{"id":2316,"date":"2022-02-25T17:41:05","date_gmt":"2022-02-25T08:41:05","guid":{"rendered":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/?page_id=2316"},"modified":"2024-07-11T09:37:28","modified_gmt":"2024-07-11T00:37:28","slug":"%e5%85%a8%e5%be%ae%e5%88%86","status":"publish","type":"page","link":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/%e7%90%86%e5%b7%a5%e7%b3%bb%e3%81%ae%e6%95%b0%e5%ad%a6c\/%e5%81%8f%e5%be%ae%e5%88%86%ef%bc%9a%e5%a4%9a%e5%a4%89%e6%95%b0%e9%96%a2%e6%95%b0%e3%81%ae%e5%be%ae%e5%88%86\/%e5%85%a8%e5%be%ae%e5%88%86\/","title":{"rendered":"\u5168\u5fae\u5206"},"content":{"rendered":"

$$ dz \\equiv f(x + dx, y + dy) – f(x, y) $$ \u3067\u5b9a\u7fa9\u3055\u308c\u308b \\( dz\\) \u3092\u95a2\u6570 \\(z\\) \u306e\u5168\u5fae\u5206\u3068\u3044\u3046\u3002
\n<\/p>\n

2\u5909\u6570\u95a2\u6570 \\( z = f(x, y) \\) \u306b\u304a\u3044\u3066\uff0c\\(x, y\\) \u304c\u305d\u308c\u305e\u308c<\/p>\n

$$x \\rightarrow x + dx, \\quad y \\rightarrow y + dy$$<\/p>\n

\u3068\u5909\u5316\u3059\u308b\u3068\u304d\uff0c\u5bfe\u5fdc\u3057\u3066 \\(z\\) \u3082\u5909\u5316\u3059\u308b\u3002\u3053\u3053\u3067
\n$$ dz \\equiv f(x + dx, y + dy) – f(x, y) $$ \u3067\u5b9a\u7fa9\u3055\u308c\u308b \\( dz\\) \u3092\u95a2\u6570 \\(z\\) \u306e\u5168\u5fae\u5206<\/b><\/u><\/span>\u3068\u3044\u3046\u3002<\/p>\n

\\begin{eqnarray} dz &=& f(x + dx, y + dy) – f(x, y) \\\\
\n&=& f(x + dx, y+dy) – f(x, y+dy) + f(x, y+dy) – f(x, y) \\\\
\n&=& \\frac{\\partial}{\\partial x} f(x, y+dy) dx + \\frac{\\partial}{\\partial y} f(x,y) dy \\end{eqnarray}<\/p>\n

\u6700\u5f8c\u306e\u7b2c1\u9805\u306f\uff0c<\/p>\n

$$\\frac{\\partial}{\\partial x} f(x, y+dy) dx \\simeq
\n\\frac{\\partial}{\\partial x} \\left( f(x, y) + \\frac{\\partial f}{\\partial y} dy\\right) dx$$ \u3068\u306a\u308a\uff0c\u7121\u9650\u5c0f\u5909\u5316\u306e2\u6b21\u306e\u9805\uff0c\u3064\u307e\u308a \\( dx\\,dy \\) \u306b\u6bd4\u4f8b\u3059\u308b\u9805\u306f\u7121\u8996\u3067\u304d\u308b\u3068\u3057\u3066\uff0c<\/p>\n

$$\\frac{\\partial}{\\partial x} f(x, y+dy) dx \\Rightarrow \\frac{\\partial}{\\partial x} f(x, y) dx$$<\/p>\n

\u3068\u306a\u308b\u3002\u6700\u7d42\u7684\u306b2\u5909\u6570\u95a2\u6570 \\(z = f(x, y) \\) \u306e\u5168\u5fae\u5206\u306f\uff0c<\/p>\n

$$dz = \\frac{\\partial f}{\\partial x} dx + \\frac{\\partial f}{\\partial y} dy$$<\/p>\n

\u3068\u306a\u308b\u3002\u3053\u306e\u3088\u3046\u306a\u8868\u8a18\u306f\u4ed6\u306e\u6388\u696d\uff0c\u305f\u3068\u3048\u3070\u71b1\u529b\u5b66\u3067\u3082\u898b\u304b\u3051\u307e\u3059\u3088\u306d\u3002\uff08\u4ee5\u524d\uff0c\u5b66\u79d1\u306e\u300c\u5730\u7403\u71b1\u529b\u5b66\u300d\u3068\u3044\u3046\u6388\u696d\u3082\u62c5\u5f53\u3057\u305f\u3053\u3068\u304c\u3042\u3063\u305f\u306e\u3067\u3002\uff09<\/p>\n","protected":false},"excerpt":{"rendered":"

$$ dz \\equiv f(x + dx, y + dy) – f(x, y) $$ \u3067\u5b9a\u7fa9\u3055\u308c\u308b \\( dz\\) \u3092\u95a2\u6570 \\(z\\) \u306e\u5168\u5fae\u5206\u3068\u3044\u3046\u3002<\/p>

\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":33,"featured_media":0,"parent":2226,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"inline_featured_image":false,"footnotes":""},"class_list":["post-2316","page","type-page","status-publish","hentry","nodate","item-wrap"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2316","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/users\/33"}],"replies":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/comments?post=2316"}],"version-history":[{"count":3,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2316\/revisions"}],"predecessor-version":[{"id":9204,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2316\/revisions\/9204"}],"up":[{"embeddable":true,"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/pages\/2226"}],"wp:attachment":[{"href":"https:\/\/home.hirosaki-u.ac.jp\/relativity\/wp-json\/wp\/v2\/media?parent=2316"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}