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</style> <![endif]--><!--[if gte mso 9]><xml> <o:shapedefaults v:ext="edit" spidmax="2054"/> </xml><![endif]--><!--[if gte mso 9]><xml> <o:shapelayout v:ext="edit"> <o:idmap v:ext="edit" data="2"/> </o:shapelayout></xml><![endif]--> <div align="center" class="MsoNormal" style="text-align: center;"><!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/> </v:shapetype><v:shape id="_x0031__x0020_Imagen" o:spid="_x0000_s2053" type="#_x0000_t75"
alt="leibnizgottfried.jpg" style='position:absolute;left:0;text-align:left;
margin-left:-25.2pt;margin-top:-54.4pt;width:245.25pt;height:546.75pt;
z-index:-3;visibility:visible;mso-wrap-style:square;mso-wrap-distance-left:9pt;
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o:title="leibnizgottfried" gain="45875f" blacklevel="13107f"/> </v:shape><![endif]--><!--[if !vml]--><span style="position: relative; z-index: -3;"><span style="height: 729px; left: -34px; position: absolute; top: -73px; width: 327px;"><img alt="leibnizgottfried.jpg" height="729" src="file:///C:/DOCUME%7E1/INVITA%7E1.USU/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image002.jpg" v:shapes="_x0031__x0020_Imagen" width="327" /></span></span><!--[endif]--><b><span lang="ES-MX" style="color: grey; font-family: "Comic Sans MS";">ANTECEDENTES HISTORICOS DEL CÁLCULO<o:p></o:p></span></b></div><div class="MsoNormal" style="text-align: justify;"><b><span style="color: blue; font-size: 12pt; line-height: 115%;">El Cálculo Infitesimal</span></b><span style="color: blue;"> <b>es la rama de las matemáticas que comprende el estudio y aplicaciones del Cálculo Diferencial e Integral.</b></span><b><span style="color: blue;"> </span></b><b><span style="color: blue;">El cálculo se interesa en el cambio y en el movimiento; trata de cantidades que se aproximan a otras cantidades.</span></b><b><span style="color: blue;"> <span lang="ES-MX">E</span></span></b><b><span style="color: blue;">l calculo diferencial Se origina en el<span> </span>siglo XVII al realizar estudios sobre el movimiento, es decir, al estudiar la velocidad delos cuerpos al caer al vacio ya que cambia de un momento a otro.<o:p></o:p></span></b></div><div class="MsoNormal" style="text-align: justify;"><b><i><span style="color: red; font-size: 22pt; line-height: 115%;">◊</span></i></b><b><i><span style="color: red;"> LOS CIENTÍFICOS MÁS SOBRESALIENTES DEL CÁLCULO DIFERENCIAL<o:p></o:p></span></i></b></div><div class="MsoNormal" style="text-align: justify;"><b><span lang="ES-MX" style="color: blue;">Isaac Newton (fue el primero en inventar el calculo), Pierre Fermat (determino los máximos y mínimos) Nicolás Oresme, Johannes Kepler</span></b><span lang="ES-MX" style="color: blue;">,<b> Isaac Barrow (invento el triángulo de Barrow), Joseph-Louis Lagrange, J. G. Leathem, Leonhard Euler (la simbología <i>f(x)</i> se debe a el)<br />
Simón Lhuilier, Agustín –Louis Cauchy<br />
Karl Weierstrass, Peter Gustav Dirichtel<br />
Jacobo Bernoulli (introduce la palabra función), Niels Henrik Abel (1802-1829) y Evariste Galois (1811-1832).<o:p></o:p></b></span></div><div align="center" class="MsoNormal" style="text-align: center;"><b><s><span lang="ES-MX" style="color: grey; font-family: Papyrus; font-variant: small-caps;">HISTORIA DEL CÁLCULO<o:p></o:p></span></s></b></div><div align="center" class="MsoNormal" style="text-align: center;"><b><span>Los primeros pasos fueron dados por los </span></b><!--[if gte vml 1]><v:shape id="Imagen_x0020_2"
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o:title=""/> </v:shape><![endif]--><!--[if !vml]--><span style="height: 144px; left: 0px; margin-left: 0px; margin-top: 0px; position: absolute; width: 113px; z-index: -1;"><img height="144" src="file:///C:/DOCUME%7E1/INVITA%7E1.USU/CONFIG%7E1/Temp/msohtmlclip1/01/clip_image004.jpg" v:shapes="Imagen_x0020_2" width="113" /></span><!--[endif]--><b><span>matemáticos griegos.</span></b><span><o:p></o:p></span></div><div class="MsoNormal" style="text-align: justify;"><b><span>Zenón de Elea: argumentó que el movimiento es imposible. Leucipo, Demócrito y Antifon hicieron contribuciones al método exhaustivo. Arquímedes usó el método exhaustivo para encontrar la aproximación al área de un círculo.<br />
Tres matemáticos que hicieron<span> </span>contribuciones importantes:</span></b><span><br />
<b>**Cavalieri:</b></span><b><span style="color: black; font-family: "Arial","sans-serif"; font-size: 20pt; line-height: 115%;"> </span></b><b><span>pensó en un área como formada por componentes que eran líneas y luego sumó su número infinito de 'indivisibles'.<br />
**Roverbal:</span></b><b><span style="color: black; font-family: "Arial","sans-serif"; font-size: 26pt; line-height: 115%;"> </span></b><b><span>afirmó que esto tendía a 1/(<i>m+1) cuando n tiende a infinito, calculando así el área.</i><br />
**Fermat: También fue más riguroso en su acercamiento pero no dio demostraciones. Generalizó la parábola y la hipérbola.<br />
<i>Tanto Torricelli como Barrow estudiaron el problema del movimiento con velocidad variable. La derivada de la distancia es la velocidad y la operación inversa nos lleva de la velocidad a la distancia. </i></span></b><span><o:p></o:p></span></div><div class="MsoNormal"><b><i><span style="color: red; font-size: 10pt; line-height: 115%;">Fuente: Historia del calculo.pdf- adobe<span> </span>Reader<o:p></o:p></span></i></b></div><div align="center" class="MsoNormal" style="text-align: center;"><!--[if gte vml 1]><v:shape
id="_x0030__x0020_Imagen" o:spid="_x0000_s2051" type="#_x0000_t75" alt="Isaac Newton 5.jpg"
style='position:absolute;left:0;text-align:left;margin-left:-.2pt;
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</div><div class="MsoNormal" style="text-align: justify;"><!--[if gte vml 1]><v:shape id="_x0032__x0020_Imagen"
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</div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-PHCYKDBaInC0P9LHjibw-K3eJsorULUeWuZB5ui9zvt0H5ZbElWVOhFqkdVg4MbdsjKpBtm1mAdMOJztqaSOYORCwQdDHpJQQEni6fJ1gMNk2cuFYjacx6hm_xfnO7lX2UeIqKSmIE0/s1600/CECYTE.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="198" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi-PHCYKDBaInC0P9LHjibw-K3eJsorULUeWuZB5ui9zvt0H5ZbElWVOhFqkdVg4MbdsjKpBtm1mAdMOJztqaSOYORCwQdDHpJQQEni6fJ1gMNk2cuFYjacx6hm_xfnO7lX2UeIqKSmIE0/s200/CECYTE.JPG" width="200" /></a></div><div align="center" class="MsoNormal" style="text-align: center;"><b><span lang="ES-MX" style="font-size: 14pt; line-height: 115%;">Colegio de Estudios Científicos Y Tecnológicos del Estado de Oaxaca<br />
