姝¤繋瑷晱鑰冪爺绉樼睄鑰冪爺缍�(w菐ng)!    鐮旂┒鐢熸嫑鐢熶俊鎭恫(w菐ng)    鑰冨崥鐪熼涓嬭級    鑰冪爺鐪熼涓嬭級    鍏ㄧ珯鏂囩珷绱㈠紩
鏂囩珷鎼滅储
   
  楂樼礆鎼滅储   

 鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 鑰冪爺绉樼睄鑰冪爺缍�(w菐ng) >> 鏂囩珷涓績 >> 灏堟キ(y猫)瑾� >> 姝f枃  瀹夊窘甯寖澶у銆婃暩(sh霉)瀛稿垎鏋愩€嬪ぇ缍辨湰绉戞暀瀛稿ぇ缍�

鏂拌仦璩囪▕
鏅€氭枃绔� 涓婃捣甯�50瀹跺柈浣嶇恫(w菐ng)涓婃帴鍙楀挩瑭㈠拰鍫卞悕
鏅€氭枃绔� 鍖椾含澶у鐢�“灏辨キ(y猫)涔嬪”鐮旂┒鐢熷皥鍫存嫑鑱樺牬闈㈢伀鐖�
鏅€氭枃绔� 寤堝ぇ濂崇爺绌剁敓琚妗堢祩瀵╁垽姹� 鍏囨墜琚垽姝诲垜
鏅€氭枃绔� 寤f澅鍏牎缍�(w菐ng)涓婅│榛炶€冪爺鍫卞悕灏囬枊濮�
鏅€氭枃绔� 2004骞寸ⅸ澹寳浜嫑鐢熷柈浣嶅牨鍚嶉粸涓€瑕�
鏅€氭枃绔� 娲涢櫧楂樻柊鍗€(q奴)21鍚嶇ⅸ澹爺绌剁敓琚仒鐐轰腑灞ら牁灏�
鏅€氭枃绔� 娴欐睙鐪佺ⅸ澹爺绌剁敓鍫卞悕寰炰笅鍛ㄤ竴闁嬪
鏅€氭枃绔� 2004骞翠笂?锛熺礀^(q奴)缍�(w菐ng)涓婂牨鍚嶆檪闁撳畨鎺掕〃
鏅€氭枃绔� 寤f澅锛氱爺绌剁敓鍏ュ鑰冭│2003骞磋捣閲嶅ぇ瑾�(di脿o)鏁�
鏅€氭枃绔� 2004骞村叏鍦嬬爺鎷涗笂?锛熺礀^(q奴)鍫卞悕榛炰竴瑕借〃
瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 瀵у澶у04骞寸ⅸ澹爺绌剁敓瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 澶ч€i惖閬撳闄�04骞寸ⅸ澹帴鏀惰(di脿o)鍔戠敓婧愬熀鏈師鍓�
鏅€氭枃绔� 鍚夋灄澶у寤鸿ō宸ョ▼瀛搁櫌04骞寸爺绌剁敓瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 婧窞甯寖瀛搁櫌(婧窞澶у绫�)05鐮旂┒鐢熻(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 浣虫湪鏂ぇ瀛�04骞磋€冪爺瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 娌堥櫧寤虹瓚宸ョ▼瀛搁櫌04骞寸爺绌剁敓瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 澶╂触甯寖澶у鏀挎不鑸囪鏀垮闄�05骞寸ⅸ澹(di脿o)鍔戦渶姹�
鏅€氭枃绔� 绗簩蹇楁効鑰冪爺瑾�(di脿o)鍔戠▼搴忕瓟鐤�
鏅€氭枃绔� 涓婃捣澶у04骞寸爺绌剁敓鎷涙敹绲�(t菕ng)鑰冪敓瑾�(di脿o)鍔戜俊鎭�
鏅€氭枃绔� 寤hタ澶у04骞寸ⅸ澹爺绌剁敓瑾�(di脿o)鍔戜俊鎭�

鍙嬫儏鎻愮ず锛氭湰绔欐彁渚涘叏鍦�400澶氭墍楂樼瓑闄㈡牎鎷涙敹纰╁+銆佸崥澹爺绌剁敓鍏ュ鑰冭│姝峰勾鑰冪爺鐪熼銆佽€冨崥鐪熼銆佺瓟妗�锛岄儴鍒嗗鏍℃洿鏂拌嚦2012骞达紝2013骞�锛涘潎鎻愪緵鏀惰不涓嬭級銆� 涓嬭級娴佺▼锛� 鑰冪爺鐪熼 榛炴搳鈥�鑰冪爺瑭﹀嵎鈥濃€濅笅杓�; 鑰冨崥鐪熼 榛炴搳鈥�鑰冨崥瑭﹀嵎搴�鈥� 涓嬭級 

鈥�1鈥�
鏁�(sh霉) 瀛� 灏� 妤�(y猫)
銆婃暩(sh霉)瀛稿垎鏋愩€嬫暀瀛稿ぇ缍�
瀛告檪锛�289 瀛告檪 瀛稿垎锛�17
鐞嗚珫瀛告檪锛�289 瀛告檪
閬╃敤灏堟キ(y猫)锛氭暩(sh霉)瀛歌垏鏁�(sh霉)瀛告噳鐢�
澶х侗鍩�(zh铆)绛嗕汉锛氬緪闅涘畯 澶х侗瀵╁畾浜猴細浣曞畻绁�
瑾槑
鏁�(sh霉)瀛稿垎鏋愭槸鍥涘勾鍒舵湰绉戦櫌鏍℃暩(sh霉)瀛搁灏堟キ(y猫)蹇呬慨鐨勯噸瑕佽绋�锛屾槸
骞句箮鎵€鏈夋暩(sh霉)瀛稿悗绻艰绋嬬殑鍩虹銆傞€氶亷鏁欏锛屼娇瀛哥敓姝g⒑鐞嗚В鍜屾帉鎻�
鏁�(sh霉)瀛稿垎鏋愮殑鍩烘湰姒傚康銆佸熀鏈悊璜�锛屽熀鏈帉鎻℃暩(sh霉)瀛稿垎鏋愪腑鐨勮珫璀夋柟娉�锛�
杓冪啛绶村湴鐛插緱鏈绋嬫墍瑕佹眰鐨勫熀鏈紨绠楄兘鍔�銆傞€氶亷鏈绋嬬殑瀛哥繏浣�
瀛哥敓鍏锋湁杓冨挤鐨勮嚜瀛歌兘鍔涘拰閬嬬敤鎵€瀛哥煡璀樿В姹虹浉闂滃晱椤岀殑瀹氭€у垎
鏋�銆佸畾閲忓垎鏋愯兘鍔�锛岀偤閫蹭竴姝ュ缈掓暩(sh霉)瀛稿皥妤�(y猫)瑾茬▼鎵撲笅蹇呰鐨勫熀绀庛€�
鏈绋嬫暀瀛哥附鏅傛暩(sh霉)绱勭偤 240+49=289 瀛告檪銆傜繏椤岃閲囩敤姣忕珷涓€娆�
鏂瑰紡铏曠悊銆傝瑳鎺堟檪鏁�(sh霉)鑸囩繏椤岃鏅傛暩(sh霉)涔嬫瘮澶ц嚧鐐� 5 : 1.
