{"id":60,"date":"2014-07-16T08:40:35","date_gmt":"2014-07-16T06:40:35","guid":{"rendered":"http:\/\/www.prime.il.pw.edu.pl\/?page_id=60"},"modified":"2015-12-28T18:09:56","modified_gmt":"2015-12-28T17:09:56","slug":"aproksymacja","status":"publish","type":"page","link":"https:\/\/www.prime.il.pw.edu.pl\/?page_id=60","title":{"rendered":"Rozwi\u0105zywanie problem\u00f3w"},"content":{"rendered":"<p>Program <strong>Prime <\/strong>dostarcza licznych narz\u0119dzi s\u0142u\u017c\u0105cych do rozwi\u0105zywania szerokiej gamy problem\u00f3w matematycznych. Mo\u017cna z jego wykorzystaniem rozwi\u0105zywa\u0107 uk\u0142ady r\u00f3wna\u0144, zar\u00f3wno numerycznie jak te\u017c i symbolicznie, oraz w przypadku parametryzacji bada\u0107 wp\u0142yw parametr\u00f3w na rozwi\u0105zanie. Dost\u0119pne s\u0105 tak\u017ce narz\u0119dzia do rozwi\u0105zywania problem\u00f3w nieliniowych oraz r\u00f3wna\u0144 r\u00f3\u017cniczkowych. Mo\u017cna tak\u017ce rozwi\u0105zywa\u0107 zadania optymalizacyjne \u2013 maksymalizowa\u0107 i minimalizowa\u0107 funkcje. Omawianie rozwi\u0105zywania r\u00f3\u017cnorodnych problem\u00f3w rozpoczniemy od aproksymacji.<br \/>\nMiejsca zerowe dowolnej funkcji pozwala wyznaczy\u0107 funkcja <strong>root <\/strong>(liczba pojedyncza wskazuje na to, \u017ce ka\u017cde wywo\u0142anie tej funkcji wyznacza jeden pierwiastek). Wszystkie miejsca zerowe wielomianu pozwala nam wyznaczy\u0107 funkcja <strong>polyroots<\/strong>.<br \/>\nPotrafimy ju\u017c rozwi\u0105za\u0107 numerycznie uk\u0142ad r\u00f3wna\u0144 liniowych z wykorzystaniem odwracania macierzy. W tym miejscu nauczymy si\u0119 rozwi\u0105zywa\u0107 uk\u0142ady r\u00f3wna\u0144 liniowych tak\u017ce symbolicznie i to z wykorzystaniem wyspecjalizowanej funkcji <strong>lsolve<\/strong>.<br \/>\nNa koniec poznamy Solve Block &#8211; najbardziej z\u0142o\u017cone narz\u0119dzie do rozwi\u0105zywania r\u00f3\u017cnych problem\u00f3w. Dost\u0119pne s\u0105 w nim takie funkcje jak: <strong>find<\/strong>, <strong>maximize<\/strong>, <strong>minimize<\/strong>, <strong>odesolve<\/strong>.<br \/>\nOstatnia funkcja z <strong>Solve Block<\/strong> to <strong>odesolve<\/strong>. S\u0142u\u017cy ona do rozwi\u0105zywania r\u00f3wna\u0144 r\u00f3\u017cniczkowych. <\/p>\n<p><a id=\"69df391e8eb2a\" rel=\"wp-video-lightbox\" href=\"https:\/\/www.youtube.com\/watch?v=imLw5a4s0-0&#038;rel=0&#038;width=1280&#038;height=720\" title=\"\">08-01 {4:42} Aproksymacja funkcj\u0105 liniow\u0105<\/a>    <script>\r\n    \/* <![CDATA[ *\/\r\n    jQuery(document).ready(function($){\r\n        $(function(){\r\n            var width = $(window).innerWidth();\r\n            var setwidth = parseFloat(1280);\r\n            var ratio = parseFloat(0.5625);\r\n            var height = parseFloat(720);\r\n            var link = 'https:\/\/www.youtube.com\/watch?v=imLw5a4s0-0&amp;rel=0&amp;width=1280&amp;height=720';\r\n            if(width < setwidth)\r\n            {\r\n                height = Math.floor(width * 0.5625);\r\n                \/\/console.log(\"device width \"+width+\", set width \"+1280+\", ratio \"+0.5625+\", new height \"+ height);\r\n                var new_url = wpvl_paramReplace('width', link, width);\r\n                var new_url = wpvl_paramReplace('height', new_url, height);\r\n                $(\"a#69df391e8eb2a\").attr('href', new_url);\r\n                \/\/console.log(new_url);\r\n            }\r\n        });\r\n    });\r\n    \/* ]]> *\/\r\n    <\/script><br \/>\n<a id=\"69df391e8ec16\" rel=\"wp-video-lightbox\" href=\"https:\/\/www.youtube.com\/watch?v=CyROFh7oTpY&#038;rel=0&#038;width=1280&#038;height=720\" title=\"\">08-02 {5:43} Wyznaczanie miejsc zerowych wielomian\u00f3w<\/a>    <script>\r\n    \/* <![CDATA[ *\/\r\n    jQuery(document).ready(function($){\r\n        $(function(){\r\n            var width = $(window).innerWidth();\r\n            var setwidth = parseFloat(1280);\r\n            var ratio = parseFloat(0.5625);\r\n            var height = parseFloat(720);\r\n            var link = 'https:\/\/www.youtube.com\/watch?v=CyROFh7oTpY&amp;rel=0&amp;width=1280&amp;height=720';\r\n            if(width < setwidth)\r\n            {\r\n                height = Math.floor(width * 0.5625);\r\n                \/\/console.log(\"device width \"+width+\", set width \"+1280+\", ratio \"+0.5625+\", new height \"+ height);\r\n                var new_url = wpvl_paramReplace('width', link, width);\r\n                var new_url = wpvl_paramReplace('height', new_url, height);\r\n                $(\"a#69df391e8ec16\").attr('href', new_url);\r\n                \/\/console.log(new_url);\r\n            }\r\n        });\r\n    });\r\n    \/* ]]> *\/\r\n    <\/script><br \/>\n<a id=\"69df391e8ec84\" rel=\"wp-video-lightbox\" href=\"https:\/\/www.youtube.com\/watch?v=vL6fkjdajIY&#038;rel=0&#038;width=1280&#038;height=720\" title=\"\">08-03 {5:36} Rozwi\u0105zywanie numeryczne i symboliczne uk\u0142ad\u00f3w r\u00f3wna\u0144<\/a>    <script>\r\n    \/* <![CDATA[ *\/\r\n    jQuery(document).ready(function($){\r\n        $(function(){\r\n            var width = $(window).innerWidth();\r\n            var setwidth = parseFloat(1280);\r\n            var ratio = parseFloat(0.5625);\r\n            var height = parseFloat(720);\r\n            var link = 'https:\/\/www.youtube.com\/watch?v=vL6fkjdajIY&amp;rel=0&amp;width=1280&amp;height=720';\r\n            if(width < setwidth)\r\n            {\r\n                height = Math.floor(width * 0.5625);\r\n                \/\/console.log(\"device width \"+width+\", set width \"+1280+\", ratio \"+0.5625+\", new height \"+ height);\r\n                var new_url = wpvl_paramReplace('width', link, width);\r\n                var new_url = wpvl_paramReplace('height', new_url, height);\r\n                $(\"a#69df391e8ec84\").attr('href', new_url);\r\n                \/\/console.log(new_url);\r\n            }\r\n        });\r\n    });\r\n    \/* ]]> *\/\r\n    <\/script><br \/>\n<a id=\"69df391e8ece2\" rel=\"wp-video-lightbox\" href=\"https:\/\/www.youtube.com\/watch?v=FhOOHwtG_AY&#038;rel=0&#038;width=1280&#038;height=720\" title=\"\">08-04 {15:02} Solve Block i jego funkcje<\/a>    <script>\r\n    \/* <![CDATA[ *\/\r\n    jQuery(document).ready(function($){\r\n        $(function(){\r\n            var width = $(window).innerWidth();\r\n            var setwidth = parseFloat(1280);\r\n            var ratio = parseFloat(0.5625);\r\n            var height = parseFloat(720);\r\n            var link = 'https:\/\/www.youtube.com\/watch?v=FhOOHwtG_AY&amp;rel=0&amp;width=1280&amp;height=720';\r\n            if(width < setwidth)\r\n            {\r\n                