2021骞�鍖椾含甯寖澶у(xu茅)纰╁＋鐮旂┒鐢熸嫑鐢熻€冭│鑰冪爺澶х侗

鍖椾含甯寖澶у(xu茅)纰╁＋鐮旂┒鐢熷叆瀛�(xu茅)鑰冭│鏁�(sh霉)瀛�(xu茅)鍒嗘瀽澶х侗

鍙冭€冩浉: 
1锛�鏁�(sh霉)瀛�(xu茅)鍒嗘瀽绗簩鐗堜笂銆佷笅,  闄崇磤(j矛)淇瓑, 楂樼瓑鏁欒偛鍑虹増绀�, 2004.    
2锛�绨℃槑鏁�(sh霉)瀛�(xu茅)鍒嗘瀽 绗簩鐗�,  閮囦腑涓圭瓑, 楂樼瓑鏁欒偛鍑虹増绀�锛� 2009.   
3锛�鏁�(sh霉)瀛�(xu茅)鍒嗘瀽绗�3鐗�(1-3鍐�), 閯(xu茅)瀹夌瓑绶ㄨ憲, 鍖椾含甯寖澶у(xu茅)鍑虹増绀�,  2010銆�

涓€銆佸鏁�(sh霉)闆嗚垏鍑芥暩(sh霉)

鑰冭│鍏�(n猫i)瀹�锛氬鏁�(sh霉)姒傚康鍙婃€ц唱(zh矛)锛岀⒑鐣屽師鐞�锛岄枆鍗€(q奴)闁撳瀹氱悊锛�鍑芥暩(sh霉)鐨勬蹇靛強琛ㄧず娉�锛屽嚱鏁�(sh霉)鐨勬湁鐣屾€�銆佸柈瑾�(di脿o)鎬с€佸懆鏈熸€у拰濂囧伓鎬�锛屽京(f霉)鍚堝嚱鏁�(sh霉)銆佸弽鍑芥暩(sh霉)銆佸垎娈靛嚱鏁�(sh霉)鍜岄毐鍑芥暩(sh霉)锛屽熀鏈垵绛夊嚱鏁�(sh霉)鐨勬€ц唱(zh矛)鍙婂叾鍦栧舰锛屽垵绛夊嚱鏁�(sh霉)锛屽嚱鏁�(sh霉)闂�(gu膩n)绯荤殑寤虹珛.

鑰冭│瑕佹眰锛�

1锛�鐞嗚В瀵︽暩(sh霉)姒傚康,鎺屾彙瀵︽暩(sh霉)鐨勫皬鏁�(sh霉)琛ㄧず鍙婃€ц唱(zh矛).

2锛�鎺屾彙纰虹晫姒傚康骞舵渻鎳�(y墨ng)鐢ㄧ⒑鐣屽師鐞�.

3锛�鎺屾彙闁夊崁(q奴)闁撳姒傚康骞舵渻鎳�(y墨ng)鐢ㄩ枆鍗€(q奴)闁撳瀹氱悊.

4锛�鐞嗚В鍑芥暩(sh霉)鐨勬蹇�,鎺屾彙鍑芥暩(sh霉)鐨勮〃绀烘硶,鏈冨缓绔嬫噳(y墨ng)鐢ㄥ晱椤岀殑鍑芥暩(sh霉)闂�(gu膩n)绯�.

5锛庢帉鎻″嚱鏁�(sh霉)鐨勬湁鐣屾€с€佸柈瑾�(di脿o)鎬�銆佸懆鏈熸€у拰濂囧伓鎬э紟

6锛庢帉鎻″京(f霉)鍚堝嚱鏁�(sh霉)銆佸垎娈靛嚱鏁�(sh霉)銆佸弽鍑芥暩(sh霉)鍙婇毐鍑芥暩(sh霉)鐨勬蹇碉紟

7锛庢帉鎻″熀鏈垵绛夊嚱鏁�(sh霉)鐨勬€ц唱(zh矛)鍙婂叾鍦栧舰,鐞嗚В鍒濈瓑鍑芥暩(sh霉)鐨勬蹇�.

