微積分與高考數(shù)學(xué)（第2版）

第１章　函數(shù)１ !!!!!!!!!!!!!!!!!!!!!!
１．１　函數(shù)的概念１ !!!!!!!!!!!!!!!!!!!!!!!
１．１．１　實(shí)數(shù)與數(shù)集２ !!!!!!!!!!!!!!!!!!!!
１．１．２　區(qū)間２ !!!!!!!!!!!!!!!!!!!!!!!
１．１．３　鄰域與去心鄰域２ !!!!!!!!!!!!!!!!!!
１．１．４　有界集３ !!!!!!!!!!!!!!!!!!!!!!
１．１．５　函數(shù)３ !!!!!!!!!!!!!!!!!!!!!!!
１．２　隱函數(shù)與反函數(shù)５ !!!!!!!!!!!!!!!!!!!!!
１．２．１　隱函數(shù)５ !!!!!!!!!!!!!!!!!!!!!!
１．２．２　反函數(shù)５ !!!!!!!!!!!!!!!!!!!!!!
１．２．３　反三角函數(shù)６ !!!!!!!!!!!!!!!!!!!!
習(xí)題１．２ ８ !!!!!!!!!!!!!!!!!!!!!!!!
１．３　參數(shù)方程與極坐標(biāo)９ !!!!!!!!!!!!!!!!!!!!
１．３．１　參數(shù)方程表示的函數(shù)９ !!!!!!!!!!!!!!!!
１．３．２　極坐標(biāo)９ !!!!!!!!!!!!!!!!!!!!!!
１．３．３　極坐標(biāo)與直角坐標(biāo)的關(guān)系１１ !!!!!!!!!!!!!
１．３．４　極坐標(biāo)中常見的曲線１２ !!!!!!!!!!!!!!!
習(xí)題１．３ １４ !!!!!!!!!!!!!!!!!!!!!!!!
１．４　初等函數(shù)１４ !!!!!!!!!!!!!!!!!!!!!!!!
１．４．１　基本初等函數(shù)１４ !!!!!!!!!!!!!!!!!!
１．４．２　復(fù)合函數(shù)與初等函數(shù)１７ !!!!!!!!!!!!!!!
習(xí)題１．４ １８
第２章　極限２０ !!!!!!!!!!!!!!!!!!!!!!
２．１　數(shù)列的極限２０ !!!!!!!!!!!!!!!!!!!!!!!
２．１．１　數(shù)列與極限的定義２１ !!!!!!!!!!!!!!!!
２．１．２　極限的運(yùn)算２３ !!!!!!!!!!!!!!!!!!!
習(xí)題２．１ ２５ !!!!!!!!!!!!!!!!!!!!!!!!
２．２　連續(xù)函數(shù)與函數(shù)的極限２６ !!!!!!!!!!!!!!!!!!
２．２．１　函數(shù)的極限與連續(xù)函數(shù)的定義２６ !!!!!!!!!!!
２．２．２　函數(shù)的單側(cè)極限２８ !!!!!!!!!!!!!!!!!
習(xí)題２．２ ２９ !!!!!!!!!!!!!!!!!!!!!!!!
２．３　極限的嚴(yán)格定義２９ !!!!!!!!!!!!!!!!!!!!!
２．３．１　數(shù)列極限的嚴(yán)格定義３０ !!!!!!!!!!!!!!!
２．３．２　一般函數(shù)極限的嚴(yán)格定義３１ !!!!!!!!!!!!!
２．３．３　極限的性質(zhì)３２ !!!!!!!!!!!!!!!!!!!
２．４　連續(xù)函數(shù)的性質(zhì)３４ !!!!!!!!!!!!!!!!!!!!!
２．４．１　連續(xù)的嚴(yán)格定義３４ !!!!!!!!!!!!!!!!!
２．４．２　閉區(qū)間內(nèi)連續(xù)函數(shù)的性質(zhì)３５ !!!!!!!!!!!!!
習(xí)題２．４ ３７ !!!!!!!!!!!!!!!!!!!!!!!!
２．５　自然常數(shù)ｅ ３８ !!!!!!!!!!!!!!!!!!!!!!!
