n'(,u( &$ "#s&!$$! "#$ (n'#$#c'!  "# $& c&%&c("&" &n&$*'(c& "#$ #s'u"(&n'#+ %!'#nc(&n"! .&cu$'&"#s c!)n('(/&s "# !"#n su%#(!  $& &,s'&cc(ón 3&c($('& 3&c($('& su c!%#ns(ó c!%#ns(ón n "# $&s $##s "# $& n&'u&$#5&  "# $!s c!nc#%'!s c!nc#%'!s .un"&#n'&$#s .un"&#n'&$#s #n $!s u# s# ,&s&n $!s '!"!s %&& #$ &n-$(s(s  #$ "(s#8! "# s(s'#&s "# (n)#n(#*& 3!& #n $&s #)$&s "# $& "#!s'&c(ón ! #.u'&c(ón ()u!s&  "# $& #9%$(c&c(ón /-$("& Es'&,$#c# un $#n)u&# c!;n+ ,-s(c!+ %&& c!un(c&s# c!n !'!s %!.#s(!n&$#s  %&& &"#$&n'& #s'u"(!s # (n/#s'()&c(!n#s &/&n5&"&s

OBJETIVO ESPECÍFICO DEL CURSO 221 (n'!"uc( &$ #s'u"(&n'# #n #$ &n#! "# $!s &$)!('!s "# #"ucc(ón "# G&uss  G&uss< =!"&n #n s(s'#&s "# #cu&c(!n#s "# !"#n 2>2  ?>?+ %#('(n"!$# ("#n'(.(c& $!s '(%!s "# s!$uc(ón  su (n'#%#'&c(ón )-.(c&+ %&& %!s'#(!#n'# )&&n'(5& un& #! c!%#ns(ón "# su )#n#&$(5&c(ón 222 @#s#n'& un c!nun'! .un"&#n'&$ R n+ c!n sus !%#&c(!n#s c!! un !"#$! u# s# #$&c(!n& #s'uc'u&$#n'# c!n '!"!s $!s "#-s c!nun'!s u# s# #s'u"(&-n #n #$ cus! 22? Es'u"(& #$ c!nun'! "# $&s &'(c#s "# c!%!n#n'#s #&$#s R 9nB 9nB "#s'&c&n"! '#s &s%#c'!s .un"&#n'&$#s &s*: •

E$ %(#! c!#s%!n"# & $& #s'uc'u& "# #s'# c!nun'! c!! un #s%&c(! /#c'!(&$+ c!n sus &%$(c&c(!n#s  %!%(#"&"#s c&&c'#*s'(c&s u# $! c!n/(#'#n+ #n s( (s!+ #n un !,#'! "# #s'u"(! "# $&s &'#-'(c&s

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2210. A%$(c& #$ &n-$(s(s /#c'!(&$ #n $& s!$uc(ón "# %!,$#&s #$&c(!n&"!s c!n $& .*s(c&  #n $!s cu&$#s $&s s('u&c(!n#s u# s# )#n#&n+ %!%(c(&n #$ &n-$(s(s  $& c#&'(/("&" "#$ #s'u"(&n'# c!ns'('un"!s# #n s('u&c(!n#s %!,$#-'(c&s (n'#)&"!&s L!s '#&s "#s&!$$&"!s c!#s%!n"#n &: S(s'#&s "# .u#5&s c!%$&n&#s  c!ncu#n'#s  /#$!c("&"#s #$&'(/&s 2211 Es'u"(& $&s cón(c&s+ ,&! un #n.!u# c&'#s(&n!+ &%!/#c&n"! %&& su "#'#(n&c(ón+ $!s #$##n'!s /#c'!(&$#s '&,&&"!s "#s&!$$&n"! un #s'u"(! &n&$*'(c! "# sus #cu&c(!n#s  c&&c'#(5-n"!$&s c!! c&s!s %&'(cu$&#s "# $& #cu&c(ón )#n#&$ "# s#)un"! )&"! #n "!s /&(&,$#s 2212 . @#s#n'& $&s %!%(#"&"#s ó%'(c&s "# $&s cón(c&s  &%$(c&$&s #n $& s!$uc(ón "# s('u&c(!n#s %-c'(c&s u# %!%(c(#n $& &%$(&c(ón "# $!s '#&s  #$ '&,&! 221? @$&n'#& s('u&c(!n#s %!,$#-'(c&s (n'#)&"&s+ #n $&s cu&$#s s# u'($(5&n #$ &! n;#! %!s(,$# "# #$##n'!s '#ó(c!s Es'&s s# %u#"#n %$&n'#& "#s"# un c!(#n5! %! #'&%&s+ (n'#)&n"! #n .!& s#cu#nc(&$ $!s '#&s "#s&!$$&"!s 2214 Es'&,$#c# $!s .un"&#n'!s  n#9!s #u#("!s c!n $!s %!#c'!s "# &u$& u# '(#n#n #s'# cus! c!! %##u(s('! ! c!#u(s('! #s%#c(&$#n'# c!n #$ cus! "# F$)#,& $(n#&$  $& s#cu#nc(& "# $!s c-$cu$!s