浜屻€佹暩(sh霉)鍒楄垏涓€鍏冨嚱鏁�(sh霉)鐨勬サ闄�

鑰冭│鍏�(n猫i)瀹癸細鏁�(sh霉)鍒楁サ闄愬拰鍑芥暩(sh霉)妤甸檺锛堢啊绋辨サ闄愶級鐨勫畾缇�锛屾暩(sh霉)鍒楃殑涓�銆佷笅妤甸檺锛屽嚱鏁�(sh霉)鐨勫柈鍋�(c猫)妤甸檺(鑷畩閲忚定浜庡柈榛炴檪鍑芥暩(sh霉)鐨勫乏妤甸檺鑸囧彸妤甸檺锛岃嚜璁婇噺瓒ㄤ簬姝ｆ垨璨�(f霉)鐒￠檺澶ф檪鍑芥暩(sh霉)鐨勬サ闄�)锛屽嚱鏁�(sh霉)鐨勫柈鍋�(c猫)涓�銆佷笅妤甸檺锛岀劇绐皬閲忓拰鐒＄澶ч噺鐨勬蹇靛強鍏堕棞(gu膩n)绯伙紝鐒＄灏忛噺鐨勬€ц唱(zh矛)鍙婄劇绐皬閲忕殑姣旇純锛屾サ闄愮殑鎬ц唱(zh矛)锛屾サ闄愬瓨鍦ㄧ殑鍏╁€嬪垽鍒ユ簴(zh菙n)鍓�: 鏌タ(Cauchy)婧�(zh菙n)鍓囧拰鍠(di脿o)鏈夌晫婧�(zh菙n)鍓�, 鍏╁€嬮噸瑕佹サ闄�锛�鑷村瘑鎬у畾鐞�锛岃仛榛炲畾鐞嗭紝鏁�(sh霉)鍒楁サ闄愮殑鏂芥墭鐖捐尐(Stolz)瀹氱悊锛屽嚱鏁�(sh霉)妤甸檺鐨勬捣娑�(Heine)瀹氱悊锛�闁嬮泦銆侀枆闆嗗拰绶婇泦锛屾湁闄愯钃嬪畾鐞�.

鑰冭│瑕佹眰锛�

1锛庢帉鎻℃サ闄愮殑姒傚康(鍖呮嫭鏌愪竴妤甸檺閬庣▼涓暩(sh霉)鍒楁垨鍑芥暩(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁�)锛岀悊瑙ｅ嚱鏁�(sh霉)宸︽サ闄愯垏鍙虫サ闄愮殑姒傚康浠ュ強鍑芥暩(sh霉)妤甸檺瀛樺湪鑸囧乏銆佸彸妤甸檺涔嬮枔鐨勯棞(gu膩n)绯伙紟

2锛庢帉鎻℃サ闄愮殑鎬ц唱(zh矛)(鏈夌晫鎬�銆佸敮涓€鎬с€佷繚铏熸€с€佺畻琛�(sh霉)鎬ц唱(zh矛)銆佷繚搴忔€�銆佸ぞ閫兼€ц唱(zh矛)绛�).

3锛庢帉鎻℃サ闄愬瓨鍦ㄧ殑鏌タ婧�(zh菙n)鍓囷紝骞舵渻鍒╃敤瀹冨垽鏂锋サ闄愮殑瀛樺湪鑸囧惁.

4锛�鎺屾彙妤甸檺瀛樺湪鐨勫柈瑾�(di脿o)鏈夌晫婧�(zh菙n)鍓�锛岃兘澶犵敤鍏跺垽鏂锋暩(sh霉)鍒楁敹鏂傛垨鍦ㄦ煇涓€妤甸檺閬庣▼涓嚱鏁�(sh霉)鏀舵杺锛屽苟鍦ㄥ彲鑳界殑鎯呮硜涓嬫眰鍑烘サ闄�.

5锛�鎺屾彙鑷村瘑鎬у畾鐞�(鏈夌晫鏁�(sh霉)鍒楀繀鏈夋敹鏂傚瓙鍒�)锛岃仛榛炲畾鐞�(鏈夌晫鐒＄榛為泦鑷冲皯鏈変竴鍊嬭仛榛�).

6锛�鎺屾彙鍒╃敤鍏╁€嬮噸瑕佹サ闄愭眰妤甸檺鐨勬柟娉曪紝鏈冪敤鏂芥墭鐖捐尐瀹氱悊姹傛サ闄愶紟

7锛庢帉鎻＄劇绐皬閲�銆佺劇绐ぇ閲忕殑姒傚康锛屾帉鎻＄劇绐皬閲忕殑姣旇純鏂规硶锛屾渻鐢ㄧ瓑鍍圭劇绐皬閲忔眰妤甸檺锛�

8锛庢帉鎻″嚱鏁�(sh霉)閫ｇ簩(x霉)鎬х殑姒傚康(鍚乏閫ｇ簩(x霉)鑸囧彸閫ｇ簩(x霉))锛屾渻鍒ゅ垾鍑芥暩(sh霉)闁撴柗榛炵殑椤炲瀷锛�

9锛�鎺屾彙娴锋秴瀹氱悊骞舵渻鍒╃敤瀹冨垽鏂锋サ闄愮殑瀛樺湪鑸囧惁.

