{"id":851,"date":"2019-02-04T22:14:59","date_gmt":"2019-02-04T19:14:59","guid":{"rendered":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/?page_id=851"},"modified":"2019-03-27T19:29:37","modified_gmt":"2019-03-27T16:29:37","slug":"maths_in_posts_advanced","status":"publish","type":"page","link":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/maths_in_posts\/maths_in_posts_advanced\/","title":{"rendered":"\u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bc\u03b2\u03cc\u03bb\u03c9\u03bd \u03c3\u03b5 \u03ac\u03c1\u03b8\u03c1\u03b1 \u03ba\u03b1\u03b9 \u03c3\u03b5\u03bb\u03af\u03b4\u03b5\u03c2 (\u03c0\u03c1\u03bf\u03b7\u03b3\u03bc\u03ad\u03bd\u03b7)"},"content":{"rendered":"

\u0395\u03af\u03b4\u03b1\u03bc\u03b5 \u03c3\u03c4\u03b7\u03bd \u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd \u03ba\u03b1\u03b9 \u03c3\u03c5\u03bc\u03b2\u03cc\u03bb\u03c9\u03bd \u03c3\u03b5 \u03ac\u03c1\u03b8\u03c1\u03b1 \u03ba\u03b1\u03b9 \u03c3\u03b5\u03bb\u03af\u03b4\u03b5\u03c2<\/a> \u03c0\u03c9\u03c2 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03b5\u03b9\u03c3\u03ac\u03b3\u03bf\u03c5\u03bc\u03b5 \u03bc\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u03c3\u03cd\u03bc\u03b2\u03bf\u03bb\u03b1 \u03ba\u03b1\u03b9 \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03b9\u03c2 \u03c3\u03b5 \u03ad\u03bd\u03b1 \u03ac\u03c1\u03b8\u03c1\u03bf \u03ae \u03c3\u03b5 \u03bc\u03b9\u03b1 \u03c3\u03b5\u03bb\u03af\u03b4\u03b1.<\/p>\n

\u0395\u03b4\u03ce \u03b8\u03b1 \u03b4\u03bf\u03cd\u03bc\u03b5 \u03c0\u03c9\u03c2 \u03bc\u03c0\u03bf\u03c1\u03bf\u03cd\u03bc\u03b5 \u03bd\u03b1 \u03b5\u03b9\u03c3\u03ac\u03b3\u03bf\u03c5\u03bc\u03b5 \u03c0\u03b9\u03bf \u03c0\u03c1\u03bf\u03b7\u03b3\u03bc\u03ad\u03bd\u03b1 \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03b1. \u03a0\u03c1\u03bf\u03c3\u03ad\u03be\u03c4\u03b5 \u03c0\u03c9\u03c2 \u03c3\u03b5 \u03ba\u03ac\u03c0\u03bf\u03b9\u03b5\u03c2 \u03c0\u03b5\u03c1\u03b9\u03c0\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2 \u03b4\u03b5\u03bd \u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bc\u03b5 \u03c4\u03b1 \u03b4\u03b9\u03c0\u03bb\u03ac \u03b4\u03bf\u03bb\u03ac\u03c1\u03b9\u03b1 \u03ae \u03c4\u03b9\u03c2 \u03c4\u03b5\u03c4\u03c1\u03ac\u03b3\u03c9\u03bd\u03b5\u03c2 \u03b1\u03b3\u03ba\u03cd\u03bb\u03b5\u03c2. \u0397 \u03b5\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03be\u03b5\u03ba\u03b9\u03bd\u03ac\u03b5\u03b9 \u03bc\u03b5 \u03c4\u03b7\u03bd (\u03b1\u03bd\u03ac\u03c0\u03bf\u03b4\u03b7) \u03c0\u03bb\u03ac\u03b3\u03b9\u03b1 \u03b3\u03c1\u03b1\u03bc\u03bc\u03ae (\\). \u039a\u03b1\u03b9 \u03c6\u03c5\u03c3\u03b9\u03ba\u03ac \u03c3\u03c4\u03b7\u03bd \u03b1\u03c1\u03c7\u03ae \u03c4\u03bf\u03c5 \u03ac\u03c1\u03b8\u03c1\u03bf\u03c5 \u03ae \u03c4\u03b7\u03c2 \u03c3\u03b5\u03bb\u03af\u03b4\u03b1\u03c2 \u03bc\u03b1\u03c2 \u03c0\u03c1\u03ad\u03c0\u03b5\u03b9 \u03bd\u03b1 \u03c5\u03c0\u03ac\u03c1\u03c7\u03b5\u03b9 \u03b7 \u03bf\u03b4\u03b7\u03b3\u03af\u03b1 [latexpage]<\/code><\/p>\n