</span></b><b><span lang="ES-MX"><span> </span><br />
<span> </span><span> </span></span></b><b><span lang="ES-MX" style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">EMSaD 05 “TEPETLAPA”</span></b><b><span lang="ES-MX"><o:p></o:p></span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div class="MsoNormal" style="text-align: justify;"><b><span lang="ES-MX">MATERIA: CÁLCULO DIFERENCIAL<o:p></o:p></span></b></div><div class="MsoNormal" style="text-align: justify;"><b><span lang="ES-MX">DOCENTE: ING. JOSE LUIS VERA ORTEGA<o:p></o:p></span></b></div><div class="MsoNormal" style="text-align: justify;"><b><span lang="ES-MX">TEMAS:<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="text-align: justify; text-indent: -18pt;"><!--[if !supportLists]--><span lang="ES-MX" style="font-family: Wingdings; font-size: 9pt; line-height: 115%;"><span>Ø<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><!--[endif]--><b><span lang="ES-MX" style="font-family: Papyrus; font-size: 9pt; line-height: 115%;">ANTECEDENTES DEL CÁLCULO<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="text-align: justify; text-indent: -18pt;"><!--[if !supportLists]--><span lang="ES-MX" style="font-family: Wingdings; font-size: 9pt; line-height: 115%;"><span>Ø<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><!--[endif]--><b><span lang="ES-MX" style="font-family: Papyrus; font-size: 9pt; line-height: 115%;">HISTORIA DEL CALCULO<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;"><!--[if !supportLists]--><span lang="ES-MX" style="font-family: Wingdings; font-size: 9pt; line-height: 115%;"><span>Ø<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><!--[endif]--><b><span lang="ES-MX" style="font-family: Papyrus; font-size: 9pt; line-height: 115%;">UN POCO DE HISTORIA Y EL NACIMIENTO DEL CACLULO<o:p></o:p></span></b></div><div class="MsoNormal" style="text-align: justify;"><b><span lang="ES-MX">EQUIPO: </span></b><b><span lang="ES-MX" style="font-size: 16pt; line-height: 115%;">#</span></b><b><span lang="ES-MX"> 7<o:p></o:p></span></b></div><div class="MsoNormal" style="text-align: justify;"><b><span lang="ES-MX">INTEGRANTES DEL EQUIPO:<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpFirst" style="text-align: justify; text-indent: -18pt;"><!--[if !supportLists]--><span lang="ES-MX" style="font-family: Wingdings;"><span>ü<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><!--[endif]--><b><span lang="ES-MX">WILFRIDO LOPEZ HERNANDEZ<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpMiddle" style="text-align: justify; text-indent: -18pt;"><!--[if !supportLists]--><span lang="ES-MX" style="font-family: Wingdings;"><span>ü<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><!--[endif]--><b><span lang="ES-MX">ODALIA<span> </span>CARRO GARCIA<o:p></o:p></span></b></div><div class="MsoListParagraphCxSpLast" style="text-align: justify; text-indent: -18pt;"><!--[if !supportLists]--><span lang="ES-MX" style="font-family: Wingdings;"><span>ü<span style="font-family: "Times New Roman"; font-size-adjust: none; font-size: 7pt; font-stretch: normal; font-style: normal; font-variant: normal; font-weight: normal; line-height: normal;"> </span></span></span><!--[endif]--><b><span lang="ES-MX">LAURA A. GUZMAN PERALES<o:p></o:p></span></b></div><div class="MsoNormal" style="text-align: justify;"><br />
</div><div align="center" class="MsoNormal" style="text-align: center;"><b><i><span lang="ES-MX" style="font-family: "Bradley Hand ITC";">SAN ANTONIO TEPETLAPA<o:p></o:p></span></i></b></div>wilfredohttp://www.blogger.com/profile/04259722142555543163noreply@blogger.com0tag:blogger.com,1999:blog-1341240192813526.post-34394908700889066362011-08-31T17:57:00.000-07:002011-08-31T18:02:28.251-07:00MaPa CONCEPTUAL<link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_editdata.mso" rel="Edit-Time-Data"></link><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link><style>
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<span style="font-size: large;"><b>/ESTA INTEGRADO POR/</b></span><br />
<span style="font-size: large;"><b>/</b></span><br />
<span style="font-size: large;"><b>/</b></span><br />
<span style="font-size: large;"><b>/</b></span></div><span lang="EN-US" style="font-size: large;"><o:p> </o:p></span><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link><style>
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<span style="font-size: large;"><b><span style="color: #943634;">EL CÁLCULO INFINITESIMAL:</span></b><span> <b>es la rama de las matemáticas que comprende el estudio y aplicaciones del Cálculo Diferencial. <span>Cálculo Diferencial:</span></b></span><b><span style="color: black; font-family: Papyrus; line-height: 115%;"> </span></b><b><span>Se origina en le siglo XVII al realizar estudios sobre el movimiento, es decir, al estudiar la velocidad delos cuerpos al caer al vacio ya que cambia de un momento a otro.</span></b><span lang="EN-US"><o:p></o:p></span></span> </div><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: large;"><b><span lang="ES-MX"><o:p></o:p></span></b></span></div><div style="text-align: center;"><span style="font-size: large;"><b>/</b></span></div><div style="text-align: center;"><span style="font-size: large;"><b>/</b></span></div><div style="text-align: center;"><span style="font-size: large;"><b>/,</b></span></div><div class="MsoNormal"><span style="font-size: large;"><b><span lang="EN-US"><o:p> </o:p></span></b></span><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link><style>
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</style> </div><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: large;"><i style="color: blue;"><b><span lang="ES-MX">HISTORIA DEL CÁLCULO: </span></b></i></span><br />
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<div class="MsoNormal"><span style="font-size: large;"><b><i><span>Los primeros pasos fueron dados por los matemáticos griegos. </span></i></b><span lang="EN-US"><br />