10锛�鐞嗚В闁嬮泦銆侀枆闆嗙殑姒傚康鍜屾€ц唱(zh矛)锛屾帉鎻＄穵闆嗚垏闁嬭钃嬬殑姒傚康銆佹湁闄愯钃嬪畾鐞�.

涓夈€佷竴鍏冨嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)

鑰冭│鍏�(n猫i)瀹�锛氬嚱鏁�(sh霉)閫ｇ簩(x霉)鐨勬蹇靛拰鎬ц唱(zh矛)锛屽嚱鏁�(sh霉)闁撴柗榛炵殑椤炲瀷锛屽垵绛夊嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�锛岄枆鍗€(q奴)闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛).

鑰冭│瑕佹眰锛�

1锛�鐞嗚В閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬蹇�銆佹€ц唱(zh矛)鍜屽垵绛夊嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�,鎺屾彙闁夊崁(q奴)闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)(鏈夌晫鎬�銆佹渶澶у€煎拰鏈€灏忓€煎畾鐞�銆佷粙鍊煎畾鐞嗙瓑),骞舵渻鎳�(y墨ng)鐢ㄩ€欎簺鎬ц唱(zh矛)锛�

2锛庣悊瑙ｉ€ｇ簩(x霉)鍑芥暩(sh霉)鐨勪竴鑷撮€ｇ簩(x霉)鎬ф蹇�,鎺屾彙鏈夌晫闁夊崁(q奴)闁撲笂鐨勬捣娑�-搴锋墭鐖�(Heine-Cantor)涓€鑷撮€ｇ簩(x霉)瀹氱悊.

鍥�銆佷竴鍏冨嚱鏁�(sh霉)寰垎瀛�(xu茅)

鑰冭│鍏�(n猫i)瀹癸細灏�(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑姒傚康鍜岄棞(gu膩n)绯�锛�灏�(d菐o)鏁�(sh霉)鐨勫咕浣曟剰缇╁拰鐗╃悊鎰忕京锛�寰垎鐨勫咕浣曟剰缇╋紝鍑芥暩(sh霉)鐨勫彲灏�(d菐o)鎬ц垏閫ｇ簩(x霉)鎬т箣闁撶殑闂�(gu膩n)绯伙紝骞抽潰鏇茬窔鐨勫垏绶氬拰娉曠窔锛屽皫(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑鍥涘墖閬嬬畻锛屽熀鏈垵绛夊嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)锛屽京(f霉)鍚堝嚱鏁�(sh霉)銆佸弽鍑芥暩(sh霉)銆侀毐鍑芥暩(sh霉)浠ュ強鍙冩暩(sh霉)鏂圭▼鎵€纰哄畾鐨勫嚱鏁�(sh霉)鐨勫井鍒嗘硶锛岄珮闅庡皫(d菐o)鏁�(sh霉)锛岃悐甯冨凹鑼叉眰灏�(d菐o)鍏紡锛屼竴闅庡井鍒嗗舰寮忕殑涓嶈畩鎬�锛屽井鍒嗕腑鍊煎畾鐞�锛屾嘲鍕�(Taylor)鍏紡锛屾礇蹇呴仈(d谩)(L'Hospital)娉曞墖锛屽嚱鏁�(sh霉)鍠(di脿o)鎬х殑鍒ゅ垾锛屽嚱鏁�(sh霉)鐨勬サ鍊�锛屽嚱鏁�(sh霉)鐨勬渶澶у€煎拰鏈€灏忓€�锛屽嚱鏁�(sh霉)鍦栧舰鐨勫嚬鍑告€�銆佹嫄榛炲強婕歌繎绶�锛屽嚱鏁�(sh霉)鍦栧舰鐨勬弿绻紝鎻掑€煎闋呭紡鍜屾柟绋嬭繎浼兼眰鏍�.