鏈ぇ缍辨墍鍒楀収(n猫i)瀹硅垏鍚勭珷鏅傛暩(sh霉)鍍呬緵鍙冭€�銆傛暀甯彲浣滈仼鑸囪(di脿o)鏁�銆�
鏁欏澶х侗
鈥�2鈥�
涓€銆� 鍑芥暩(sh霉)锛�10+2 瀛告檪锛�
瀵︽暩(sh霉)姒傝堪锛岀禃灏嶅€艰垏涓嶇瓑寮�銆�
鍗€(q奴)闁撹垏閯板煙锛岀⒑鐣屽師鐞�銆�
鍑芥暩(sh霉)姒傚康锛屽嚱鏁�(sh霉)鐨勫咕绋〃绀烘硶锛屽嚱鏁�(sh霉)鐨勫洓鍓囬亱绠�锛屽京鍚堝嚱鏁�(sh霉)锛屽弽鍑芥暩(sh霉)锛屽熀鏈垵绛夊嚱鏁�(sh霉)锛�
鍒濈瓑鍑芥暩(sh霉)銆�
鍏锋湁鏌愪簺鐗规€х殑鍑芥暩(sh霉)銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛� 绨¤浠嬬垂瀵︽暩(sh霉)鎬ц唱(zh矛)鍙婄禃灏嶅€艰垏涓嶇瓑寮忥紱
2锛� 閲嶉粸闂¤堪涓�銆佷笅纰虹晫姒傚康鍙婄⒑鐣屽師鐞嗭紝閫欎竴閮ㄥ垎鏄噸榛�锛屼篃鏈変竴瀹氱殑闆e害锛屽彲閫�
閬庝緥椤屽拰缈掗璁撳鐢熷姞寮风悊瑙�锛�
3锛� 鍦ㄤ粙绱逛竴鑸嚱鏁�(sh霉)姒傚康鐨勫悓鏅傦紝寮疯(di脿o)鍩烘湰鍒濈瓑鍑芥暩(sh霉)鍜屽垵绛夊嚱鏁�(sh霉)鐨勯噸瑕佹€�銆傚挤鍖栧鐢�
灏嶄竴鑸€ц垏鐗规畩鎬т箣闁撹警璀夐棞绯荤殑瑾嶈瓨銆�
浜�銆� 鏁�(sh霉)鍒楁サ闄愶紙8+2 瀛告檪锛�
鏁�(sh霉)鍒�锛屾暩(sh霉)鍒楁サ闄愮殑蔚-N 瀹氱京銆�
鏀舵杺鏁�(sh霉)鍒楃殑鎬ц唱(zh矛)锛氬敮涓€鎬�銆佹湁鐣屾€�銆佷繚搴忥紙铏燂級鎬�銆佽揩鏂傛€с€佸洓鍓囬亱绠楁硶鍓�銆�
鏁�(sh霉)鍒楁サ闄愬瓨鍦ㄧ殑姊濅欢銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庣啊鍠粙绱规暩(sh霉)鍒楁サ闄愭蹇电敘(ch菐n)鐢熺殑姝峰彶閬庣▼锛屽緸涓湅鍒板毚鏍肩殑蔚-N 瀹氱京鐢�(ch菐n)鐢熺殑蹇呯劧鎬�
鍜岄噸瑕佹€�锛屼娇瀛哥敓鐪熸鎺ュ彈楂樺害鎶借薄銆佸舰寮忓寲鐨勎�-N 瀹氱京銆傚叾娆�锛岄€氶亷灏嵨�-N 瀹氱京鐨勫墫
鏋愬拰涓€浜涘吀鍨嬩緥椤岀殑娣卞叆鍒嗘瀽锛屼娇瀛哥敓姝g⒑鐞嗚В鏁�(sh霉)鍒楁サ闄愮殑蔚-N 瀹氱京锛屽苟瀛告渻閬嬬敤瀹冧締椹�
璀夋暩(sh霉)鍒楁サ闄�銆�
2锛庡湪浠嬬垂鏀舵杺鏁�(sh霉)鍒楃殑鍚勭ó鎬ц唱(zh矛)鏅�锛岀獊鍑哄挤瑾�(di脿o)杩杺鎬у畾鐞嗘槸姹傛サ闄愮殑涓€绋噸瑕佹柟娉�锛�
骞舵寚鍑虹敤杩杺鎬ф眰妤甸檺鏅傜殑涓€浜涘師鍓囧拰鏂规硶銆�
4锛� 瑕佹眰瀛哥敓鐔熺反鎺屾彙閲嶈妤甸檺锛� e
n
n
n
??
??
)
1
1(lim 锛屽苟娉ㄦ剰灏囦竴浜涙暩(sh霉)鍒楁サ闄愯綁鍖栫偤涓�
杩伴噸瑕佹サ闄愬舰寮�銆�
涓�銆� 鍑芥暩(sh霉)妤甸檺锛�10+2 瀛告檪锛�
鍑芥暩(sh霉)妤甸檺鐨勎�-M 瀹氱京鍜屛�-未瀹氱京锛屽柈鍋存サ闄愩€�
鍑芥暩(sh霉)妤甸檺鐨勬€ц唱(zh矛)锛氬敮涓€鎬�銆佸眬閮ㄦ湁鐣屾€с€佸眬閮ㄤ繚铏熸€�銆佷笉绛夊紡鎬ц唱(zh矛)銆佽揩鏂傛€�銆佸洓鍓囬亱
绠�銆�
鈥�3鈥�
鍑芥暩(sh霉)妤甸檺瀛樺湪鐨勬浠讹細姝哥祼鍘熷墖鍜屾煰瑗挎簴鍓�銆�
鍏╁€嬮噸瑕佹サ闄�銆�
鐒$灏忛噺鍙婂叾闅庣殑姣旇純锛涜铏� 0锛宱锛岋綖锛涚劇绐ぇ閲忓強鍏堕殠鐨勬瘮杓�銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庡湪浠嬬垂鍚勭ó椤炲瀷鐨勬サ闄愬畾缇╀箣鍓嶏紝鍏堢洿瑙€鎻忚堪妤甸檺锛岀劧鍚庨€氶亷娣卞叆鍒嗘瀽妤甸檺鐨勫惈
缇╋紝灏庡嚭妤甸檺鐨勫毚鏍肩殑褰㈠紡鍖栫殑瀹氱京銆�
2锛庤姹傚鐢熺啛绶存帉鎻″嚱鏁�(sh霉)妤甸檺鐨勬€ц唱(zh矛)鍜屽叐鍊嬮噸瑕佹サ闄愶紝骞剁啛绶寸敤浜庤瓑鏄庢垨瑷堢畻鍑芥暩(sh霉)
妤甸檺銆�
鍥涖€� 鍑芥暩(sh霉)鐨勯€g簩(x霉)鎬э紙10+2 瀛告檪锛�
閫g簩(x霉)鎬ф蹇�锛岄枔鏂烽粸鍙婂叾鍒嗛锛屽湪鍗€(q奴)闁撲笂閫g簩(x霉)鐨勫嚱鏁�(sh霉)銆�
閫g簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛氬眬閮ㄦ湁鐣屾€�銆佸眬閮ㄤ繚铏熸€�銆佸洓鍓囬亱绠椼€佸京鍚堥亱绠�锛岄枆鍗€(q奴)闁撲笂閫g簩(x霉)鍑�
鏁�(sh霉)鐨勬€ц唱(zh矛)锛屽弽鍑芥暩(sh霉)鐨勯€g簩(x霉)鎬�锛屼竴鑷撮€g簩(x霉)鎬�銆�
鍒濈瓑鍑芥暩(sh霉)鐨勯€g簩(x霉)鎬с€�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庨棥鏄庨€g簩(x霉)鎬ф蹇电殑閲嶈鎬у強閫g簩(x霉)鎬х殑鐩磋鎻忚堪鍜屽毚鏍煎畾缇╀箣闁撶殑鑱�(li谩n)绯�銆�
2锛庨噸榛炲垎鏋愬苟寮疯(di脿o)涓€鑷撮€g簩(x霉)鎬х殑鐗瑰緛锛屼互鍙婂畠鑸囬€g簩(x霉)鎬т箣闁撶殑閲嶈宸垾銆�
浜�銆佸鏁�(sh霉)鐨勪竴浜涘熀鏈畾鐞嗭紙10+4 瀛告檪锛�
纰虹晫鑸囩⒑鐣屽瓨鍦ㄥ畾鐞�銆傚崁(q奴)闁撳瀹氱悊?锛熸寷榄囪珬绻欒暅t銆傝嚧瀵嗘€у畾鐞�銆傝仛榛炲畾鐞嗐€傛湁闄愬京
钃嬪畾鐞�銆�
闂滀簬闁夊崁(q奴)闁撲笂閫g簩(x霉)鍑芥暩(sh霉)鎬ц唱(zh矛)鐨勫咕鍊嬪畾鐞嗙殑鍤存牸璀夋槑銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庢湰绔犲畾鐞嗗潎鍦ㄥ柈瑾�(di脿o)鏈夌晫瀹氱悊鐨勫墠鎻愪笅瑷庤珫銆�
2锛庡缓璀颁互鍗€(q奴)闁撳瀹氱悊鐐轰富瑕佸伐鍏疯瓑鏄庡叾浠栧畾鐞�銆�
3锛庡湪鐢ㄩ棞浜庡鏁�(sh霉)瀹屽倷鎬х殑骞惧€嬪畾鐞嗚瓑鏄庨棞浜庨枆鍗€(q奴)闁撲笂閫g簩(x霉)鍑芥暩(sh霉)鎬ц唱(zh矛)鐨勫咕鍊嬪畾鐞嗙殑鏁�
瀛搁亷绋嬩腑锛屾噳娉ㄦ剰鍩归(y菐ng)瀛哥敓鍤村瘑鎺ㄧ悊鐨勮兘鍔�銆�
鍏�銆佸皫鏁�(sh霉)鑸囧井鍒嗭紙12+2 瀛告檪锛�
灏庢暩(sh霉)姒傚康锛氬皫鏁�(sh霉)鐨勫畾缇╋紙灏庢暩(sh霉)銆佸乏灏庢暩(sh霉)銆佸彸灏庢暩(sh霉)浠ュ強鑸囬€g簩(x霉)鎬ч枔闂滅郴锛�銆傚皫鏁�(sh霉)骞句綍鎰�
缇┿€佺墿鐞嗘剰缇�銆傚皫鍑芥暩(sh霉)鐨勬蹇�銆�
姹傚皫娉曞墖锛氬皫鏁�(sh霉)鐨勫洓鍓囬亱绠�銆傚弽鍑芥暩(sh霉)鐨勫皫鏁�(sh霉)銆傚京鍚堝嚱鏁�(sh霉)鐨勫皫鏁�(sh霉)?锛涱姠鍘╅啸鈻宼鑸囧叕寮�銆�
寰垎锛氬井鍒嗘蹇�銆傚井鍒嗙殑閬嬬畻娉曞墖锛堜竴闅庡井鍒嗗舰寮忕殑涓嶈畩鎬э級銆�
鈥�4鈥�
杩戜技瑷堢畻鑸囪宸及瑷堛€�
楂橀殠灏庢暩(sh霉)鍙婇亱绠楋紙娉ㄦ剰锛氳悐甯冨凹鑼插叕寮忥級銆傞珮闅庡井鍒嗐€�
鍙冮噺鏂圭▼鎵€纰哄畾鐨勫嚱鏁�(sh霉)鐨勫皫鏁�(sh霉)銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛� 浠ユ洸绶氱殑鍒囩窔銆佺洿绶氶亱鍕曠殑鐬檪閫熷害鐐鸿儗鏅�锛屽紩鍏ュ皫鏁�(sh霉)鐨勬蹇�銆�
2锛� 姹傚皫娉曞墖涓憲閲嶈瑳娓呭京鍚堝嚱鏁�(sh霉)鐨勬眰灏庢硶鍓囷紙閺堝紡娉曞墖锛�銆�
3锛� 寰垎鐨勮▓绠椾腑鎳夋敞鎰忎粙绱逛竴闅庡井鍒嗗舰寮忕殑涓嶈畩鎬т互鍙婃噳鐢ㄥ井鍒嗚繎浼艰▓绠楀強瑾ゅ樊
浼拌▓銆�
涓�銆佸井鍒嗗鍩烘湰瀹氱悊鑸囦笉瀹氬紡妤甸檺锛�12+2 瀛告檪锛�
涓€煎畾鐞嗭細璨婚Μ锛團ermat锛夊畾鐞嗏€斺€斾簣鍌欏畾鐞�銆備腑鍊煎畾鐞嗭紙Rolle銆丩agrange銆丆auchy
涓夊ぇ涓€煎畾鐞嗭級銆傚皫鏁�(sh霉)妤甸檺瀹氱悊銆�
涓嶅畾寮忔サ闄愶細
0
0
鍨嬩笉瀹氬紡妤甸檺銆�
?
?
鍨嬩笉瀹氬紡妤甸檺銆傚叾瀹冮鍨嬬殑涓嶅畾寮忔サ闄�
锛� ,,0 ?????
00
,0,1 ?
?
绛夐鍨嬶級
娉板嫆瀹氱悊銆傚付鐨簽璜撅紙Peano锛夊瀷浣欓爡鐨勬嘲鍕掑叕寮忋€傛噳鐢紙杩戜技瑷堢畻锛屾眰妤甸檺锛�銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛� 钁楅噸浠嬬垂涓夊ぇ寰垎涓€煎畾鐞嗗強鍏惰瓑鏄�锛屽畠鍊戞槸鍒╃敤灏庢暩(sh霉)鐨勫眬閮ㄦ€ц唱(zh矛)鎺ㄦ柗鍑芥暩(sh霉)鐨勬暣
楂旀€ф厠(t脿i)鐨勬湁鍔涘伐鍏�銆�
2锛� 浠ュ皫鏁�(sh霉)鐐哄伐鍏峰湪姹備笉瀹氬紡妤甸檺鏅傦紝鎳夋敞鎰忕緟姣斿锛圠'Hospital锛夋硶鍓囨垚绔嬬殑姊濅欢锛�
浠ュ強鍏跺畠椤炲瀷闁撶殑杞夊寲鏂规硶銆�
3锛� 娉板嫆瀹氱悊鏄敤澶氶爡寮忚繎浼艰〃绀哄嚱鏁�(sh霉)骞剁敤浠ラ€茶鍜岃繎浼艰▓绠楄垏鐞嗚珫鍒嗘瀽鐨勪竴鍊嬮噸瑕�
宸ュ叿銆傛敞鎰忎粙绱瑰咕绋及瑷堝強棣厠鍕炴灄锛圡aclaurin锛夊叕寮忋€�
4锛� 鍒╃敤 Taylor 鍏紡閫茶杩戜技瑷堢畻鏅�锛屾敞鎰忚垏鍓嶇珷鐢紙涓€闅庯級寰垎閫茶杩戜技瑷堢畻姣旇純銆�
鍏�銆侀亱鐢ㄥ皫鏁�(sh霉)鐮旂┒鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛�10+2 瀛告檪锛�
鍑芥暩(sh霉)鐨勫柈瑾�(di脿o)鎬�銆傛サ鍊肩殑蹇呰姊濅欢銆傛サ鍊肩殑鍏╁€嬪厖鍒嗘浠讹紙绗笁鍊嬪厖鍒嗘浠跺彲浣滈伕璎涘収(n猫i)
瀹癸級銆傛渶澶у€艰垏鏈€灏忓€�銆�
鍑芥暩(sh霉)鐨勫嚫鎬ц垏鎷愰粸鐨勬蹇点€傚嚱鏁�(sh霉)鍑告€х殑鍒ゅ畾銆傚嚱鏁�(sh霉)鍑告€х殑鎳夌敤銆�
婕歌繎绶氥€傚嚱鏁�(sh霉)浣滃湒銆�
鏂圭▼杩戜技瑙�銆�
鈥�5鈥�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛� 娉ㄦ剰浠嬬垂鍑芥暩(sh霉)鍠(di脿o)鎬э紙鍖呮嫭鍠(di脿o)鍗€(q奴)闁擄級鐨勫垽瀹氭柟娉曚互鍙婂埄鐢ㄥ柈瑾�(di脿o)鎬ц瓑鏄庝竴浜涗笉绛�
寮忕殑鎶€宸с€�
2锛� 钁楅噸浠嬬垂鍑芥暩(sh霉)妤靛€肩殑鍒ゅ畾鍙婄壒瀹氭儏褰笅鍑芥暩(sh霉)鏈€澶у€�锛屾渶灏忓€肩殑纰哄畾锛屽苟浠嬬垂瀹冨€�
鐨勬噳鐢�銆�
3锛� 钁楅噸浠嬬垂鍑芥暩(sh霉)鍑告€х殑瀹氱京鍙婂垽瀹氭柟娉�锛屽苟娉ㄦ剰浠嬬垂瀹冨€戠殑鎳夌敤锛屽瑭规.锛圝ensen锛�
涓嶇瓑寮忕瓑钁楀悕涓嶇瓑寮�锛屾噳鐢ㄩ儴鍒嗗彲浣滅偤瀛哥敓瑷庤珫鐢�銆�
4锛� 钁楅噸璎涙竻鍑芥暩(sh霉)浣滃湒鐨勬椹�锛屽苟浠ュ渚嬭鏄�銆�
涔�銆佷笉瀹氱⿳鍒嗭紙10+2 瀛告檪锛�
鍘熷嚱鏁�(sh霉)鑸囦笉瀹氱⿳鍒嗘蹇�?锛涱姠鐥塭鍒嗚〃銆傜窔鎬ч亱绠楁硶鍓�銆傛彌鍏冪⿳鍒嗘硶銆傚垎閮ㄧ⿳鍒嗘硶銆�
鏈夌悊鍑芥暩(sh霉)绌嶅垎娉曘€備笁瑙掑嚱鏁�(sh霉)鏈夌悊寮忕殑绌嶅垎.骞剧ó鐒$悊鍑芥暩(sh霉)鐨勭⿳鍒�銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庤璁撳鐢熸槑浜嗗師鍑芥暩(sh霉)鑸囦笉瀹氱⿳鍒嗙殑闂滅郴锛堟敞鎰忚垏涓嬩竴绔犫€滃師鍑芥暩(sh霉)瀛樺湪瀹氱悊鈥濈浉鍛�
鎳夛級锛屾眰鍘熷嚱鏁�(sh霉)锛堣垏涓嶅畾绌嶅垎锛夐亱绠楀拰姹傚皫鏁�(sh霉)锛堣垏寰垎锛夐亱绠椾箣闁撶殑闂滅郴锛屽緸鑰岀悊瑙e熀鏈�
绌嶅垎鍏紡鐨勬湰璩�(zh矛)銆�
2锛庤憲鍔涘紩灏庡鐢熸帉鎻″拰鐔熺反閬嬬敤涓嶅畾绌嶅垎鐨勫熀鏈叕寮�锛岀窔鎬ч亱绠楁硶鍓囧拰鎻涘厓绌嶅垎娉�銆�
鍒嗛儴绌嶅垎娉曘€傛敞鎰忓熀鏈⿳鍒嗛亱绠楃殑鍘熷墖鑸囨妧宸�锛岄€欐槸鏈珷鐨勯噸榛炪€�
3锛庡湪璎涙巿鏈夌悊鍑芥暩(sh霉)锛屼笁瑙掑嚱鏁�(sh霉)鏈夌悊鏁�(sh霉)浠ュ強骞剧ó鐒$悊鍑芥暩(sh霉)鐨勭⿳鍒嗘硶鏅�锛岃璁撳鐢熺悊瑙�
鍩烘湰绌嶅垎鎶€琛撶殑涓€鑸噳鐢ㄦ€濊矾鍜屾眰閫欏咕椤炲嚱鏁�(sh霉)绌嶅垎鐨勫叿楂旀妧宸�銆�
鍗�銆佸畾绌嶅垎锛�14+2 瀛告檪锛�
鏇查倞姊舰闈㈢⿳鑸囪畩鍔涗綔鍔熲€斺€斿紩鍑哄畾绌嶅垎姒傚康銆傚畾绌嶅垎瀹氱京銆傚畾绌嶅垎鐨勫咕浣曟剰缇�?锛�?br/>绌嶇殑蹇呰姊濅欢銆傦紙閬斿竷锛変笂鍜�銆佷笅鍜屽強鍏舵€ц唱(zh矛)?锛熺厼e鐨勫厖瑕佹浠躲€�
鍙⿳鐨勫厖鍒嗘浠垛€斺€斿彲绌嶅嚱鏁�(sh霉)椤烇紙闁夊崁(q奴)闁撲笂鐨勯€g簩(x霉)鍑芥暩(sh霉)锛屾湁鏈夐檺鍊嬮枔鏂烽粸鐨勬湁鐣屽嚱鏁�(sh霉)锛�
鍠(di脿o)鏈夌晫鍑芥暩(sh霉)锛�銆�
瀹氱⿳鍒嗙殑鎬ц唱(zh矛)锛氱窔鎬ч亱绠楁€ц唱(zh矛)锛屽皪鍗€(q奴)闁撶殑鍙姞鎬с€佸柈瑾�(di脿o)鎬�銆佺禃灏嶅彲绌嶆€с€佺⿳鍒嗭紙绗竴锛�
涓€煎畾鐞�銆傜⿳鍒嗙浜屼腑鍊煎畾鐞嗐€�
寰⿳鍒嗗鍩烘湰瀹氱悊锛堝師鍑芥暩(sh霉)瀛樺湪瀹氱悊锛�銆侼ewton-Leibniz 鍏紡銆傚畾绌嶅垎鐨勬彌鍏冩硶銆傚畾
绌嶅垎鐨勫垎閮ㄧ⿳鍒嗘硶銆�
鐢� ?
x
dt
t1
1
瀹氱京灏嶆暩(sh霉)鍑芥暩(sh霉)锛屽皪鏁�(sh霉)鍑芥暩(sh霉)鑸囨寚鏁�(sh霉)鍑芥暩(sh霉)鐨勫熀鏈€ц唱(zh矛)銆�
鐒$闄愬弽甯哥⿳鍒嗙殑姒傚康锛岀劇鐣屽嚱鏁�(sh霉)鍙嶅父绌嶅垎鐨勬蹇�銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
鈥�6鈥�
1锛庢繁 鍒荤悊 瑙e苟 鏈冩噳鐢� 瀹氱⿳ 鍒嗙殑 瀹氱京鍜� 鎬ц唱(zh矛) 锛岃畩 涓婇檺 鐨勫畾绌� 鍒嗗強 鍏跺皫 鏁�(sh霉)锛�
Newton-Leibniz 鍏紡锛屽畾绌嶅垎鐨勬彌鍏冩硶鑸囧垎閮ㄧ⿳鍒嗘硶绛夐噸榛炲収(n猫i)瀹�銆�
2锛� 闂滀簬鍑芥暩(sh霉)鍙⿳鎬х殑瑷庤珫锛岃姹傚鐢熺悊瑙e叾鎬濇兂鑸囨柟娉�銆�
3锛� 鍙嶅父绌嶅垎姒傚康鏄湰绔犲熀鏈蹇电殑鑷劧寤朵几銆傝鍚屾檪璁撳鐢熷姞娣卞皪瀹氱⿳鍒嗭紙鍙婃サ闄愶級
鐨勬蹇佃垏鏂规硶鐨勭悊瑙�锛屽苟娉ㄦ剰鑸囩鈥滃崄涓夆€濋儴鍒嗗懠鎳�銆�
鍗佷竴銆佸畾绌嶅垎鐨勬噳鐢紙8+2 瀛告檪锛�
骞抽潰鍦栧舰鐨勯潰绌嶏紝宸茬煡鎴潰闈㈢⿳鍑芥暩(sh霉)鐨勭珛楂旈珨绌�锛屾棆杞夐珨鐨勯珨绌嶃€傛洸绶氱殑寮ч暦鑸囧姬寰�
鍒�銆佹洸鐜囥€佹棆杞夐珨鐨勫伌闈㈢⿳銆傜墿鐞嗘噳鐢紙澹撳姏銆佸姛銆佸紩鍔�銆侀潨鍔涜窛鑸囬噸蹇冪瓑锛�銆�
骞冲潎鍊�銆�
*瀹氱⿳鍒嗙殑杩戜技瑷堢畻锛堟褰㈡硶銆佹媼鐗╃窔锛�銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
鐢ㄥ畾绌嶅垎鐨勫熀鏈€濇兂鍜屽井鍏冨垎鏋愭硶璨┛鍚勭ó鎳夌敤鍟忛锛岄€氶亷鍚勭ó鎳夌敤鍔犳繁灏嶇⿳鍒嗘€濇兂
鏂规硶鐨勭悊瑙�銆傛帉鎻$敤寰厓鍒嗘瀽娉曡В椤岀殑绋嬪簭銆�
鍗佷簩銆佹暩(sh霉)闋呯礆鏁�(sh霉)锛�12+2 瀛告檪锛�
鐒$绱氭暩(sh霉)姒傚康鈥斺€旂劇绐礆鏁�(sh霉)鑸囧叾閮ㄥ垎鍜屾暩(sh霉)鍒楃殑闂滅郴銆傜礆鏁�(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁�銆傜礆鏁�(sh霉)鐨勭啊鍠�
鎬ц唱(zh矛)銆傜礆鏁�(sh霉)鏀舵杺鐨勫繀瑕佹浠�銆傜礆鏁�(sh霉)鏀舵杺鐨� Cauchy 婧栧墖銆�
姝i爡绱氭暩(sh霉)鏀舵杺鐨勫熀鏈畾鐞嗭紙 ? ?