\u03a0\u03b1\u03c1\u03b1\u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n
\u03a3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03bf<\/strong><\/td>\n\u0393\u03c1\u03ac\u03c6\u03bf\u03c5\u03bc\u03b5<\/strong><\/td>\n\u0395\u03bc\u03c6\u03b1\u03bd\u03af\u03b6\u03b5\u03c4\u03b1\u03b9<\/strong><\/td>\n<\/tr>\n
\u03a3\u03c4\u03bf\u03af\u03c7\u03b9\u03c3\u03b7 (\u03c3\u03c4\u03bf\u03bd \u03c7\u03b1\u03c1\u03b1\u03ba\u03c4\u03ae\u03c1\u03b1 \u03c0\u03bf\u03c5 \u03b1\u03ba\u03bf\u03bb\u03bf\u03c5\u03b8\u03b5\u03af \u03c4\u03bf &<\/code>)<\/p>\n

\u039f \u03b1\u03c3\u03c4\u03b5\u03c1\u03af\u03c3\u03ba\u03bf\u03c2 (*<\/code>) \u03b4\u03b7\u03bb\u03ce\u03bd\u03b5\u03b9 \u03bd\u03b1 \u03bc\u03b7\u03bd \u03b1\u03c1\u03b9\u03b8\u03bc\u03b7\u03b8\u03b5\u03af \u03b7 \u03c3\u03c7\u03ad\u03c3\u03b7<\/td>\n

\begin{align*}
\nx &= y\\
\nxxxxxx &=y\\
\nx &=yyyyyyy
\n\end{align*}<\/code><\/td>\n		\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n<\/td>\n<\/tr>\n

\u0391\u03c1\u03af\u03b8\u03bc\u03b7\u03c3\u03b7 \u03c3\u03c7\u03ad\u03c3\u03b5\u03c9\u03bd<\/td>\n\begin{equation} \label{eq:poly}
\nP_{N-1}(x)=\sum_{j=0}^{N-1}{a_jx^j}
\n\end{equation}<\/code><\/td>\n		<\/a><\/p>\n

(1) <\/span>   <\/span>\"\begin{equation*} <\/p>\n<\/td>\n<\/tr>\n

\u0391\u03bd\u03b1\u03c6\u03bf\u03c1\u03ac \u03c3\u03b5 \u03c3\u03c7\u03ad\u03c3\u03b7<\/td>\n\u038c\u03c0\u03c9\u03c2 \u03c3\u03c4\u03b7 \u03c3\u03c7\u03ad\u03c3\u03b7 (\ref{eq:poly}<\/code>)<\/td>\n\u038c\u03c0\u03c9\u03c2 \u03c3\u03c4\u03b7 \u03c3\u03c7\u03ad\u03c3\u03b7 (1<\/a>)<\/td>\n<\/tr>\n
\u03a0\u03af\u03bd\u03b1\u03ba\u03b5\u03c2, \u03bf\u03c1\u03af\u03b6\u03bf\u03c5\u03c3\u03b5\u03c2 (\u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bc\u03b5 $$ $$<\/code>)<\/p>\n

\u0391\u03bd \u03b4\u03b5\u03bd \u03b8\u03ad\u03bb\u03bf\u03c5\u03bc\u03b5 \u03c3\u03c4\u03bf\u03af\u03c7\u03b9\u03c3\u03b7 \u03c0\u03b1\u03c1\u03b1\u03bb\u03b5\u03af\u03c0\u03bf\u03c5\u03bc\u03b5 \u03c4\u03b1 &<\/code><\/td>\n