</span><b><span style="color: red;">Zenón de Elea</span></b><b><span>, alrededor de 450 a. C., planteó una serie de problemas que estaban basados en el infinito. Por ejemplo, argumentó que </span></b><i><span>el movimiento es imposible.</span></i><span lang="EN-US"><br />
</span><b><span style="color: red;">Leucipo, Demócrito y Antifon</span></b><b><span> hicieron contribuciones al método exhaustivo *Arquímedes: usó el método exhaustivo para encontrar la aproximación al área de un círculo. <span style="color: red;">Cavalieri</span>: pensó en un área como formada por componentes que eran líneas y luego sumó su número infinito de 'indivisibles'. Demostró, usando estos métodos, que la integral de <span>xn entre 0 y a era an+1/(n+1) mostrando el resultado para ciertos valores de n e infiriendo el resultado general.</span></span></b><span style="color: black; font-family: "Arial","sans-serif"; line-height: 115%;"> </span><b><span lang="EN-US" style="color: red;">roverbal: </span><span lang="EN-US">afirmó que esto tendía a 1/(m+1) cuando n tiende a infinito, calculando así el área.</span></b><span lang="EN-US" style="color: black; font-family: "Perpetua","serif"; line-height: 115%;"> </span><b><span lang="EN-US" style="color: red;">Fermat</span><span lang="EN-US">: También fue más riguroso en su acercamiento pero no dio demostraciones. Generalizó la parábola y la hipérbola.</span></b><span lang="EN-US" style="color: black; font-family: "Arial","sans-serif"; line-height: 115%;"> </span><b><span lang="ES-MX">El término 'cálculo integral' fue sugerido por Jacobo Bernoulli en 1690.</span></b></span></div><div class="MsoNormal"><span style="font-size: large;"><b><span lang="ES-MX"><i>/</i></span></b></span></div><div class="MsoNormal"><span style="font-size: large;"><b><span lang="ES-MX"><i>/Y/</i></span></b></span></div><div class="MsoNormal"><span style="font-size: large;"><b><span lang="ES-MX"><i>/</i></span></b></span></div><div class="MsoNormal"><br />
</div></div><div align="center" class="MsoNormal" style="text-align: center;"><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_filelist.xml" rel="File-List"></link><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_themedata.thmx" rel="themeData"></link><link href="file:///C:%5CDOCUME%7E1%5CINVITA%7E1.USU%5CCONFIG%7E1%5CTemp%5Cmsohtmlclip1%5C01%5Cclip_colorschememapping.xml" rel="colorSchemeMapping"></link><style>
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</style> </div><div align="center" class="MsoNormal" style="text-align: center;"><span style="font-size: large;"><i style="color: blue;"><b><span lang="ES-MX">UN POCO DE HISTORIA Y EL NACIMIENTO DEL CÁLCULO: </span></b></i></span><br />
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<div class="MsoNormal"><span style="font-size: large;"><b><span>Newton y Leibniz son considerados los inventores del cálculo, o más bien dicho, coinventores, fueron ellos quienes dieron a los procedimientos infinitesimales de sus antecesores inmediatos, Barrow y Fermat, la unidad algorítmica y la precisión necesaria como método novedoso y de generalidad suficiente para su desarrollo posterior.</span><span lang="EN-US">Los discípulos de Newton y Leibniz se basaron en sus trabajos para resolver diversos problemas de física, astronomía e ingeniería.</span></b><b><span lang="EN-US" style="color: black; font-family: "Perpetua","serif"; line-height: 115%;"> </span><span lang="EN-US">Un problema importante fue definir el significado de la palabra función. Euler, Lagrange y el matemático francés Fourier aportaron soluciones, pero fue el matemático alemán Dirichlet quien propuso su definición en los términos actuales. El conocimiento matemático del mundo moderno está avanzando más rápido que nunca. </span></b><b><span><o:p></o:p></span></b></span></div></div><span style="font-size: large;"><br />
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wilfredohttp://www.blogger.com/profile/04259722142555543163noreply@blogger.com0tag:blogger.com,1999:blog-1341240192813526.post-70152534314830403142011-08-31T17:35:00.000-07:002011-08-31T17:35:08.546-07:00UN POCO DE HISTORI@ Y EL N@CIMIENTO DEL C@LCULO☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻☻<br />
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<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBhS8yBKzndxJ_6EAD72vhqhWOgpg2-auMKf_P87_RCpjsQbVntBGLVLCEd7hPEI6SDv04RoYaiWXw9OWHLcUcM0GUFwJsB5HZsf6iaJkuz1E8neblkuPx8d3lNWIhj8YPdXvmPOWzcis/s1600/leibnizgottfried.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgBhS8yBKzndxJ_6EAD72vhqhWOgpg2-auMKf_P87_RCpjsQbVntBGLVLCEd7hPEI6SDv04RoYaiWXw9OWHLcUcM0GUFwJsB5HZsf6iaJkuz1E8neblkuPx8d3lNWIhj8YPdXvmPOWzcis/s1600/leibnizgottfried.jpg" /></a></div><span style="color: black; font-family: Perpetua; font-size: 26pt;"> </span><br />
<div style="color: red;"><span style="font-family: Perpetua; font-size: 26pt;">Detrás </span><span style="font-family: Perpetua; font-size: 26pt;">de cualquier invento, descubrimiento o nueva teoría, existe, indudablemente, la evolución de ideas que hacen posible su nacimiento. </span><span style="font-size: 26pt;"><span style="font-family: "Wingdings 2"; font-size: 85%;"></span></span><span style="font-family: Perpetua; font-size: 26pt;">Newton </span><span style="font-family: Perpetua; font-size: 26pt;">y Leibniz son considerados los inventores del cálculo, o más bien dicho, </span><span style="font-family: Perpetua; font-size: 26pt;">coinventores, fueron </span><span style="font-family: Perpetua; font-size: 26pt;">ellos quienes dieron a los procedimientos infinitesimales de sus antecesores inmediatos, Barrow y Fermat, la unidad algorítmica y la precisión necesaria como método novedoso y de generalidad suficiente para su desarrollo posterior. </span></div><br />