METODOLOGIA E$ cus! s# "#s&!$$&- #"(&n'# $& #9%!s(c(ón "# $!s '#&s %! %&'# "#$ %!.#s!+ ,usc&n"! un& %&'(c(%&c(ón &c'(/& "#$ #s'u"(&n'# S# %!)&&- &"#-s '&$$##s+ c!n ,&s# #n %!,$#&s s#$#cc(!n&"!s %! #$ c!!"(n&"! "#$ cus!  "#s&!$$&"!s %! !n('!#s

EVALUACION Es'& s# #.#c'u&- #"(&n'#  %u#,&s %&c(&$#s "# ()u&$ /&$! 20B # (n"(/("u&$#s+ c!n $& s()u(#n'# "(s'(,uc(ón: 1 2 ? 4 

E/&$u&c(ón: E/&$u&c(ón: E/&$u&c(ón: E/&$u&c(ón: E/&$u&c(ón:

Inc$u# &s'& $& S#cc(ón 6 Inc$u# "#s"# $& S#cc(ón 7 &s'& $& 10 Inc$u# "#s"# $& S#cc(ón 11 &s'& $& 1 Inc$u# "#s"# $& S#cc(ón 16 &s'& $& 21 Inc$u# "#s"# $& S#cc(ón 22 &s'& $& 27

CONTENIDO RESUMIDO S(s'#&s "# #cu&c(!n#s $(n#&$#s  -$)#,& &'(c(&$ L& .unc(ón "#'#(n&n'# V#c'!#s )#!'(c!s V#c'!#s c!!"#n&"!s

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F$)#,& /#c'!(&$ V#c'!#s "# $& .*s(c&  &%$(c&c(!n#s "# $!s /#c'!#s )#!'(c!s & $& .*s(c& Cón(c&s

CONTENIDO DETALLADO Sección 1 S(s'#&s "# #cu&c(!n#s $(n#&$#s 292  ?9? In'#%#'&c(ón )#!'(c& Sección . M'!"! "# #"ucc(ón "# G&uss M'!"! "# #"ucc(ón "# G&uss =!"&n+ &%$(c&"!s & s(s'#&s 292  ?9? Sección !. D#.(n(c(ón "# Rn  !%#&c(!n#s #n R n @!"uc'! #sc&$& #n'# n<'u%$&s En#'u%$&s !'!)!n&$#s C!,(n&c(ón $(n#&$ "# n<'u%$&s M&'(c#s "# !"#n 9n I)u&$"&" "# &'(c#s A$)un!s '(%!s "# &'(c#s: nu$&+ ("#n'("&"+ '(&n)u$& (n.#(!+ "(&)!n&$+ #sc&$&+ .($&  c!$un& Sección ". O%#&c(!n#s #n R9n @!%(#"&"#s "# $& su&+ u$'(%$(c&c(ón %! un #sc&$& @!%(#"&"#s "# $& u$'(%$(c&c(ón %! un #sc&$& C!,(n&c(ón $(n#&$ "# &'(c#s @!"uc'! "# &'(c#s @!%(#"&"#s "#$ %!"uc'! #n'# &'(c#s A%$(c&c(!n#s "#$ %!"uc'! &'(c(&$ Sección # M&'(5 '&s%u#s'& @!%(#"&"#s M&'(5 s('(c& M&'(5 &n'(s('(c& @!%(#"&"#s S(s'#& "# #cu&c(!n#s $(n#&$#s SELB C!nun'! s!$uc(ón M&'(5 #sc&$!n&"& M&'(5 #sc&$!n&"& #"uc("& Ecu&c(ón &'(c(&$ #u(/&$#n'# "# un SEL +nB M'!"! "# #"ucc(ón "# G&uss  "# G&uss =!"&n Sección $. !"#$!s