２．５．１　銀行復(fù)利的問題３８ !!!!!!!!!!!!!!!!!
２．５．２　ｅ的應(yīng)用４０ !!!!!!!!!!!!!!!!!!!!
習(xí)題２．５ ４１ !!!!!!!!!!!!!!!!!!!!!!!!
２．６　漸近線４２ !!!!!!!!!!!!!!!!!!!!!!!!!
習(xí)題２．６ ４４ !!!!!!!!!!!!!!!!!!!!!!!!
第３章　一元微分學(xué)４６ !!!!!!!!!!!!!!!!!!!
３．１　導(dǎo)數(shù)的概念４６ !!!!!!!!!!!!!!!!!!!!!!!
３．１．１　導(dǎo)數(shù)的例子４６ !!!!!!!!!!!!!!!!!!!
３．１．２　導(dǎo)數(shù)的定義４８ !!!!!!!!!!!!!!!!!!!
習(xí)題３．１ ５１ !!!!!!!!!!!!!!!!!!!!!!!!
３．２　導(dǎo)數(shù)的基本公式與四則運(yùn)算求導(dǎo)法則５
習(xí)題３．２ ５５ !!!!!!!!!!!!!!!!!!!!!!!!
３．３　其他求導(dǎo)法則５６ !!!!!!!!!!!!!!!!!!!!!!
３．３．１　反函數(shù)與復(fù)合函數(shù)求導(dǎo)法則５６ !!!!!!!!!!!!
３．３．２　隱函數(shù)與參數(shù)方程求導(dǎo)法則５９ !!!!!!!!!!!!
習(xí)題３．３ ６２ !!!!!!!!!!!!!!!!!!!!!!!!
３．４　高階導(dǎo)數(shù)６６ !!!!!!!!!!!!!!!!!!!!!!!!
習(xí)題３．４ ７０ !!!!!!!!!!!!!!!!!!!!!!!!
３．５　微分７０ !!!!!!!!!!!!!!!!!!!!!!!!!!
習(xí)題３．５ ７２ !!!!!!!!!!!!!!!!!!!!!!!!
３．６　洛必達(dá)法則７２ !!!!!!!!!!!!!!!!!!!!!!!
３．６．１?。?
０和∞∞
型未定式７３ !!!!!!!!!!!!!!!!!
３．６．２　其他型未定式７４ !!!!!!!!!!!!!!!!!!
習(xí)題３．６ ７６ !!!!!!!!!!!!!!!!!!!!!!!!
３．７　極值的判定和最值７６ !!!!!!!!!!!!!!!!!!!!
習(xí)題３．７ ８０ !!!!!!!!!!!!!!!!!!!!!!!!
３．８　函數(shù)的凸向和作圖８１ !!!!!!!!!!!!!!!!!!!!
３．８．１　凸函數(shù)、曲線的凸向及拐點(diǎn)８１ !!!!!!!!!!!!
３．８．２　函數(shù)的分析作圖法８２ !!!!!!!!!!!!!!!!
習(xí)題３．８ ８４ !!!!!!!!!!!!!!!!!!!!!!!!
３．９　微分中值定理８５ !!!!!!!!!!!!!!!!!!!!!!
習(xí)題３．９ ８９ !!!!!!!!!!!!!!!!!!!!!!!!
３．１０　泰勒公式８９ !!!!!!!!!!!!!!!!!!!!!!!
習(xí)題３．１０ ９２ !!!!!!!!!!!!!!!!!!!!!!!
第４章　一元積分學(xué)９３ !!!!!!!!!!!!!!!!!!!
４．１　積分的概念與性質(zhì)９３ !!!!!!!!!!!!!!!!!!!!
４．１．１　定積分的概念９３ !!!!!!!!!!!!!!!!!!
４．１．２　定積分的簡(jiǎn)單性質(zhì)９５ !!!!!!!!!!!!!!!!
習(xí)題４．１ ９６ !!!!!!!!!!!!!!!!!!!!!!!!
４．２　微積分基本定理９７
４．２．１　微積分基本定理第一部分９７ !!!!!!!!!!!!!