<div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: center; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Perpetua; font-size: 26pt; font-style: italic; font-weight: bold;"><span style="background-color: #6fa8dc;">EL SIGLO XVII Y LA DISPUTA POR LA CREACIÓN DEL CÁLCULO</span> </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Perpetua; font-size: 26pt;"><span> <span style="color: blue;"> </span></span><span style="color: blue;">En </span></span><span style="color: blue; font-family: Perpetua; font-size: 26pt;">sus comienzos el cálculo fue desarrollado para estudiar cuatro<span> </span>problemas científicos y matemáticos: </span></div><div style="color: blue; direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 26pt;"><span style="font-family: "Wingdings 2"; font-size: 85%;"></span></span><span style="font-family: Perpetua; font-size: 26pt;">Encontrar </span><span style="font-family: Perpetua; font-size: 26pt;">la tangente a una curva en un punto. </span></div><div style="color: blue; direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 26pt;"><span style="font-family: "Wingdings 2"; font-size: 85%;"></span></span><span style="font-family: Perpetua; font-size: 26pt;">Encontrar </span><span style="font-family: Perpetua; font-size: 26pt;">el valor máximo o mínimo de una cantidad. </span></div><div style="color: blue; direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 26pt;"><span style="font-family: "Wingdings 2"; font-size: 85%;"></span></span><span style="font-family: Perpetua; font-size: 26pt;">Encontrar </span><span style="font-family: Perpetua; font-size: 26pt;">la longitud de una curva, el área de una región y el volumen de un sólido. </span></div><div class="separator" style="clear: both; color: blue; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCHkrvYJxAs5-6yVIOTiVlnn4En9Y8Nv-xbi_5HEfH7zXUKJ2RAGnj7wvgLCGUesooDD8eB3EbBXO6Eq3UVQ3ljskynWx98UU40tXp09386hmwobPgYvfl4CkvxIyJTz2fHljEpRyQ22o/s1600/Isaac+Newton+5.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCHkrvYJxAs5-6yVIOTiVlnn4En9Y8Nv-xbi_5HEfH7zXUKJ2RAGnj7wvgLCGUesooDD8eB3EbBXO6Eq3UVQ3ljskynWx98UU40tXp09386hmwobPgYvfl4CkvxIyJTz2fHljEpRyQ22o/s200/Isaac+Newton+5.jpg" width="193" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: blue; font-family: Perpetua; font-size: 26pt;">En parte estos problemas fueron analizados por las mentes más brillantes de este siglo, concluyendo en la obra cumbre del filósofo-matemático alemán Gottfried Wilhelm Leibniz y el físico-matemático inglés Isaac Newton: la creación del cálculo. </span><span style="color: black; font-family: Perpetua; font-size: 26pt;"></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"> <div style="background-color: #ffd966; color: red; direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: center; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-family: Perpetua; font-size: 35pt; font-weight: bold;">EL SIGLO XVIII </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Perpetua; font-size: 26pt;"><span> <span style="color: yellow;"> </span><span style="background-color: #b45f06; color: yellow;"> </span></span><span style="background-color: #b45f06; color: yellow;">Los discípulos de Newton y Leibniz se basaron en sus trabajos para resolver diversos problemas de física, astronomía e ingeniería, lo que les permitió, al mismo tiempo, crear campos nuevos dentro de las matemáticas. Los hermanos Bernoulli inventaron el cálculo de variaciones y el matemático francés Monge la geometría descriptiva. Lagrange, también francés, dio un tratamiento completamente analítico de la mecánica, realizó contribuciones al estudio de las ecuaciones diferenciales y la teoría de números, y desarrolló la teoría de grupos. Laplace escribió </span></span><span style="background-color: #b45f06; color: yellow; font-family: Perpetua; font-size: 26pt; font-style: italic;">Teoría analítica de las probabilidades (1812) y el clásico Mecánica celeste (1799-1825), que le valió el sobrenombre de "el Newton francés". </span></div><div style="background-color: #b45f06; direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: yellow; font-family: Perpetua; font-size: 26pt;"><span> </span>El gran matemático del siglo fue el suizo Euler, quien aportó ideas fundamentales sobre el cálculo y otras ramas de las matemáticas y sus aplicaciones</span><span style="color: black; font-family: Perpetua; font-size: 26pt;"><span style="color: yellow;">.</span> </span></div></div><span style="background-color: orange;"> </span><span style="color: black; font-family: Perpetua; font-size: 26pt;"></span> <div style="background-color: #b4a7d6; direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: center; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Perpetua; font-size: 33pt; font-style: italic; font-weight: bold;">EL SIGLO XIX </span></div><span style="color: black; font-family: Perpetua; font-size: 26pt;">Un </span><span style="color: black; font-family: Perpetua; font-size: 26pt;">problema importante fue definir el significado de la palabra función. Euler, Lagrange y el matemático francés Fourier aportaron soluciones, pero fue el matemático alemán </span><span style="color: black; font-family: Perpetua; font-size: 26pt;">Dirichlet</span><span style="color: black; font-family: Perpetua; font-size: 26pt;"> quien propuso su definición en los términos actuales. </span><br />
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<div style="color: blue; direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: center; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-family: Perpetua; font-size: 26pt; font-style: italic; font-weight: bold;"><span style="background-color: #ea9999;">SIGLO XX Y NUESTROS DÍAS</span> </span></div><span style="color: black; font-family: Perpetua; font-size: 26pt;"><span> </span><span style="color: red;">Es </span></span><span style="color: red; font-family: Perpetua; font-size: 26pt;">importante el aporte realizado por Lebesgue referido a la integración y a la teoría de la medida y las modificaciones y generalizaciones realizadas por matemáticos que lo sucedieron. </span><br />
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<b style="background-color: yellow; color: #20124d;"><span style="font-family: Perpetua; font-size: 26pt;">○○○○○○○○○○○○○○○○○○○○○○ =></span></b><span style="color: black; font-family: Perpetua; font-size: 26pt;"> </span> wilfredohttp://www.blogger.com/profile/04259722142555543163noreply@blogger.com0tag:blogger.com,1999:blog-1341240192813526.post-28656740165102380552011-08-31T17:22:00.000-07:002011-08-31T17:22:45.792-07:00HISTORI@ DEL C@LCULO<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjloVueoiaCieayDWH_bsXVUmPSgP9zWQD04O4VnvtR_xEwGz1WdGMEAxVKfu37vJiKs2pDOk_Y1oV-y7nKLg71y1D5rTqYkyEWqIExsj8XAzGriom8mFe5GIhH6uAVVwxF1_AMpNJL7kE/s1600/ZenonElea2kk.JPG" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjloVueoiaCieayDWH_bsXVUmPSgP9zWQD04O4VnvtR_xEwGz1WdGMEAxVKfu37vJiKs2pDOk_Y1oV-y7nKLg71y1D5rTqYkyEWqIExsj8XAzGriom8mFe5GIhH6uAVVwxF1_AMpNJL7kE/s320/ZenonElea2kk.JPG" width="320" /></a></div><div style="color: lime;"><span style="font-size: large;"><span style="font-family: Arial; font-weight: bold;">▼▼▼▼▼▼▼▼▼▼▼▼▼▼▼▼▼ </span></span></div><div style="color: lime;"><br />