鑰冭│瑕佹眰锛�

1锛�鐞嗚В灏�(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑姒傚康锛岀悊瑙ｅ皫(d菐o)鏁�(sh霉)鑸囧井鍒嗙殑闂�(gu膩n)绯�锛岀悊瑙ｅ皫(d菐o)鏁�(sh霉)鐨勫咕浣曟剰缇╋紝鏈冩眰骞抽潰鏇茬窔鐨勫垏绶氭柟绋嬪拰娉曠窔鏂圭▼锛屼簡瑙ｅ皫(d菐o)鏁�(sh霉)鐨勭墿鐞嗘剰缇╋紝鏈冪敤灏�(d菐o)鏁�(sh霉)鎻忚堪涓€浜涚墿鐞嗛噺锛岀悊瑙ｅ嚱鏁�(sh霉)鐨勫彲灏�(d菐o)鎬ц垏閫ｇ簩(x霉)鎬т箣闁撶殑闂�(gu膩n)绯伙紟

2锛庢帉鎻″皫(d菐o)鏁�(sh霉)鐨勫洓鍓囬亱绠楁硶鍓�銆佸京(f霉)鍚堝嚱鏁�(sh霉)鐨勬眰灏�(d菐o)娉曞墖锛屾帉鎻″熀鏈垵绛夊嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)鍏紡锛庝簡瑙ｅ井鍒嗙殑鍥涘墖閬嬬畻娉曞墖鍜屼竴闅庡井鍒嗗舰寮忕殑涓嶈畩鎬�锛�鏈冩眰鍑芥暩(sh霉)鐨勫井鍒嗭紟

3锛庣悊瑙ｉ珮闅庡皫(d菐o)鏁�(sh霉)鐨勬蹇�銆佽悐甯冨凹鑼叉眰灏�(d菐o)鍏紡锛屾渻姹備竴浜涚啊鍠嚱鏁�(sh霉)鐨勯珮闅庡皫(d菐o)鏁�(sh霉)锛�

4锛庢渻姹傚垎娈靛嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)锛屾渻姹傞毐鍑芥暩(sh霉)鍙婂弽鍑芥暩(sh霉)鐨勫皫(d菐o)鏁�(sh霉).

5锛庢帉鎻＄緟鐖�(Rolle)瀹氱悊銆佹媺鏍兼湕鏃�(Lagrange)涓€煎畾鐞�銆佹煰瑗�(Cauchy)涓€煎畾鐞嗐€侀仈(d谩)甯冨皫(d菐o)鍑芥暩(sh霉)浠嬪€煎畾鐞嗗拰娉板嫆(Taylor)瀹氱悊(甯跺咕绋綑闋呯殑)锛�

6锛庢帉鎻℃礇蹇呴仈(d谩)娉曞墖浠ュ強鐢ㄦ礇蹇呴仈(d谩)娉曞墖姹傛湭瀹氬紡妤甸檺鐨勬柟娉曪紟

7锛庣悊瑙ｅ嚱鏁�(sh霉)鐨勬サ鍊兼蹇�锛屾帉鎻＄敤灏�(d菐o)鏁�(sh霉)鍒ゆ柗鍑芥暩(sh霉)鐨勫柈瑾�(di脿o)鎬у拰姹傚嚱鏁�(sh霉)妤靛€肩殑鏂规硶锛屾帉鎻″嚱鏁�(sh霉)鏈€澶у€煎拰鏈€灏忓€肩殑姹傛硶鍙婂叾鎳�(y墨ng)鐢紟

8锛庢渻鐢ㄥ皫(d菐o)鏁�(sh霉)鍒ゆ柗鍑芥暩(sh霉)鍦栧舰鐨勫嚬鍑告€�锛屾渻姹傚嚱鏁�(sh霉)鍦栧舰鐨勬嫄榛炰互鍙婃按骞�銆侀墰鐩村拰鏂滄几杩戠窔锛屾渻鎻忕躬鍑芥暩(sh霉)鐨勫湒褰紟

9锛庣悊瑙ｆ彃鍊煎闋呭紡鍜屾柟绋嬭繎浼兼眰鏍癸紟

浜斻€佷竴鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)

鑰冭│鍏�(n猫i)瀹癸細鍘熷嚱鏁�(sh霉)鍜屼笉瀹氱⿳鍒嗙殑姒傚康锛屼笉瀹氱⿳鍒嗙殑鍩烘湰鎬ц唱(zh矛)锛屽熀鏈嚱鏁�(sh霉)鐨勭⿳鍒嗗叕寮�,瀹氱⿳鍒�(鎸囬粠鏇肩⿳鍒�)鐨勬蹇靛拰鍩烘湰鎬ц唱(zh矛)锛屽畾绌嶅垎涓€煎畾鐞�锛岀⿳鍒嗕笂銆佷笅闄愬嚱鏁�(sh霉)鍙婂叾灏�(d菐o)鏁�(sh霉)锛�榛庢浖鍙⿳鐨勫垽鍒ユ簴(zh菙n)鍓囷紝鐗涢爴涓€钀婂竷灏艰尐(Newton-Leibniz)鍏紡锛屼笉瀹氱⿳鍒嗗拰瀹氱⿳鍒嗙殑鎻涘厓绌嶅垎娉曡垏鍒嗛儴绌嶅垎娉�锛屾湁鐞嗗嚱鏁�(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)鐨勬湁鐞嗗紡鍜岀啊鍠劇鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒�锛�鍙嶅父(寤ｇ京)绌嶅垎锛屽畾绌嶅垎鐨勬噳(y墨ng)鐢�.