n
nn
uu )0( 鏀舵杺鐨勫厖瑕佹浠舵槸锛氬畠鐨勯儴鍒嗗拰鏁�(sh霉)鍒�? ?n
S 鏈�
涓婄晫锛�銆�
姣旇純鍒ゅ垾娉曞強鍏舵サ闄愬舰寮�銆傛瘮鍊硷紙D`Alembert锛夊垽鍒ユ硶鍙婂叾妤甸檺褰㈠紡銆傛牴鍊硷紙Cauchy锛�
鍒ゅ垾娉曞強鍏舵サ闄愬舰寮�銆�
锛圕auchy锛夌⿳鍒嗗垽鍒ユ硶銆傛媺璨濓紙Raabe锛夊垽鍒ユ硶銆�
浜ら尟绱氭暩(sh霉)锛岃悐甯冨凹鑼诧紙Leibniz锛夊垽鍒ユ硶銆�
闃胯矟鐖撅紙Abel锛夊垽鍒ユ硶銆傜媱鍒╁厠闆凤紙Dirichlet锛夊垽鍒ユ硶銆�
绲曞皪鏀舵杺鑸囨浠舵敹鏂傘€�
*绲曞皪鏀舵杺绱氭暩(sh霉)鐨勯噸鎺掑畾鐞�銆�*绲曞皪鏀舵杺绱氭暩(sh霉)鐨勪箻绌嶏紙Cauchy 瀹氱悊锛�銆傛浠舵敹鏂傜礆鏁�(sh霉)鐨�
榛庢浖锛圧iemann锛夊畾鐞嗐€�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛� 闂℃槑绱氭暩(sh霉)鑸囷紙鍏堕儴鍒嗗拰锛夋暩(sh霉)鍒楃殑鑱�(li谩n)绯昏垏杞夊寲銆�
2锛� 璎涙竻涓€鑸爡绱氭暩(sh霉)鑸囨闋呯礆鏁�(sh霉)涔嬮枔鐨勮伅(li谩n)绯伙紝閲嶈姝i爡绱氭暩(sh霉)鍦ㄨ◣璜栨暩(sh霉)闋呯礆鏁�(sh霉)鏅傜殑鍩烘湰
浣滅敤銆�
3锛� 璎涙竻涓€鑸爡绱氭暩(sh霉)鐨勭禃灏嶆敹鏂傝垏姊濅欢鏀舵杺鐨勫崁(q奴)鍒ヨ垏鑱�(li谩n)绯�锛屾敞鎰忛€欏叐绋敹鏂傛€х殑涓嶅悓
鎬ц唱(zh矛)鑸囦綔鐢ㄣ€�
鈥�7鈥�
4锛� 灏嶇礆鏁�(sh霉)鏀舵杺鐨勫垽鍒ュ畾鐞嗕富瑕佽瑳鏄庡浣曟噳鐢ㄥ強鎳夌敤涓渶瑕佹敞鎰忕殑鍟忛銆侫bel璁婃彌锛堝嵆
鍒嗛儴姹傚拰鍏紡锛夊€煎緱閲嶈銆侫bel 鍒ゅ垾娉曡垏 Dirichlet 鍒ゅ垾娉曠殑蹇呰鎬у彲浣滅啊鍠粙绱癸紙鍙冭
瀹楀簭骞筹細闂滀簬 Dirichlet 鍜� Abel 鍒ゅ垾娉曠殑蹇呰鎬�锛屾暩(sh霉)瀛哥殑瀵﹁笎鑸囪獚璀�锛�1990锛堬級锛�72-75锛�銆�
鍗佷笁銆佸弽甯哥⿳鍒嗭紙6+2 瀛告檪锛�
鐒$闄愮⿳鍒嗙殑绲曞皪鏀舵杺鑸囨浠舵敹鏂�銆傜劇绐⿳鍒嗚垏鐒$绱氭暩(sh霉)鐨勮伅(li谩n)绯�銆傛瘮杓冨垽鍒ユ硶鍙婂叾妤�
闄愬舰寮�?锛熸寷楂嬭e娉曞強鍏舵サ闄愬舰寮�銆傜⿳鍒嗙浜屼腑鍊煎畾鐞�銆傞樋璨濈埦鍒ゅ垾娉曡垏鐙勫埄鍏嬮浄鍒ゅ垾娉曘€�
鐒$晫鍑芥暩(sh霉)鍙嶅父绌嶅垎鐨勬煰瑗挎簴鍓�銆傜劇鐣屽嚱鏁�(sh霉)鍙嶅父绌嶅垎鐨勭禃灏嶆敹鏂傝垏姊濅欢鏀舵杺銆傜劇鐣屽嚱鏁�(sh霉)
鍙嶅父绌嶅垎鐨勬瘮杓冨垽鍒ユ硶?锛熸寷楂嬭e娉曞強鍏舵サ闄愬舰寮�銆傞樋璨濈埦鍒ゅ垾娉曡垏鐙勫埄鍏嬮浄鍒ゅ垾娉�銆傜劇
鐣屽嚱鏁�(sh霉)鍙嶅父绌嶅垎鑸囩劇绐檺鍙嶅父绌嶅垎鐨勮伅(li谩n)绯汇€�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庢敞鎰忓叐鍨嬪弽甯哥⿳鍒嗗拰鐒$绱氭暩(sh霉)鐨勮伅(li谩n)绯�锛屽畾绌嶅垎姒傚康鑸囨€ц唱(zh矛)浠ュ強鍑芥暩(sh霉)妤甸檺姒傚康鑸囨€�
璩�(zh矛)鐨勮伅(li谩n)绯伙紱鍏╁瀷鍙嶅父绌嶅垎鐩镐簰闁撶殑鑱�(li谩n)绯�銆�
2锛庝互鐒$闄愬弽甯哥⿳鍒嗙偤鍩虹锛屽钩琛屽湴寤虹珛鐒$晫鍑芥暩(sh霉)鍙嶅父绌嶅垎鐨勬湁闂滃収(n猫i)瀹�銆�
3锛庢湰绔犲彧瑷庤珫鍏╁瀷鍙嶅父绌嶅垎鐨勬杺鏁f€у晱椤�銆傝嚦浜庡叐鍨嬪弽甯哥⿳鍒嗙殑瀹氱京鑸囩啊鍠€ц唱(zh矛)鍙�
瑷堢畻锛屽彲瀹夋帓鍒板畾绌嶅垎鐨勬渶鍚庝竴绡€(ji茅)銆�
鍗佸洓銆佸嚱鏁�(sh霉)鍒楄垏鍑芥暩(sh霉)闋呯礆鏁�(sh霉)锛�10+2 瀛告檪锛�
鍑芥暩(sh霉)鍒楃殑鏀舵杺鑸囦竴鑷存敹鏂�銆傚嚱鏁�(sh霉)鍒楀湪鍗€(q奴)闁撲笂涓€鑷存敹鏂傜殑鍏呰姊濅欢銆�
鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勬敹鏂傝垏涓€鑷存敹鏂�銆傚嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鍦ㄥ崁(q奴)闁撲笂涓€鑷存敹鏂傜殑鍏呭垎蹇呰姊濅欢銆�
鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鍦ㄥ崁(q奴)闁撲笂涓€鑷存敹鏂傜殑鍏呭垎姊濅欢锛歐eierstrass 鍎�(y艒u)绱氭暩(sh霉)鍒ゅ垾娉�銆侫bel 鍒ゅ垾娉�銆�
Dirichlet 鍒ゅ垾娉�銆�
涓€鑷存敹鏂傚嚱鏁�(sh霉)鍒楃殑妤甸檺鍑芥暩(sh霉)鐨勯€g簩(x霉)鎬у畾鐞嗐€侀€愰爡绌嶅垎瀹氱悊銆傞€愰爡姹傚皫瀹氱悊銆備竴鑷存敹鏂�
鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勯€g簩(x霉)鎬�锛岄€愰爡绌嶅垎銆侀€愰爡姹傚皫瀹氱悊銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庝互鍑芥暩(sh霉)鍒楀湪鍗€(q奴)闁撲笂鐨勶紙榛炴厠(t脿i)锛夋敹鏂傝垏涓€鑷存敹鏂傜偤鍩虹锛屽缓绔嬪嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鍦ㄥ崁(q奴)闁撲笂
鐨勶紙榛炴厠(t脿i)锛夋敹鏂傝垏涓€鑷存敹鏂傜殑姒傚康鍙婃€ц唱(zh矛)銆�
2锛庢繁鍏ヨ瑳瑙d竴鑷存敹鏂傛€ф蹇�锛岃瑳娓呭畠鍜岄粸鎱�(t脿i)鏀舵杺涔嬮枔鐨勫崁(q奴)鍒�锛岄伕璎涘吀鍨嬩緥椤岃鏄庘€滈潪
涓€鑷存敹鏂傗€�銆�
3锛庣穵瀵嗚伅(li谩n)绯绘暩(sh霉)闋呯礆鏁�(sh霉)鐨勬湁闂滃収(n猫i)瀹�锛岃瑳杩板嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鐨勪竴鑷存敹鏂傛€х殑鍒ゅ垾瀹氱悊锛岄棥鏄�
濡備綍鎳夌敤閫欎簺鍒ゅ垾瀹氱悊浠ュ強鎳夌敤鏅傛噳鐣舵敞鎰忕殑鍟忛銆傚畾鐞嗙殑璀夋槑閬庣▼鍙瑳寰楃啊鐣ヤ竴浜�銆�
4锛庯紙鑸囪◣璜� Weierstrass 鍎�(y艒u)绱氭暩(sh霉)鍒ゅ垾娉曠浉閰嶅悎锛夈€傞€氶亷鑸変緥璎涙竻锛堟垨甯冭嚨浣滄キ(y猫)璁撳鐢�
娉ㄦ剰锛� ?