</div><span style="font-size: large;"><span style="color: black; font-family: Arial; font-weight: bold;">Zenón de Elea,</span><span style="color: black; font-family: Arial; font-weight: bold;">planteó una serie de problemas que estaban basados en el infinito. Por ejemplo, argumentó que </span><span style="color: #4f81bd; font-family: Arial; font-weight: bold;">el movimiento es imposible.</span></span> <br />
<div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><span><span style="color: #4f81bd; font-family: "Wingdings 2";"></span></span><span style="color: black; font-family: Arial; font-weight: bold;"></span><span style="color: black; font-family: Arial; font-weight: bold;">Leucipo</span><span style="color: black; font-family: Arial; font-weight: bold;">, Demócrito y </span><span style="color: black; font-family: Arial; font-weight: bold;">Antifon</span><span style="color: black; font-family: Arial; font-weight: bold;"> hicieron contribuciones al método exhaustivo .</span><span></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><span><span style="color: #4f81bd; font-family: "Wingdings 2";"></span></span><span style="color: black; font-family: Arial; font-weight: bold;">Arquímedes </span><span style="color: black; font-family: Arial; font-weight: bold;">usó el método exhaustivo para encontrar la aproximación al área de un círculo. Esto, por supuesto, es un ejemplo temprano de integración </span></span><span style="font-size: large;"><span style="color: black; font-family: Arial; font-weight: bold;">que llevó a valores aproximados de π.</span></span><span style="font-size: large;"><span style="color: black; font-family: Arial; font-weight: bold;"> </span></span> <div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><span style="color: black; font-family: Perpetua; font-weight: bold;">Tres matemáticos que hicieron<span> </span>contribuciones importantes:</span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><span style="color: black; font-family: Perpetua;"> </span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><!--[if ppt]--><span style="font-size: large;"><span><span style="color: #4f81bd; font-family: "Wingdings 2";"></span></span><span style="color: black; font-family: Perpetua;"></span></span><span style="font-size: large;"><b><span style="color: black; font-family: Arial;">Cavalieri</span><span style="color: black; font-family: Arial; font-weight: bold;">: </span></b></span></div><span style="font-size: large;"><b><span style="color: black; font-family: Arial;">Demostró, usando estos métodos, que la integral de </span><span style="color: black; font-family: Arial; font-style: italic;">xn</span><span style="color: black; font-family: Arial; font-style: italic;"> entre 0 y a era an+1/(n+1) mostrando el resultado para ciertos valores de n e infiriendo </span><span style="color: black; font-family: Arial; font-style: italic;">el resultado general</span><span style="color: black; font-family: Arial; font-style: italic;"> </span><span style="color: black; font-family: Arial;"> </span></b></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><b><span style="color: black; font-family: Arial;">ROVERBAL: afirmó que esto tendía a 1/(</span><span style="color: black; font-family: Arial; font-style: italic;">m+1) cuando n tiende a infinito, calculando así el área.</span></b></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><b><span style="color: black; font-family: Perpetua;"> FERMAT: También fue más riguroso en su acercamiento pero no dio demostraciones. Generalizó la parábola y la hipérbola.</span></b></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"> <div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><b><span><span style="color: #4f81bd; font-family: "Wingdings 2";">TRIANGULO DE BARROW. </span></span><span style="color: black; font-family: Arial;">El segundo dio un método de tangentes a una curva en el que la tangente está dada como el límite de una cuerda cuando los puntos se acercan uno a otro y que es conocido como </span><span style="color: black; font-family: Arial; font-style: italic;">el triángulo diferencial de Barrow. </span></b></span><span style="font-size: large;"><b><span></span></b></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><b><span><span style="color: #4f81bd; font-family: "Wingdings 2";"></span></span><span style="color: black; font-family: Arial; font-style: italic;">CALCULO INTEGRAL: el término 'cálculo integral' fue sugerido por Jacobo </span><span style="color: black; font-family: Arial; font-style: italic;">Bernoulli</span><span style="color: black; font-family: Arial; font-style: italic;"> en 1690. </span></b></span> </div><span style="color: #1f497d; font-family: "Franklin Gothic Book"; font-size: 36pt;">Los hechos de las disputas </span><span style="color: #1f497d; font-family: "Franklin Gothic Book"; font-size: 36pt; font-style: italic;">Newton-Leibniz</span><span style="color: black; font-family: Perpetua; font-size: 26pt;"> </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Perpetua; font-size: 26pt;"> </span><span style="font-size: 24pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">v</span></span><span style="color: black; font-family: Arial; font-size: 24pt; font-style: italic;">Newton describe en un manuscrito de 1669 su método de las fluxiones; este manuscrito circuló entre los miembros de un selecto grupo de matemáticos británicos, pero no se publicó. </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"> <div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: center; unicode-bidi: embed;"><span style="color: #bed3f9; font-family: Perpetua; font-size: 54pt; font-variant: normal; font-weight: bold; letter-spacing: 0pt; text-transform: none;">En la actualidad</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: center; unicode-bidi: embed;"> </div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 26pt;"><span style="color: #4f81bd; font-family: "Wingdings 2"; font-size: 85%;"></span></span><span style="color: black; font-family: Perpetua; font-size: 26pt; font-weight: bold;">En toda la comunidad científica otorga a ambos el honor de haber descubierto el cálculo. Sin embargo, en la actualidad se siguen las notaciones que usaba Leibniz para simbolizar </span><span style="color: black; font-family: Perpetua; font-size: 26pt; font-style: italic; font-weight: bold;">diferenciales e integrales. </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Perpetua; font-size: 26pt; font-style: italic; font-weight: bold;"><span style="color: #cc0000;">☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺☺</span>☺ </span></div> <span style="color: #bed3f9; font-family: Perpetua; font-size: 54pt; font-variant: normal; font-weight: bold; letter-spacing: 0pt; text-transform: none;"><br />