T(%!s "# s!$uc(ón "# un SEL @!,$#&s "# &%$(c&c(ón #n "(.##n'#s

M&'(c#s #$##n'&$#s @!%(#"&"#s M&'(c#s #u(/&$#n'#s In/#s& "# un& Sección % &'(5 cu&"&"& @!%(#"&"#s 3&c'!(5&c(ón "# un& &'(5 #n '(n!s "# &'(c#s #$##n'&$#s

Sección &.

A$)!('!s %&& #$ c-$cu$! "# $& (n/#s&

Sección '. D#'#(n&n'#s: "#.(n(c(ón+ #n!#s  c!.&c'!#s "#s&!$$! %! c!.&c'!#s @!%(#"&"#s "# $!s "#'#(n&n'#s C-$cu$! "# un "#'#(n&n'# u'($(5&n"! sus %!%(#"&"#s Sección (). D#'#(n&n'#s # (n/#s& C-$cu$! "# $& (n/#s& %! $& &"un'& R#)$& "# C&#

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Sección (. @!,$#&s "# &%$(c&c(ón & $& G#!#'*& Euc$("(&n&  & $& T()!n!#'*& "# #s'!s cu&'! %!"uc'!s Esc&$&+ /#c'!(&$+ '(%$#  (9'!B Sección  * !. V#c'! "#s$(5&n'# A%$(c&c(!n#s "# $!s /#c'!#s )#!'(c!s #n $& s!$uc(ón "# &$)un!s %!,$#&s #n $& .*s(c& M+,e-+ ( S(s'#&s "# .u#5&s D#sc!%!s(c(ón "# un /#c'! #n sus c!%!n#n'#s #c'&n)u$&#s M'!"!s )-.(c!s  &n&$*'(c!s @!,$#&s "# /#$!c("&"#s #$&'(/&s G-.(c!s "# "#s%$&5&(#n'!s G-.(c!s M+,e-+ . "# /#$!c("&"#s Ecu&c(ón /#c'!(&$ ,-s(c& u# ()# #s'&s s('u&c(!n#s Sección ". E$ c!n! c(cu$& S#cc(!n#s cón(c&s L& #cu&c(ón )#n#&$ "#$ 2K )&"! #n "!s /&(&,$#s  su #$&c(ón c!n $&s cón(c&s L& c(cun.##nc(& D#.(n(c(ón c!! $u)& )#!'(c! Ecu&c(!n#s  '&s$&c(!n#s Sección # L& %&-,!$& D#.(n(c(ón c!! $u)& )#!'(c! Ecu&c(!n#s T&s$&c(!n#s E$##n'!s ,-s(c!s @!%(#"&"#s ó%'(c&s R#$&c(ón c!n $& #cu&c(ón )#n#&$ "#$ 2K )&"! @!,$#&s "# &%$(c&c(ón Sección $. L& #$(%s# D#.(n(c(ón c!! $u)& )#!'(c! Ecu&c(!n#s T&s$&c(!n#s E$##n'!s ,-s(c!s @!%(#"&"#s ó%'(c&s R#$&c(ón c!n $& #cu&c(ón "# 2 ! )&"! @!,$#&s "# &%$(c&c(ón Sección % L& (%,!$&. D#.(n(c(ón c!! $u)& )#!'(c! Ecu&c(!n#s T&s$&c(!n#s E$##n'!s ,-s(c!s @!%(#"&"#s ó%'(c&s R#$&c(ón c!n $& #cu&c(ón "# 2K )&"! @!,$#&s "# &%$(c&c(ón BIBLIOGRAFÍA TETO GUÍA: =ARAMILLO A$,#'! OLEAS G(&$"! G#!#'*& V#c'!(&$  An&$*'(c& Un& (n'!"ucc(ón &$ -$)#,& $(n#&$ Un(/#s("&" "# An'(!u(& U "# 2006

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