n
n
xu )( 鍦ㄥ崁(q奴)闁撲笂涓€鑷存敹鏂�銆佺禃灏嶆敹鏂傚強?
n
n
xu )( 涓€鑷存敹鏂備箣闁撶殑鍗€(q奴)鍒ヨ垏鑱�(li谩n)绯汇€�
5锛庡湪璎涜堪涓€鑷存敹鏂傜殑鍑芥暩(sh霉)鍒楁垨鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勯€g簩(x霉)鎬�銆侀€愰爡绌嶅垎銆侀€愰爡姹傚皫瀹氱悊鐨勫悓
鈥�8鈥�
鏅�锛屽挤瑾�(di脿o)涓€鑷存敹鏂傛€ф浠剁殑閲嶈鎬�锛屼絾鍙堣鎸囧嚭瀹冨彧鏄厖鍒嗘浠躲€�
鍗佷簲銆佸啰绱氭暩(sh霉)锛�8+2 瀛告檪锛�
Abel 绗竴瀹氱悊銆傛敹鏂傚崐寰戯紙鏀舵杺鍗€(q奴)闁擄級鑸囨敹鏂傚煙銆傚啰绱氭暩(sh霉)鐨勪竴鑷存敹鏂傛€�銆�
鍐礆鏁�(sh霉)鐨勬€ц唱(zh矛)锛氶€g簩(x霉)鎬�銆侀€愰爡绌嶅垎銆侀€愰爡寰垎銆佸洓鍓囬亱绠�銆�
Taylor 绱氭暩(sh霉)鑸� Maclaurin 绱氭暩(sh霉)銆�
鍑芥暩(sh霉)灞曢枊鎴愬啰绱氭暩(sh霉)鐨勬浠�銆傚垵绛夊嚱鏁�(sh霉)鐨勫啰绱氭暩(sh霉)灞曢枊銆傚嚱鏁�(sh霉)鐨� Taylor 灞曢枊鍦ㄨ繎浼艰▓绠�
涓殑鎳夌敤銆�
*鐢ㄥ啰鍑芥暩(sh霉)瀹氱京鎸囨暩(sh霉)鍑芥暩(sh霉)鍙婃寮﹀嚱鏁�(sh霉)銆佷綑寮﹀嚱鏁�(sh霉)銆�
*寰╄畩閲忕殑鎸囨暩(sh霉)鍑芥暩(sh霉)鑸� Euler 鍏紡銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庨€氶亷瑷庤珫鏀舵杺鍗婂緫鑸囨敹鏂傚崁(q奴)闁擄紙鍩燂級寮勬竻瀹冨€戝湪鐮旂┒鍐礆鏁�(sh霉)锛堜綔鐐轰竴椤炵壒娈婄殑鈥滄€�
璩�(zh矛)濂解€濈殑鍑芥暩(sh霉)闋呯礆鏁�(sh霉)锛夌殑涓€鑷存敹鏂傛€ф柟闈㈢殑浣滅敤锛屾敞鎰忚垏鈥滃嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鈥濋儴鍒嗙殑鐩告噳鍏�(n猫i)瀹�
涔嬮枔鐨勮伅(li谩n)绯汇€�
2锛庡湪瑷庤珫鍐礆鏁�(sh霉)鐨勬€ц唱(zh矛)鏅�锛岃閫氶亷鍏稿瀷渚嬮瑾槑绱氭暩(sh霉)姹傚拰鐨勪竴浜涚啊鍠殑鍩烘湰鐨勬柟娉�銆�
3锛庡湪璎涙巿 Taylor 绱氭暩(sh霉)鏅傦紝瑕侀棥鏄庡畠鑸囧墠闈㈢殑 Taylor 鍏紡鐨勫崁(q奴)鍒ヨ垏鑱�(li谩n)绯�銆�
4锛庡皪浜庡嚱鏁�(sh霉)鐨� Taylor 灞曢枊锛岃闂℃槑瀹冣€滅洿鎺ュ睍闁嬧€濈殑鏍规摎(j霉)銆佹€濇兂鑸囨柟娉曟椹熴€傛洿瑕�
璁撳鐢熸帉鎻♀€滈枔鎺ュ睍闁嬧€濈殑鎬濇兂鑸囨柟娉�銆�
5锛庤垑渚嬭鏄庤繎浼艰▓绠楃殑鎬濇兂鑸囨柟娉曪紙鍖呮嫭鏁�(sh霉)蟺銆乪 鐨勮繎浼艰▓绠楄垏蟺銆乪 鏄劇鐞嗘暩(sh霉)鐨勮瓑
鏄庣瓑锛夈€�
鍗佸叚銆丗ourier 绱氭暩(sh霉)锛�10+2 瀛告檪锛�
涓夎绱氭暩(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)绯荤殑姝d氦鎬�銆�
浠� 2蟺鐐哄懆鏈熺殑鍑芥暩(sh霉)鐨� Fourier 绱氭暩(sh霉)鐨勬敹鏂傚畾鐞�銆�
浠� 2蟺鐐哄懆鏈熺殑鍑芥暩(sh霉)鐨� Fourier 灞曢枊銆傚鍑芥暩(sh霉)鑸囧伓鍑芥暩(sh霉)鐨� Fourier 灞曢枊銆備互 2l 鐐哄懆鏈�
鐨勫嚱鏁�(sh霉)鐨� Fourier 灞曢枊銆�
鏀舵杺瀹氱悊鐨勮瓑鏄庯細Bessel 涓嶇瓑寮�銆俁iemann-Lebesgue 瀹氱悊銆侳ourier 绱氭暩(sh霉)鐨勯儴鍒嗗拰鍏�
寮�銆傚畾鐞嗚瓑鏄�銆�
涓€鑷存敹鏂傛€у畾鐞�:Fourier 绱氭暩(sh霉)鐨勯€愰爡绌嶅垎鑸囬€愰爡寰垎銆俉eierstrass 鍑芥暩(sh霉)閫艰繎瀹氱悊銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庨€氶亷 Fourier 绱氭暩(sh霉)鐨勬暀瀛革紝瑕佹眰瀛哥敓鎺屾彙 Fourier 绱氭暩(sh霉)銆丗ourier 绯绘暩(sh霉)鐨勬蹇靛強鍏�
瑷堢畻鍏紡銆傚苟鍊熷姪鏀舵杺瀹氱悊寮勬竻涓€鍑芥暩(sh霉)鑸囧叾 Fourier 绱氭暩(sh霉)涔嬮枔鐨勯棞绯�銆�
2锛庤姹傚鏈冩噳鐢ㄤ笂杩版蹇�銆佸叕寮忓拰瀹氱悊銆佹寜瑕佹眰灏囧嚱鏁�(sh霉)灞曢枊鎴� Fourier 绱氭暩(sh霉)銆�
鈥�9鈥�
鍗佷竷銆佸鍏冨嚱鏁�(sh霉)鐨勬サ闄愯垏閫g簩(x霉)锛�10+2 瀛告檪锛�
骞抽潰榛為泦姒傚康锛堥劙鍩熴€佸収(n猫i)榛�銆佺晫榛炪€侀枊闆�銆侀枆闆�銆侀枆鍩熺瓑锛夈€�
骞抽潰榛為泦鐨勫熀鏈畾鐞嗏€斺€斿崁(q奴)鍩熷瀹氱悊銆佽仛榛炲畾鐞嗐€佹湁闄愯钃嬪畾鐞�銆�
浜屽厓鍑芥暩(sh霉)姒傚康銆�
浜岄噸妤甸檺銆傜疮娆℃サ闄�銆�
浜屽厓鍑芥暩(sh霉)鐨勯€g簩(x霉)鎬�銆佸京鍚堝嚱鏁�(sh霉)鐨勯€g簩(x霉)鎬у畾鐞�銆佹湁鐣岄枆鍩熶笂閫g簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)銆�
n 缍┖闁撹垏 n 鍏冨嚱鏁�(sh霉)鐨勬蹇�銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庤姹傚鐢熺悊瑙e钩闈㈤粸闆嗘蹇�銆傚钩闈㈤粸闆嗙殑鍩烘湰瀹氱悊鍜屾湁鐣屽煙涓婇€g簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍙�
椤炴瘮浜庝竴缍洿绶氫腑鐨勭浉鎳夊畾鐞嗕粙绱癸紝涓嶄綔璀夋槑銆�
2锛庝簩鍏冨嚱鏁�(sh霉)銆佷簩閲嶆サ闄愩€佷簩鍏冨嚱鏁�(sh霉)鐨勯€g簩(x霉)鎬х瓑鍏�(n猫i)瀹规槸鏈珷閲嶉粸锛岃寮疯(di脿o)瀹冨€戝拰涓€鍏�
鍑芥暩(sh霉)涓殑鐩告噳姒傚康涔嬮枔鍗€(q奴)鍒ワ紙鑸囪伅(li谩n)绯伙級銆�
鍗佸叓銆佸鍏冨嚱鏁�(sh霉)寰垎瀛革紙16+2 瀛告檪锛�
鍋忓皫鏁�(sh霉)姒傚康鍙婂叾骞句綍鎰忕京銆佸叏寰垎姒傚康銆佸叏寰垎鐨勫咕浣曟剰缇╁強鎳夌敤銆�
寰╁悎鍑芥暩(sh霉)鐨勬眰灏庢硶鍓囧強鍏ㄥ井鍒嗚▓绠�锛屼竴闅庡井鍒嗗舰寮忕殑涓嶈畩鎬�銆�
鏂瑰悜灏庢暩(sh霉)鑸囨搴�銆�
楂橀殠鍋忓皫鏁�(sh霉)銆侀珮闅庡井鍒�銆�
浜屽厓鍑芥暩(sh霉)鐨勫井鍒嗕腑鍊煎畾鐞嗚垏娉板嫆鍏紡銆備簩鍏冨嚱鏁�(sh霉)鐨勬サ鍊�銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛� 鎳夐噸榛炲姞寮峰亸灏庢暩(sh霉)鐨勮▓绠楄〒绶�锛岀壒鍒ユ槸寰╁悎鍑芥暩(sh霉)鐨勫亸灏庤▓绠�銆�
2锛� 鍏ㄥ井鍒嗘蹇佃灏嶇収涓€鍏冨嚱鏁�(sh霉)寰垎姒傚康璎涜В銆傝寮勬竻鍙井鎬ф浠�锛屽彲寰垏閫g簩(x霉)銆佸彲
寰垏鍋忓皫瀛樺湪锛屽彲寰垏鍋忓皫閫g簩(x霉)涔嬮枔鐨勫崁(q奴)鍒ヨ垏鑱�(li谩n)绯�銆�
3锛� 浜屽厓鍑芥暩(sh霉)妤靛€间篃鎳夊皪鐓т竴鍏冨嚱鏁�(sh霉)妤靛€艰瑳瑙�锛屽挤瑾�(di脿o)澶氬厓鍑芥暩(sh霉)妤靛€煎晱椤岄仩姣斾竴鍏冨嚱鏁�(sh霉)
妤靛€煎晱椤屽京闆�銆�
鍗佷節銆侀毐鍑芥暩(sh霉)瀛樺湪瀹氱悊锛�10+4 瀛告檪锛�
闅卞嚱鏁�(sh霉)姒傚康銆傞毐鍑芥暩(sh霉)瀹氱悊銆傞毐鍑芥暩(sh霉)姹傚皫銆�
闅卞嚱鏁�(sh霉)绲勬蹇�銆傞毐鍑芥暩(sh霉)绲勫畾鐞嗐€傞毐鍑芥暩(sh霉)绲勬眰灏�銆傚弽鍑芥暩(sh霉)绲勮垏鍧愭璁婃彌銆傚嚱鏁�(sh霉)琛屽垪寮�銆�
鍑芥暩(sh霉)鐩搁棞銆�
骞句綍鎳夌敤锛堝钩闈㈡洸绶氱殑鍒囩窔鑸囨硶绶�?锛熻嚮g鏇茬窔鐨勫垏绶氳垏娉曞钩闈�锛屾洸闈㈢殑鍒囧钩闈㈣垏娉曠窔锛�銆�
姊濅欢妤靛€笺€傛媺鏍兼湕鏃ヤ箻鏁�(sh霉)娉曘€�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
鈥�10鈥�
1锛� 瑕佹眰瀛哥敓娣卞叆鐞嗚В闅卞嚱鏁�(sh霉)锛堢祫锛夌殑姒傚康锛屽苟閫氶亷闅卞嚱鏁�(sh霉)锛堢祫锛夌殑鍦ㄥ咕浣曘€佸潗妯欒畩
鎻涘強姊濅欢妤靛€肩瓑鏂归潰鐨勬噳鐢ㄥ姞娣辩悊瑙i毐鍑芥暩(sh霉)锛堢祫锛夌殑姒傚康鑸囦綔鐢�銆�
2锛� 瑕佹眰瀛哥敓鎺屾彙闅卞嚱鏁�(sh霉)锛堢祫锛夌殑姹傚皫鏂规硶锛屽苟娉ㄦ剰鍦ㄩ棞浜庨毐鍑芥暩(sh霉)鐨勮◣璜栬垏瑷堢畻鏅傝€�
鎱槸鍚︽豢瓒抽毐鍑芥暩(sh霉)锛堢祫锛夊畾鐞嗙殑姊濅欢銆�
浜屽崄銆佸惈鍙冮噺绌嶅垎锛�10+2 瀛告檪锛�
鍚弮閲忓父缇╃⿳鍒嗘蹇�銆傚惈鍙冮噺甯哥京绌嶅垎鐨勯€g簩(x霉)鎬�銆佸彲绌嶆€с€佸彲寰€�銆佺⿳鍒嗘搴忕殑璁婃彌銆�
鍚弮閲忓唬缇╃⿳鍒嗙殑姒傚康锛涘惈鍙冮噺寤g京绌嶅垎鐨勬敹鏂傝垏涓€鑷存敹鏂�銆傚惈鍙冮噺寤g京绌嶅垎鐨勪竴鑷�
鏀舵杺鍒ゅ垾娉曪細Cauchy 婧栧墖銆俉eierstrass 鍒ゅ垾娉�.Abel 鍒ゅ垾娉�銆侱irichlet 鍒ゅ垾娉曘€�
鍚弮閲忓唬缇╃⿳鍒嗙殑鎬ц唱(zh矛)锛氶€g簩(x霉)鎬у畾鐞�銆佸彲寰€у畾鐞�銆佸彲绌嶆€у畾鐞�銆佺⿳鍒嗘搴忎氦鎻涘畾鐞�銆�
*Euler 绌嶅垎锛埼�-鍑芥暩(sh霉)銆丅-鍑芥暩(sh霉)锛�銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庤憲閲嶈瑳瑙e惈鍙冮噺寤g京绌嶅垎鐨勬敹鏂傝垏涓€鑷存敹鏂傛蹇�锛屽埄鐢ㄥ吀鍨嬩緥椤岃鏄庘€滈潪涓€鑷存敹
鏂傗€濄€�
2锛庡挤瑾�(di脿o)鍚弮閲忓唬缇╃⿳鍒嗚垏鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鍦ㄨ珫璀夋柟娉曚笂鐨勭浉浼兼€�锛屽皪鐓у嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鐨勬湁
闂滄蹇�銆佽◣璜栧惈鍙冮噺寤g京绌嶅垎鐨勭浉鎳夋蹇佃垏鎬ц唱(zh矛)銆�
3锛庤瑳杩颁竴鑷存敹鏂傛€у垽鍒ュ畾鐞嗘檪锛屾噳绐佸嚭閫欎簺瀹氱悊鐨勬噳鐢ㄥ強鎳夌敤鏅傛噳娉ㄦ剰鐨勫晱椤屻€�
4锛庡湪璎涜堪鍚弮閲忓唬缇╃⿳鍒嗙殑鎬ц唱(zh矛)鍚勫畾鐞嗙殑鍚屾檪锛屽挤瑾�(di脿o)涓€鑷存敹鏂傛€ф浠跺湪瀹氱悊涓殑閲�
瑕佹€э紝浣嗗張鎳夊挤瑾�(di脿o)鍙槸鍏呭垎姊濅欢銆�
浜屽崄涓€銆侀噸绌嶅垎锛�14+2 瀛告檪锛�
浜岄噸绌嶅垎姒傚康锛氱煩褰㈠崁(q奴)鍩熶笂鐨勪簩閲嶇⿳鍒�銆備簩閲嶇⿳鍒嗙殑鎬ц唱(zh矛)銆備簩閲嶇⿳鍒嗙殑鍙⿳姊濅欢銆備竴
鑸崁(q奴)鍩熶笂鐨勪簩閲嶇⿳鍒�銆�
浜岄噸绌嶅垎鐨勮▓绠楋細鍖栦簩閲嶇⿳鍒嗙偤绱绌嶅垎銆備簩閲嶇⿳鍒嗘彌鍏冩硶锛堟サ鍧愭璁婃彌鑸囦竴鑸畩鎻涳級銆�
涓夐噸绌嶅垎姒傚康?锛涱嚱類胯儰e鍒嗙偤绱绌嶅垎銆備笁閲嶇⿳鍒嗘彌鍏冩硶锛堟煴鍧愭璁婃彌銆佺悆鍧愭璁婃彌
鑸囦竴鑸畩鎻涳級銆�
閲嶇⿳鍒嗙殑鎳夌敤锛氬钩闈㈠湒褰㈢殑闈㈢⿳锛岀┖闁撶珛楂旂殑楂旂⿳锛涙洸闈㈤潰绌�锛涢噸蹇冿紝杞夊嫊鎱i噺锛屽紩
鍔涚瓑銆�
n 閲嶇⿳鍒嗐€�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛庡湪閲嶇⿳鍒嗘蹇典腑锛岃憲閲嶈瑳瑙d簩閲嶇⿳鍒嗘蹇�锛屽挤瑾�(di脿o)瀹氱京涓垎鍓�銆佹眰鍜屻€佸彇妤甸檺涓夋
椹�锛屼互鍙婂垎鍓茬殑鍒嗘硶鑸囦粙榛炲彇娉曠殑鍏╁€嬧€滀换鎰忔€р€�銆�
2锛庢繁鍏ヨ瑳瑙d簩閲嶇⿳鍒嗙殑鍙⿳鎬у晱椤�锛岃瑳娓呭彲绌嶇殑蹇呰姊濅欢銆佸厖鍒嗘浠跺強鍏呰姊濅欢銆�
3锛庨噸绌嶅垎鐨勬€ц唱(zh矛)鍙垏瀹氱⿳鍒嗘€ц唱(zh矛)灏嶆瘮锛屼綔涓€鑸粙绱�銆�
鈥�11鈥�
4锛� 寮疯(di脿o)鍜屽挤鍖栭噸绌嶅垎瑷堢畻銆�
5锛� 鐢ㄥ井鍏冩硶璎涢噸绌嶅垎鎳夌敤锛岃畵瀛哥敓鎺屾彙寰厓娉曟€濇兂锛屽苟铏曠悊瀵﹂殯鎳夌敤鍟忛锛堜富瑕佹槸
骞句綍銆佺墿鐞嗘噳鐢級銆�
6锛� n 閲嶇⿳鍒嗗彧浣滅啊瑕佷粙绱广€�
浜屽崄浜�銆� 鏇茬窔绌嶅垎鑸囨洸闈㈢⿳鍒嗭紙20+4 瀛告檪锛�
绗竴鍨嬫洸绶氱⿳鍒嗙殑姒傚康銆傜涓€鍨嬫洸绶氱⿳鍒嗙殑瑷堢畻銆傜涓€鍨嬫洸闈㈢⿳鍒嗙殑姒傚康銆傜涓€鍨嬫洸
闈㈢⿳鍒嗙殑瑷堢畻銆�
绗簩鍨嬫洸绶氱⿳鍒嗙殑姒傚康銆傜浜屽瀷鏇茬窔绌嶅垎鐨勮▓绠�銆傚叐椤炴洸绶氱⿳鍒嗙殑鑱�(li谩n)绯汇€�
Green 鍏紡銆傛洸绶氱⿳鍒嗙殑鑸囪矾鐒¢棞鎬с€�
鏇查潰?zh猫n)楣婃瘝鎷嶉拞c绗簩鍨嬫洸闈㈢⿳鍒嗘蹇�銆傜浜屽瀷鏇查潰绌嶅垎鐨勮▓绠椼€傚叐椤炴洸闈㈢⿳鍒嗙殑鑱�(li谩n)绯�銆�
Gauss 鍏紡銆係tokes 鍏紡銆傚牬璜栧垵姝ワ紙鍫寸殑姒傚康銆佹搴﹀牬銆佹暎搴﹀牬銆佹棆搴﹀牬銆佺閲忓牬
鑸囧嫝鍫达級銆�
鍏�(n猫i)瀹硅檿鐞嗗缓璀帮細
1锛� 璎涙竻鏇茬窔銆佹洸闈㈢⿳鍒嗘蹇�锛屾敞鎰忎粙绱瑰叐椤炴洸绶氥€佹洸闈㈢⿳鍒嗙殑鑳屾櫙渚嬮銆�
2锛� 鍏╅绌嶅垎鐨勮伅(li谩n)绯昏垏鍗€(q奴)鍒ユ噳浠旂窗鍒嗘瀽锛岃瑳瑙f竻妤�銆�
3锛� 鍔犲挤瀛哥敓灏嶆洸绶氱⿳鍒�銆佹洸闈㈢⿳鍒嗚▓绠楃殑瑷撶反銆�
4锛� 娣卞叆璎涜В Green 鍏紡銆丟auss 鍏紡鑸� Stokes 鍏紡锛岃畵瀛哥敓鐞嗚В涓夊ぇ钁楀悕鍏紡鐨勭簿
绁炲璩�(zh矛)銆�
5锛� 鍫磋珫鍙綔涓€鑸粙绱�銆�
娉細鍦ㄦ浠惰ū鍙殑鎯呮硜涓�锛屽彲灏嶅井鍒嗗舰寮�銆佸寰垎鑸囦竴鑸� Stokes 鍏紡浣滅啊鍠粙绱�銆�
鏁欏鍙冭€冩浉鐩�
1銆併€婃暩(sh霉)瀛稿垎鏋愩€嬭彲甯ぇ鍑虹増绀撅紝2002 骞寸 3 鐗�銆�
2銆併€婂井绌嶅垎瀛告暀绋嬨€嬭彶璧噾鍝ョ埦鑼ㄨ憲銆�

鍏嶈铂鑱叉槑锛氭湰鏂囩郴杞夎級鑷恫(w菐ng)绲�锛屽鏈変镜鐘�锛岃珛鑱�(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠h〃浣滆€呭€嬩汉瑙€榛�锛岃垏鏈恫(w菐ng)绔欑劇闂�銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊锛屽皪鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹�銆佹枃瀛楃殑鐪熷鎬�銆佸畬鏁存€�銆佸強鏅傛€ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰�锛屽苟璜嬭嚜琛屾牳瀵︾浉闂滃収(n猫i)瀹�銆�

  • 涓婁竴绡囨枃绔狅細

  • 涓嬩竴绡囨枃绔狅細
  • 鑰冨崥鍜ㄨQQ 3455265070 榛炴搳閫欓噷绲︽垜鐧�(f膩)娑堟伅 鑰冪爺鍜ㄨ QQ 3455265070 榛炴搳閫欓噷绲︽垜鐧�(f膩)娑堟伅 閮电锛� 3455265070@qq.com
    鍏徃鍚嶇ū:鏄嗗北鍓�(chu脿ng)閰蜂俊鎭鎶€鏈夐檺鍏徃 鐗堟瑠鎵€鏈�
    鑰冪爺绉樼睄缍�(w菐ng) 鐗堟瑠鎵€鏈� © kaoyanmiji.com All Rights Reserved
    鑱叉槑锛氭湰缍�(w菐ng)绔欏皧閲嶅苟淇濊鐭ヨ瓨鐢�(ch菐n)娆婏紝鏍规摎(j霉)銆婁俊鎭恫(w菐ng)绲″偝鎾瑠淇濊姊濅緥銆�锛屽鏋滄垜鍊戣綁杓夋垨寮曠敤鐨勪綔鍝佷镜鐘簡鎮ㄧ殑娆婂埄锛岃珛閫氱煡鎴戝€�锛屾垜鍊戞渻鍙婃檪鍒櫎锛