數(shù)學(xué)分析(二)教案(14.1)

1、1楚雄師范學(xué)院數(shù)學(xué)系課程教案楚雄師范學(xué)院數(shù)學(xué)系課程教案(數(shù)學(xué)分析數(shù)學(xué)分析(二)周學(xué)時(shí)周學(xué)時(shí)6節(jié))周次第16周(2008.6.92008.6.15)課題第十四章第十四章冪級(jí)數(shù)冪級(jí)數(shù)14.114.1冪級(jí)數(shù)冪級(jí)數(shù)學(xué)時(shí)2學(xué)時(shí)教學(xué)內(nèi)容（主要）一.冪級(jí)數(shù)的定義冪級(jí)數(shù)的定義二.冪級(jí)數(shù)的收斂區(qū)間冪級(jí)數(shù)的收斂區(qū)間三.冪級(jí)數(shù)的運(yùn)算冪級(jí)數(shù)的運(yùn)算教學(xué)目標(biāo)1.理解冪級(jí)數(shù)的定義2.深刻理解并掌握求冪級(jí)數(shù)收斂區(qū)間的基本方法3.深刻理解并掌握冪級(jí)數(shù)的運(yùn)算法則教學(xué)重點(diǎn)1

2、.冪級(jí)數(shù)的定義2.求冪級(jí)數(shù)收斂區(qū)間的基本方法3.冪級(jí)數(shù)的運(yùn)算法則教學(xué)難點(diǎn)1.求冪級(jí)數(shù)收斂區(qū)間的基本方法2.冪級(jí)數(shù)的運(yùn)算法則教學(xué)方法與手段分析教學(xué)方法、探索式的教學(xué)方法、講練結(jié)合以練為主教學(xué)方法(借助多媒體輔助教學(xué))教學(xué)進(jìn)程(教學(xué)設(shè)計(jì))第十四章第十四章冪級(jí)數(shù)冪級(jí)數(shù)14.114.1冪級(jí)數(shù)冪級(jí)數(shù)一.冪級(jí)數(shù)的定義冪級(jí)數(shù)的定義定義定義1(1).級(jí)數(shù)????????200102000nnnnnaxxaaxxaxxaxx???????????????

3、叫做關(guān)于的冪級(jí)數(shù).??0xx?(2).級(jí)數(shù)20120nnnnnaxaaxaxax???????????叫做關(guān)于的冪級(jí)數(shù).x3推論推論2.若在收斂又在發(fā)散則存在唯一的使得0nnnax???00x?0nnnax???1x0r?在內(nèi)絕對(duì)收斂而在外處處發(fā)散.0nnnax?????rr???rr?發(fā)散發(fā)散收斂)))(((())))(((?1x?r?0x?00xr1x定義定義2.2.設(shè)0nnnax???(1).若僅在收斂則令.0nnnax???00

4、r?(2).若在收斂則令.0nnnax?????????r??(3).若在收斂又在發(fā)散則令0nnnax???00x?0nnnax???1x001supnnnrxax??????????收斂上述的叫做收斂半徑叫做收斂區(qū)間收斂區(qū)間加上收r0nnnax?????rr?0nnnax???斂端點(diǎn)叫做收斂域.0nnnax???問(wèn)題問(wèn)題3:3:設(shè)探究收斂的收斂半徑的計(jì)算公式.0nnnax???0nnnax???探究探究:由于.????1111nnnn

5、nnnnuxaxaxaxaux??????若則??1lim0nnnala???????(1).當(dāng)時(shí)若即則絕對(duì)收??0l???????1limnnnuxlxux?????1lx?1xl?0nnnax???斂若即則發(fā)散.故.1lx?1xl?0nnnax???1rl?(2).當(dāng)時(shí)故在收斂于是0l?????1lim01nnnuxlxux???????xR?0nnnax???R.r???(3).當(dāng)時(shí)故在發(fā)l???????1limnnnuxlxux