４．２．２　微積分基本定理第二部分９９ !!!!!!!!!!!!!
習(xí)題４．２ １００ !!!!!!!!!!!!!!!!!!!!!!!
第５章　多元函數(shù)微分學(xué)１０３ !!!!!!!!!!!!!!!!
５．１　多元函數(shù)的基本概念１０３ !!!!!!!!!!!!!!!!!!
５．１．１　預(yù)備知識(shí)１０３ !!!!!!!!!!!!!!!!!!!!
５．１．２　多元函數(shù)１０４ !!!!!!!!!!!!!!!!!!!!
習(xí)題５．１ １０５ !!!!!!!!!!!!!!!!!!!!!!!
５．２　多元函數(shù)的極限與連續(xù)１０６ !!!!!!!!!!!!!!!!!
習(xí)題５．２ １０８ !!!!!!!!!!!!!!!!!!!!!!!
５．３　偏導(dǎo)數(shù)與二階偏導(dǎo)數(shù)１０９ !!!!!!!!!!!!!!!!!!
５．３．１　偏導(dǎo)數(shù)１０９ !!!!!!!!!!!!!!!!!!!!!
５．３．２　二階偏導(dǎo)數(shù)１１１ !!!!!!!!!!!!!!!!!!!
習(xí)題５．３ １１２ !!!!!!!!!!!!!!!!!!!!!!!
５．４　全微分１１２ !!!!!!!!!!!!!!!!!!!!!!!!
習(xí)題５．４ １１６ !!!!!!!!!!!!!!!!!!!!!!!
５．５　復(fù)合函數(shù)求導(dǎo)法１１６ !!!!!!!!!!!!!!!!!!!!
習(xí)題５．５ １１９ !!!!!!!!!!!!!!!!!!!!!!!
５．６　隱函數(shù)求導(dǎo)法１２０ !!!!!!!!!!!!!!!!!!!!!
習(xí)題５．６ １２１ !!!!!!!!!!!!!!!!!!!!!!!
５．７　多元函數(shù)的一階泰勒公式１２１ !!!!!!!!!!!!!!!!
習(xí)題５．７ １２３ !!!!!!!!!!!!!!!!!!!!!!!
５．８　多元函數(shù)的極值１２３ !!!!!!!!!!!!!!!!!!!!
習(xí)題５．８ １２６ !!!!!!!!!!!!!!!!!!!!!!!
第６章　微積分在高中的應(yīng)用１２７ !!!!!!!!!!!!!!
６．１　微積分的論證方法１２７ !!!!!!!!!!!!!!!!!!!
６．１．１　分析法１２７ !!!!!!!!!!!!!!!!!!!!!
６．１．２　綜合法１２９ !!!!!!!!!!!!!!!!!!!!!
６．１．３　構(gòu)造法１３０
６．１．４　舉反例法１３１ !!!!!!!!!!!!!!!!!!!!
６．１．５　計(jì)算法１３２ !!!!!!!!!!!!!!!!!!!!!
６．１．６　反證法１３３ !!!!!!!!!!!!!!!!!!!!!
６．１．７　數(shù)學(xué)歸納法１３４ !!!!!!!!!!!!!!!!!!!
６．２　微積分在高考數(shù)學(xué)中的應(yīng)用１３５ !!!!!!!!!!!!!!!
６．２．１　極坐標(biāo)及反三角函數(shù)的應(yīng)用１３５ !!!!!!!!!!!!
６．２．２　極限的應(yīng)用１３６ !!!!!!!!!!!!!!!!!!!
６．２．３　中值定理的應(yīng)用１４６ !!!!!!!!!!!!!!!!!
６．２．４　泰勒公式的應(yīng)用１５０ !!!!!!!!!!!!!!!!!
６．２．５　微積分基本定理的應(yīng)用１５７ !!!!!!!!!!!!!!
習(xí)題６（強(qiáng)基真題） １６０ !!!!!!!!!!!!!!!!!!!!!!
參考答案１６６ !!!!!!!!!!!!!!!!!!!!!!!
參考文獻(xiàn)１８１