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<p><span class="autocomment">　「　8.4　解析入門（３）級数、冪級数と項別微分・項別積分及び可微分関数のテイラー展開</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2018年4月20日 (金) 08:54時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">1 行:</td> <td colspan="2" class="diff-lineno">1 行:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=　「　8.<del class="diffchange diffchange-inline">4　解析入門（３）級数、冪級数と項別微分・項別積分及び可微分関数のテイラー展開 </del>=</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=　「　8.<ins class="diffchange diffchange-inline">4　解析入門（３）関数列の項別の積分・微分、 級数・冪級数及び可微分関数のテイラー展開 </ins>=</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　序 ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　序 ==</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">===　関数列・関数族の項別積分と項別微分&nbsp; ===</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">====　項別積分定理　　====</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">====　項別微分定理　　====</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　級数&nbsp; ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　級数&nbsp; ==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== 無限級数の収束性&nbsp; ===</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>=== 無限級数の収束性&nbsp; ===</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====　条件収束と絶対収束&nbsp; ====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====　条件収束と絶対収束&nbsp; ====</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">====　収束条件　====</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">==　幕級数（整級数）&nbsp; ==</ins></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">==&nbsp; &nbsp; ==</ins></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>&#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====　テイラー展開とテイラーの定理====</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>====　テイラー展開とテイラーの定理====</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>微分可能な関数 $f(x)$ の導関数 $f'(x) (あるいは\frac{df(x)}{dx})$ が微分可能ならば、&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>微分可能な関数 $f(x)$ の導関数 $f'(x) (あるいは\frac{df(x)}{dx})$ が微分可能ならば、&lt;br/&gt;</div></td></tr> <tr><td colspan="2" class="diff-lineno">24 行:</td> <td colspan="2" class="diff-lineno">27 行:</td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>そこでテイラーの定理について説明する。&lt;br/&gt;</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>そこでテイラーの定理について説明する。&lt;br/&gt;</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>======　テイラーの定理　 RT ======</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>======　テイラーの定理　 RT ======</div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== 無限級数　==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">===　級数と収束　　===</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">===　級数と収束　　===　正項級数の収束条件　====</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">===&nbsp; 無限級数の項別積分&nbsp; ===</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">== 整級数（幕級数）　==</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">===　整級数と収束　　===</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">====　項別微分定理　　====</ins></div></td></tr> <tr><td colspan="2">&nbsp;</td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">====　整級数の微分可能性　　====</ins></div></td></tr> <!-- diff generator: internal 2026-04-29 00:11:08 --> </table>

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<p><span class="autocomment">　8.4　解析入門（３）級数、冪級数と項別微分・項別積分及び可微分関数のテイラー展開</span></p> <table style="background-color: white; color:black;"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←前の版</td> <td colspan='2' style="background-color: white; color:black;">2018年4月18日 (水) 07:04時点における版</td> </tr> <tr><td colspan="2" class="diff-lineno">1 行:</td> <td colspan="2" class="diff-lineno">1 行:</td></tr> <tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div>=<del class="diffchange diffchange-inline">　8</del>.4　解析入門（３）級数、冪級数と項別微分・項別積分及び可微分関数のテイラー展開 =</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>=<ins class="diffchange diffchange-inline">　「　8</ins>.4　解析入門（３）級数、冪級数と項別微分・項別積分及び可微分関数のテイラー展開 =</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　序 ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　序 ==</div></td></tr> <tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　級数&nbsp; ==</div></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"><div>==　級数&nbsp; ==</div></td></tr> <!-- diff generator: internal 2026-04-29 00:11:08 --> </table>

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<p>ページの作成: =　8.4　解析入門（３）級数、冪級数と項別微分・項別積分及び可微分関数のテイラー展開 = ==　序 == ==　級数 == === 無限級数の収束…</p> <p><b>新規ページ</b></p><div>=　8.4　解析入門（３）級数、冪級数と項別微分・項別積分及び可微分関数のテイラー展開 =<br /> ==　序 ==<br /> ==　級数 ==<br /> === 無限級数の収束性 ===<br /> ====　条件収束と絶対収束 ====<br /> <br /> <br /> <br /> <br /> <br /> ====　テイラー展開とテイラーの定理====<br /> 微分可能な関数 $f(x)$ の導関数 $f'(x) (あるいは\frac{df(x)}{dx})$ が微分可能ならば、&lt;br/&gt;<br /> その導関数　$(f')'(x) (あるいは\frac{d^{2}f(x)}{dx^2})$ が考えられる。&lt;br/&gt;<br /> これをｆの2階の導関数という。&lt;br/&gt;<br /> 例えば、変数ｔの関数 $f(t)$ が時刻ｔの質点の位置とすると、&lt;br/&gt;<br /> その導関数は速度、2階導関数は加速度を表すことを第2章の力学で学んだ。&lt;br/&gt;<br /> さらに高階の微分が可能な関数を考え、その性質を考察しよう。&lt;br/&gt;<br /> =====　テイラー展開とテイラーの定理=====<br /> テイラー展開、テイラー級数についての入門書は<br /> *[[wikibooks_ja:解析学基礎/テイラー級数|解析学基礎/テイラー級数（ウィキブックス）]]<br /> より高度なテイラーの定理などは以下の記事を。但し証明はない。<br /> *[[wikipedia_ja:テイラー展開 |ウィキペディア(テイラー展開)]]<br /> *[[wikipedia_ja:テイラーの定理 |ウィキペディア(テイラーの定理)]]<br /> そこでテイラーの定理について説明する。&lt;br/&gt;<br /> ======　テイラーの定理　 RT ======</div>

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