height = Math.floor(width * 0.5625);\r\n                \/\/console.log(\"device width \"+width+\", set width \"+1280+\", ratio \"+0.5625+\", new height \"+ height);\r\n                var new_url = wpvl_paramReplace('width', link, width);\r\n                var new_url = wpvl_paramReplace('height', new_url, height);\r\n                $(\"a#69df391e8ece2\").attr('href', new_url);\r\n                \/\/console.log(new_url);\r\n            }\r\n        });\r\n    });\r\n    \/* ]]> *\/\r\n    <\/script><br \/>\n<a id=\"69df391e8ed3b\" rel=\"wp-video-lightbox\" href=\"https:\/\/www.youtube.com\/watch?v=7eyn8r7AmdI&#038;rel=0&#038;width=1280&#038;height=720\" title=\"\">08-05 {9:33} Rozwi\u0105zywanie r\u00f3wna\u0144 r\u00f3\u017cniczkowych<\/a>    <script>\r\n    \/* <![CDATA[ *\/\r\n    jQuery(document).ready(function($){\r\n        $(function(){\r\n            var width = $(window).innerWidth();\r\n            var setwidth = parseFloat(1280);\r\n            var ratio = parseFloat(0.5625);\r\n            var height = parseFloat(720);\r\n            var link = 'https:\/\/www.youtube.com\/watch?v=7eyn8r7AmdI&amp;rel=0&amp;width=1280&amp;height=720';\r\n            if(width < setwidth)\r\n            {\r\n                height = Math.floor(width * 0.5625);\r\n                \/\/console.log(\"device width \"+width+\", set width \"+1280+\", ratio \"+0.5625+\", new height \"+ height);\r\n                var new_url = wpvl_paramReplace('width', link, width);\r\n                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Mo\u017cna z jego wykorzystaniem rozwi\u0105zywa\u0107 uk\u0142ady r\u00f3wna\u0144, zar\u00f3wno numerycznie jak te\u017c i symbolicznie, oraz w przypadku parametryzacji bada\u0107 wp\u0142yw parametr\u00f3w na rozwi\u0105zanie. Dost\u0119pne s\u0105 tak\u017ce narz\u0119dzia do rozwi\u0105zywania problem\u00f3w nieliniowych oraz r\u00f3wna\u0144 r\u00f3\u017cniczkowych. Mo\u017cna tak\u017ce rozwi\u0105zywa\u0107 zadania optymalizacyjne \u2013 maksymalizowa\u0107 i minimalizowa\u0107 funkcje. &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.prime.il.pw.edu.pl\/?page_id=60\" class=\"more-link\">Czytaj dalej<span class=\"screen-reader-text\"> \u201eRozwi\u0105zywanie problem\u00f3w\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":57,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"_links":{"self":[{"href":"https:\/\/www.prime.il.pw.edu.pl\/index.php?rest_route=\/wp\/v2\/pages\/60"}],"collection":[{"href":"https:\/\/www.prime.il.pw.edu.pl\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.prime.il.pw.edu.pl\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.prime.il.pw.edu.pl\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.prime.il.pw.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=60"}],"version-history":[{"count":8,"href":"https:\/\/www.prime.il.pw.edu.pl\/index.php?rest_route=\/wp\/v2\/pages\/60\/revisions"}],"predecessor-version":[{"id":600,"href":"https:\/\/www.prime.il.pw.edu.pl\/index.php?rest_route=\/wp\/v2\/pages\/60\/revisions\/600"}],"up":[{"embeddable":true,"href":"https:\/\/www.prime.il.pw.edu.pl\/index.php?rest_route=\/wp\/v2\/pages\/57"}],"wp:attachment":[{"href":"https:\/\/www.prime.il.pw.edu.pl\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=60"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}