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<div style="direction: ltr; margin-bottom: 0pt; margin-left: 0in; margin-top: 0pt; text-align: center; unicode-bidi: embed;"><span style="color: #bed3f9; font-family: Perpetua; font-size: 54pt; font-variant: normal; font-weight: bold; letter-spacing: 0pt; text-transform: none;"> </span><span style="color: #bed3f9; font-family: Perpetua; font-size: 54pt; font-variant: normal; font-weight: bold; letter-spacing: 0pt; text-transform: none;"> </span></div><span style="color: black; font-family: Arial; font-size: 24pt; font-style: italic;"> </span> <span style="color: black; font-family: Arial; font-size: 26pt; font-style: italic;"> </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Arial; font-size: 26pt; font-style: italic;"> </span><span style="font-size: large;"><span style="color: black; font-family: Arial; font-style: italic;"></span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><span style="color: black; font-family: Arial; font-style: italic;"> </span></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: large;"><span style="color: black; font-family: Arial; font-size: 24pt; font-weight: bold;"> </span></span> </div>wilfredohttp://www.blogger.com/profile/04259722142555543163noreply@blogger.com0tag:blogger.com,1999:blog-1341240192813526.post-15849307209062534752011-08-31T17:06:00.000-07:002011-08-31T17:06:01.124-07:00ANTECEDENTES DELCALCULO <ol><li><span style="color: black; font-family: Papyrus; font-size: 26pt; font-weight: bold;">El Cálculo Infinitesimal</span><span style="color: black; font-family: Papyrus; font-size: 26pt;"></span><span style="color: black; font-family: Papyrus; font-size: 28pt;">: es la rama de las matemáticas que comprende el estudio y aplicaciones del Cálculo Diferencial e Integral.</span></li>
</ol><div> </div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: justify; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Papyrus; font-size: 28pt;">El cálculo se interesa en el cambio y en el movimiento; trata de cantidades que se aproximan a otras cantidades.</span></div><div style="text-align: justify;"> </div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: justify; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Papyrus; font-size: 28pt;">La escuela Rusa contemporánea concibe una gran división de esta ciencia de la siguiente manera:</span></div><div style="text-align: justify;"><span style="color: black; font-family: Papyrus; font-size: 28pt;"></span><span style="color: black; font-family: Papyrus; font-size: 26pt;">Los orígenes del calculo se remota unos 2500 años por lo menos, hasta los antiguos griegos, quienes hallaron </span><span style="color: black; font-family: Papyrus; font-size: 26pt;">areas</span><span style="color: black; font-family: Papyrus; font-size: 26pt;"> aplicando el “método de agotamiento”. Sabían como hallar el área A de cualquier polígono al dividirlo el triangulo(método de triangulación), y sumar las </span><span style="color: black; font-family: Papyrus; font-size: 26pt;">areas</span><span style="color: black; font-family: Papyrus; font-size: 26pt;"> de esto triángulos.</span></div><div style="text-align: justify;"> <div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 26pt;"><span style="color: #4f81bd; font-family: "Wingdings 2"; font-size: 85%;"></span></span><span style="color: black; font-family: Papyrus; font-size: 26pt;">EL CALCULO DIFERENCIAL: Se origina en le siglo XVII al realizar estudios sobre el movimiento, es decir, al estudiar la velocidad delos cuerpos al caer al vacio ya que cambia de un momentoa otro.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: center; text-indent: -0.3in; unicode-bidi: embed;"><span style="color: black; font-family: Papyrus; font-size: 26pt;"><span style="font-size: x-small;"><span style="background-color: lime; color: red;">CIENTIFICOS</span></span> </span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 22pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 22pt;">En 1666 </span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Isaac Newton (</span><span style="color: black; font-family: Papyrus; font-size: 22pt;">1642-1727), fue el primero en desarrollar métodos matemáticos para resolver problemas de esta índole.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 22pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 22pt;">El filosofo y matemático alemán </span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Gottfried</span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;"> </span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Wilhelm</span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;"> Leibniz </span><span style="color: black; font-family: Papyrus; font-size: 22pt;">(1646-1716), realizo investigaciones similares e ideando símbolos matemáticos que se aplican hasta nuestros días.</span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6lJogdFe0ONbus-L4Ke6FMr-f_hVqjfsCMtBEn-3Q-ng3uy9N-MyUKsQQFPBnen4px0gdE5j5t__CEf6HzwBvOg1INtLN6CqrAXj0kDG2y-LsH17QgVijNRo9QussI2YDuWS8m32MbKU/s1600/fermat.