$$\begin{matrix}a & bbb & ccccc \\ ddd & ee & f \end{matrix}$$<\/code><\/p>\n

$$\begin{smallmatrix} ...\end {smallmatrix}$$<\/code><\/p>\n

$$\begin{pmatrix} ...\end{pmatrix}$$<\/code><\/p>\n

$$\begin{bmatrix} ...\end{bmatrix}$$<\/code><\/p>\n

$$\begin{Βmatrix} ...\end{Βmatrix}$$<\/code><\/p>\n

$$\begin{vmatrix}a \ bbb \ ccccc \\ ddd \ ee \ f \end{vmatrix}$$<\/code><\/p>\n

$$\begin{Vmatrix} ...\end{Vmatrix}$$<\/code><\/p>\n

$$\begin{vmatrix}
\na_{1,1} & a_{1,2} & \cdots &a_{1,n}\\a_{2,1} & a_{2,2} & \cdots &a_{2,n}\\ \vdots & \vdots & \ddots & \vdots \\ a_{n,1} & a_{n,2} & \cdots &a_{n,n}\end{vmatrix}$$<\/code><\/td>\n

\n

  <\/span>   <\/span>\"\[\begin{matrix}a & bbb & ccccc \\ ddd & ee & f \end{matrix}\]\"<\/p>\n

  <\/span>   <\/span>\"\[\begin{smallmatrix}a & bbb & ccccc \\ ddd & ee & f \end{smallmatrix}\]\"<\/p>\n

  <\/span>   <\/span>\"\[\begin{pmatrix}a & bbb & ccccc \\ ddd & ee & f \end{pmatrix}\]\"<\/p>\n

  <\/span>   <\/span>\"\[\begin{bmatrix}a & bbb & ccccc \\ ddd & ee & f \end{bmatrix}\]\"<\/p>\n

  <\/span>   <\/span>\"\[\begin{Bmatrix}a & bbb & ccccc \\ ddd & ee & f \end{Bmatrix}\]\"<\/p>\n

  <\/span>   <\/span>\"\[\begin{vmatrix}a \ bbb \ ccccc \\ ddd \ ee \ f \end{vmatrix}\]\"<\/p>\n

  <\/span>   <\/span>\"\[\begin{Vmatrix}a \ bbb \ ccccc \\ ddd \ ee \ f \end{Vmatrix}\]\"<\/p>\n

  <\/span>   <\/span>\"\[\begin{vmatrix}<\/p>\n<\/td>\n<\/tr>\n

\u03a0\u03b5\u03c1\u03b9\u03c0\u03c4\u03ce\u03c3\u03b5\u03b9\u03c2 (\u03c7\u03c1\u03b7\u03c3\u03b9\u03bc\u03bf\u03c0\u03bf\u03b9\u03bf\u03cd\u03bc\u03b5 $$ $$<\/code>)<\/td>\n$$ multicase \begin{cases}
\ncase1 \\
\ncase2 \\
\n\end{cases}$$<\/code><\/td>\n		\n

  <\/span>   <\/span>\"\[\alpha \chi +\beta =0 \begin{cases}\alpha \ne 0 & \chi =-\frac {\beta } {\alpha }\\<\/p>\n<\/td>\n<\/tr>\n

\u03a3\u03c7\u03b5\u03b4\u03af\u03b1\u03c3\u03b7 \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ce\u03bd \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd 2 \u03b4\u03b9\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd (\u03b3\u03c9\u03bd\u03af\u03b5\u03c2 \u03c3\u03b5 \u03bc\u03bf\u03af\u03c1\u03b5\u03c2)<\/p>\n

\u03b7\u03bc(x)<\/td>\n

\begin{tikzpicture}
\n[+preamble]
\n\usepackage{pgfplots}
\n\pgfplotsset{compat=newest}
\n[/preamble]
\n\begin{axis}
\n\addplot[domain=0:360, samples=40] {sin(x)};
\n\end{axis}
\n\end{tikzpicture}<\/code><\/td>\n		\n

\"Rendered<\/p>\n<\/td>\n<\/tr>\n

\u03a3\u03c7\u03b5\u03b4\u03af\u03b1\u03c3\u03b7 \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ce\u03bd \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd 2 \u03b4\u03b9\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd (\u03b3\u03c9\u03bd\u03af\u03b5\u03c2 \u03c3\u03b5 \u03b1\u03ba\u03c4\u03af\u03bd\u03b9\u03b1)<\/p>\n