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi6lJogdFe0ONbus-L4Ke6FMr-f_hVqjfsCMtBEn-3Q-ng3uy9N-MyUKsQQFPBnen4px0gdE5j5t__CEf6HzwBvOg1INtLN6CqrAXj0kDG2y-LsH17QgVijNRo9QussI2YDuWS8m32MbKU/s200/fermat.jpg" width="149" /></a></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 22pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Pierre Fermat </span><span style="color: black; font-family: Papyrus; font-size: 22pt;">(1601-1665), matemático francés, quien en su obra habla de los métodos diseñados para determinar los máximos y mínimos, acercándose casi al descubrimiento del Cálculo Diferencial.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 22pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Nicolás </span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Oresme</span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">, </span><span style="color: black; font-family: Papyrus; font-size: 22pt;">obispo de la comunidad de </span><span style="color: black; font-family: Papyrus; font-size: 22pt;">Lisieux</span><span style="color: black; font-family: Papyrus; font-size: 22pt;">, Francia, estableció que: en la proximidad del punto de una curva en que la<span> </span>ordenada se considera máxima o mínima dicha ordenada varia mas pausadamente.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 22pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Johannes Kepler</span><span style="color: black; font-family: Papyrus; font-size: 22pt;">, tiempo después, coincide con lo establecido por </span><span style="color: black; font-family: Papyrus; font-size: 22pt;">Oresme</span><span style="color: black; font-family: Papyrus; font-size: 22pt;">, conceptos que permitieron a Fermat en su estudio de máximos y mínimos, las tangentes y las cuadraturas, igualar a cero la derivada de la función.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 22pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Isaac Barrow </span><span style="color: black; font-family: Papyrus; font-size: 22pt;">(Londres 1630-id., 4 de mayo, 1677), maestro de Newton , construyo el “triangulo característico”.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 22pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Joseph-Louis </span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;">Lagrange</span><span style="color: black; font-family: Papyrus; font-size: 22pt; font-weight: bold;"> </span><span style="color: black; font-family: Papyrus; font-size: 22pt;">(1736-1813), quien demostró por primera vez el Teorema del Valor Medio.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"> <div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 24pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Agustín –Louis </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Cauchy</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;"> </span><span style="color: black; font-family: Papyrus; font-size: 24pt;">(Paris, 21 de agosto de 1789-Sceaux, 23 de mayo de 1857), matemático francés, impulsor del Cálculo Diferencial e Integral.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 24pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Leonhard</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;"> </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Euler</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;"> </span><span style="color: black; font-family: Papyrus; font-size: 24pt;">(1707-1783). La simbología </span><span style="color: black; font-family: Symbol; font-size: 24pt;">¦</span><span style="color: black; font-family: Papyrus; font-size: 24pt;">(</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-style: italic;">x)<span> </span></span><span style="color: black; font-family: Papyrus; font-size: 24pt;">se debe a él.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 24pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Simón </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Lhuilier</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;"> </span><span style="color: black; font-family: Papyrus; font-size: 24pt;">se le debe la representación simbólica</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-style: italic;"> “</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-style: italic;">lim</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-style: italic;">”</span><span style="color: black; font-family: Papyrus; font-size: 24pt;">.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 24pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 24pt;"> </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">J. G. </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Leathem</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;"> </span><span style="color: black; font-family: Papyrus; font-size: 24pt;">propuso el símbolo </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-style: italic;"><span> </span>“tiende a”</span><span style="color: black; font-family: Papyrus; font-size: 24pt;">.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 24pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Karl </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Weierstrass</span><span style="color: black; font-family: Papyrus; font-size: 24pt;">, matemático alemán, se encargó de dar formalidad y<span> </span>estructura a la noción intuitiva de limite.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 24pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Peter Gustav </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Dirichtel</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;"> </span><span style="color: black; font-family: Papyrus; font-size: 24pt;">(1805-1859) fue quien dio la primera definición moderna de </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-style: italic;">función.</span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"><span style="font-size: 24pt;"><span style="color: #4f81bd; font-family: Wingdings; font-size: 85%;">§</span></span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Jacobo </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Bernoulli</span><span style="color: black; font-family: Papyrus; font-size: 24pt;"> introduce la palabra </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-style: italic;">“función” </span><span style="color: black; font-family: Papyrus; font-size: 24pt;">en el cálculo diferencial.</span></div><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Niels</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;"> </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Henrik</span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;"> Abel (</span><span style="color: black; font-family: Papyrus; font-size: 24pt;">1802-1829) y </span><span style="color: black; font-family: Papyrus; font-size: 24pt; font-weight: bold;">Evariste Galois </span><span style="color: black; font-family: Papyrus; font-size: 24pt;">(1811-1832). Aunque sus vidas fueron breves, sus trabajos en los campos del análisis y del algebra abstracta fueron de gran alcance.<span> </span></span><span style="color: black; font-family: Papyrus; font-size: 22pt;"><br />
</span></div> <span style="color: black; font-family: Papyrus; font-size: 26pt;"></span></div><div style="direction: ltr; margin-bottom: 0pt; margin-left: 0.3in; margin-top: 5.8pt; text-align: left; text-indent: -0.3in; unicode-bidi: embed;"> </div>wilfredohttp://www.blogger.com/profile/04259722142555543163noreply@blogger.com0tag:blogger.com,1999:blog-1341240192813526.post-87567931535021507322011-08-17T16:32:00.000-07:002011-08-17T16:32:27.869-07:00EN PERSONA<span style="font-size: large;">▼▼▼§§§▼▼</span><br />
<span style="font-size: large;"> ▼ ▼ ▼§§§▼</span><br />
<div class="separator" style="clear: both; text-align: right;"><span style="font-size: large;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVQSKXl9IdC-WeoHrSocyrtAbHN08QQMMxCeCCkTVTsTgPu4rofPK11_u3-_Nok_HZRpDNuySWnspp3WwLL6A1OfABkRoJgwYnHcNHeG4gyzLZmub2allMzPNcxVE3A_eCu_M0nvw_8ZQ/s1600/400_1247224631_carlos-alonso-gomez-gonzalez.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="150" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVQSKXl9IdC-WeoHrSocyrtAbHN08QQMMxCeCCkTVTsTgPu4rofPK11_u3-_Nok_HZRpDNuySWnspp3WwLL6A1OfABkRoJgwYnHcNHeG4gyzLZmub2allMzPNcxVE3A_eCu_M0nvw_8ZQ/s200/400_1247224631_carlos-alonso-gomez-gonzalez.jpg" width="200" /></a></span></div><span style="font-size: large;"> ▼♥▼ <span style="background-color: red;"> </span></span><span style="font-size: small;"><b style="background-color: red; color: blue;">WILFREDO LOPEZ HERNANDEZ</b></span><span style="font-size: large;"> </span><br />
<span style="font-size: large;"> ▼▼▼§§§▼</span><br />
<span style="font-size: large;"> ▼▼ <b style="background-color: white;">CALCULO DIFERENCIAL</b></span><br />
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</span></div><div style="color: purple;"><span style="font-size: large;">þþþþþþþþþþþ♥þþþþþþþþþþþ</span></div><span style="font-size: large;"><span style="color: purple;">■■■■■■■■■■■■■■■■■■■■</span></span>wilfredohttp://www.blogger.com/profile/04259722142555543163noreply@blogger.com0tag:blogger.com,1999:blog-1341240192813526.post-21614608160226171092011-08-17T16:18:00.000-07:002011-08-17T16:18:05.464-07:00soy chivas y que<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmLB-d59i0uB8jjOAn4YuRy3yOKye0btmAQ2dUj6O7ixhISpsBTFsEJGdCeq5UnKIbZNG6BxpmjEiTBt2hyphenhyphenSKpTfn_k21GmjcsLDcStUkYEWTAM4dioOo3dW55nv__FAiwu3JJRn4ahA8/s1600/648920chivas11starskk2.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgmLB-d59i0uB8jjOAn4YuRy3yOKye0btmAQ2dUj6O7ixhISpsBTFsEJGdCeq5UnKIbZNG6BxpmjEiTBt2hyphenhyphenSKpTfn_k21GmjcsLDcStUkYEWTAM4dioOo3dW55nv__FAiwu3JJRn4ahA8/s1600/648920chivas11starskk2.jpg" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrCMQHakzlaDnbeJaiP0WfB7UiNfnmEQG3qnKBV2hk_hNCo58ZhOEE5Z1ZpAS2Rgi9hh94gGzDaYmCT_K31KkwpvGbTVYmEkep7oLxPkF0hwpKP8Z2vvtG5s_8EI93nQ_wTIWac8qQMYA/s1600/a_KCMR_chivas_guadalajara_2316_20100302105954.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhrCMQHakzlaDnbeJaiP0WfB7UiNfnmEQG3qnKBV2hk_hNCo58ZhOEE5Z1ZpAS2Rgi9hh94gGzDaYmCT_K31KkwpvGbTVYmEkep7oLxPkF0hwpKP8Z2vvtG5s_8EI93nQ_wTIWac8qQMYA/s1600/a_KCMR_chivas_guadalajara_2316_20100302105954.jpg" /></a></div><br />
<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1vJvsTGc_nmUQtsYbeZWFnTQGkt0rQiEo5QU5fLIsJNISznG5jMN0NpujbiIz42BMxVGI8nvz18YawhKESo6feuwC_YLB6aPHYZK0fn9OLNfl4b1BBDszJAq7DAzN-zZeIZmzDprmHKg/s1600/400_F_20488305_ONu8YEybtKnLfL5Iiei1ZyMsXzd462sL-300x300.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh1vJvsTGc_nmUQtsYbeZWFnTQGkt0rQiEo5QU5fLIsJNISznG5jMN0NpujbiIz42BMxVGI8nvz18YawhKESo6feuwC_YLB6aPHYZK0fn9OLNfl4b1BBDszJAq7DAzN-zZeIZmzDprmHKg/s1600/400_F_20488305_ONu8YEybtKnLfL5Iiei1ZyMsXzd462sL-300x300.jpg" /><span style="color: #cc0000;"><i><span style="font-size: x-large;"><span style="font-family: Verdana,sans-serif;"> </span></span></i></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="color: #cc0000;"><i><span style="font-size: x-large;"><span style="font-family: Verdana,sans-serif;">ES EL MEJOR EQUIPO K HAY O ¿NO?</span></span></i></span></div><br />
wilfredohttp://www.blogger.com/profile/04259722142555543163noreply@blogger.com0tag:blogger.com,1999:blog-1341240192813526.post-42433602730586347502011-08-17T16:12:00.000-07:002011-08-17T16:12:33.042-07:00<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFCZfvmMV758e83_sNpJjq8Vk3GJQLr1ciitAjzS_OwzsTzQtqJenTe-y1Ze3EfiOY34Z0ECovLFOyhj2EaFrJB2ozRQk_T-SQgho-zeNiQlOOZOGrwMWUIkcdYnx2VzEGsBQOFJikhJw/s1600/superchivas.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhFCZfvmMV758e83_sNpJjq8Vk3GJQLr1ciitAjzS_OwzsTzQtqJenTe-y1Ze3EfiOY34Z0ECovLFOyhj2EaFrJB2ozRQk_T-SQgho-zeNiQlOOZOGrwMWUIkcdYnx2VzEGsBQOFJikhJw/s320/superchivas.jpg" width="256" /><span style="font-size: large;"><span style="color: #134f5c;"> </span></span></a></div><div class="separator" style="clear: both; text-align: center;"><span style="font-size: large;"><span style="color: #134f5c;">superrrrrr chivaaaaaaaaaaaaaaaass</span></span></div><br />
wilfredohttp://www.blogger.com/profile/04259722142555543163noreply@blogger.com0tag:blogger.com,1999:blog-1341240192813526.post-18445107690251392042011-08-17T16:03:00.000-07:002011-08-17T16:03:48.914-07:00<div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrEm8DsyYrUZxBFaaGPNahVV2JlsqVXhm9nc0y2lI3d9LlqEzWMiMTx5hvLNDPNwZBoR4ra6SIGYQTLUMDoeD7Hc_mK1vOeTspEPQE47PiLqnoKGxgLocnBLOpnjI1xTop02DBO3KX7Xs/s1600/Imagen+030.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjrEm8DsyYrUZxBFaaGPNahVV2JlsqVXhm9nc0y2lI3d9LlqEzWMiMTx5hvLNDPNwZBoR4ra6SIGYQTLUMDoeD7Hc_mK1vOeTspEPQE47PiLqnoKGxgLocnBLOpnjI1xTop02DBO3KX7Xs/s320/Imagen+030.jpg" width="320" /></a></div><span style="font-size: large;">makta de biologia en 3º semestre</span><br />
wilfredohttp://www.blogger.com/profile/04259722142555543163noreply@blogger.com0