\u03c3\u03c5\u03bd(x)<\/td>\n

\begin{tikzpicture}
\n[+preamble]
\n\usepackage{pgfplots}
\n\pgfplotsset{compat=newest}
\n[/preamble]
\n\begin{axis}
\n\addplot[domain=0:2 * 3.141592654, samples=40] {cos(x)};
\n\end{axis}
\n\end{tikzpicture}<\/code><\/td>\n		\n

\"Rendered<\/p>\n<\/td>\n<\/tr>\n

\u03a3\u03c7\u03b5\u03b4\u03af\u03b1\u03c3\u03b7 \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ce\u03bd \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd 3 \u03b4\u03b9\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd (\u03b3\u03c9\u03bd\u03af\u03b5\u03c2 \u03c3\u03b5 \u03bc\u03bf\u03af\u03c1\u03b5\u03c2)<\/p>\n

\u03c3\u03c5\u03bd(x) \u03b7\u03bc(y)<\/td>\n

\begin{tikzpicture}
\n[+preamble]
\n\usepackage{pgfplots}
\n\pgfplotsset{compat=newest}
\n[/preamble]
\n\begin{axis}
\n\addplot3[surf, domain=0:360, samples=40] {cos(x)*sin(y)};
\n\end{axis}
\n\end{tikzpicture}<\/code><\/td>\n		\n

\"Rendered<\/p>\n<\/td>\n<\/tr>\n

\u03a3\u03c7\u03b5\u03b4\u03af\u03b1\u03c3\u03b7 \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ce\u03bd \u03c0\u03b1\u03c1\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd 3 \u03b4\u03b9\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd (\u03b3\u03c9\u03bd\u03af\u03b5\u03c2 \u03c3\u03b5 \u03b1\u03ba\u03c4\u03af\u03bd\u03b9\u03b1)<\/p>\n

\u03c3\u03c5\u03bd(x) \u03c3\u03c5\u03bd(y)<\/td>\n

\begin{tikzpicture}
\n[+preamble]
\n\usepackage{pgfplots}
\n\pgfplotsset{compat=newest}
\n[/preamble]
\n\begin{axis}
\n\addplot3[surf, domain=0:2 * 3.141592654, samples=40] {cos(deg(x))*cos(deg(y))};
\n\end{axis}
\n\end{tikzpicture}<\/code><\/td>\n		\n

\"Rendered<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u03a0\u03a1\u039f\u03a3\u039f\u03a7\u0397<\/u>: \u0397 \u03cd\u03c0\u03b1\u03c1\u03be\u03b7 \u03c0\u03bf\u03bb\u03bb\u03ce\u03bd \u03b3\u03c1\u03b1\u03c6\u03b9\u03ba\u03ce\u03bd, \u03b9\u03b4\u03af\u03c9\u03c2 \u03c4\u03c1\u03b9\u03ce\u03bd \u03b4\u03b9\u03b1\u03c3\u03c4\u03ac\u03c3\u03b5\u03c9\u03bd \"\u03b2\u03b1\u03c1\u03b1\u03af\u03bd\u03b5\u03b9\" \u03c0\u03bf\u03bb\u03cd \u03c4\u03b7\u03bd \u03b5\u03bc\u03c6\u03ac\u03bd\u03b9\u03c3\u03b7.<\/p>\n

 <\/p>\n

\u0397 \u03c3\u03b5\u03bb\u03af\u03b4\u03b1 \u03b8\u03b1 \u03b5\u03bc\u03c0\u03bb\u03bf\u03c5\u03c4\u03af\u03b6\u03b5\u03c4\u03b1\u03b9 \u03b4\u03b9\u03b1\u03c1\u03ba\u03ce\u03c2.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

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Continue reading<\/a><\/p>\n","protected":false},"author":4636,"featured_media":0,"parent":81,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-851","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/wp-json\/wp\/v2\/pages\/851","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/wp-json\/wp\/v2\/users\/4636"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/wp-json\/wp\/v2\/comments?post=851"}],"version-history":[{"count":0,"href":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/wp-json\/wp\/v2\/pages\/851\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/wp-json\/wp\/v2\/pages\/81"}],"wp:attachment":[{"href":"https:\/\/blogs.e-me.edu.gr\/nskoulid\/wp-json\/wp\/v2\/media?parent=851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}