鑰冭│瑕佹眰锛�

1锛�鐞嗚В鍘熷嚱鏁�(sh霉)鐨勬蹇碉紝鎺屾彙涓嶅畾绌嶅垎鍜屽畾绌嶅垎鐨勬蹇碉紟鎺屾彙鍑芥暩(sh霉)鏄粠鏇煎彲绌嶇殑蹇呰姊濅欢锛屾帉鎻″嚱鏁�(sh霉)榛庢浖鍙�绌嶇殑鍒ゅ垾婧�(zh菙n)鍓�.

2锛�鎺屾彙涓嶅畾绌嶅垎鐨勫熀鏈叕寮�锛�鎺屾彙涓嶅畾绌嶅垎鍜屽畾绌嶅垎鐨勬€ц唱(zh矛)鍙婂畾绌嶅垎涓€煎畾鐞�锛屾帉鎻℃彌鍏冪⿳鍒嗘硶鑸囧垎閮�绌嶅垎娉曪紟

3锛庢帉鎻℃湁鐞嗗嚱鏁�(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)鏈夌悊寮忓拰绨″柈鐒＄悊鍑芥暩(sh霉)鐨勭⿳鍒嗭紟

4锛庣悊瑙ｇ⿳鍒嗚畩涓婇檺鐨勫嚱鏁�(sh霉)锛屾渻姹傚畠鐨勫皫(d菐o)鏁�(sh霉)锛屾帉鎻＄墰闋擄紞钀婂竷灏艰尐鍏紡锛庣悊瑙ｅ畾绌嶅垎鐨勮繎浼艰▓绠�.

5锛庣悊瑙ｅ弽甯哥⿳鍒嗙殑姒傚康鍜屾€ц唱(zh矛)锛屾帉鎻″垽鏂峰唬缇╃⿳鍒嗘敹鏂傝垏鍚︾殑鏂规硶锛屾渻瑷堢畻涓€浜涚啊鍠殑寤ｇ京绌嶅垎锛�

6锛庢帉鎻＄敤瀹氱⿳鍒嗚〃閬�(d谩)鍜岃▓绠椾竴浜涘咕浣曢噺鑸囩墿鐞嗛噺(骞抽潰鍦栧舰鐨勯潰绌嶃€佸钩闈㈡洸绶氱殑寮ч暦銆佹棆杞�(zhu菐n)楂旂殑楂旂⿳鍙婂伌(c猫)闈㈢⿳銆佸钩琛屾埅闈㈤潰绌嶇偤宸茬煡鐨勭珛楂旈珨绌�,鍙婂姛銆佸紩鍔�銆佸鍔涖€佽唱(zh矛)蹇�銆佸舰蹇冪瓑)鍙婂嚱鏁�(sh霉)鐨勫钩鍧囧€硷紟

鍏�銆佺劇绐礆鏁�(sh霉)

鑰冭│鍏�(n猫i)瀹�:锛堜竴锛夊父鏁�(sh霉)闋呯礆鏁�(sh霉)锛氭敹鏂傝垏鐧�(f膩)鏁ｇ殑姒傚康锛屾敹鏂傜礆鏁�(sh霉)鐨勫拰鐨勬蹇碉紝绱氭暩(sh霉)鐨勫熀鏈€ц唱(zh矛)鑸囨敹鏂傜殑蹇呰姊濅欢锛屽咕浣曠礆鏁�(sh霉)鑸囷紝p绱氭暩(sh霉)鍙婂叾鏀舵杺鎬�锛屾闋呯礆鏁�(sh霉)鏀舵杺鎬х殑鍒ゅ垾娉曪紝浜ら尟绱氭暩(sh霉)鑸囪悐甯冨凹鑼ㄥ畾鐞�锛屼换鎰忛爡绱氭暩(sh霉)鐨勭禃灏嶆敹鏂傝垏姊濅欢鏀舵杺.锛堜簩锛夊嚱鏁�(sh霉)闋呯礆鏁�(sh霉)锛氭敹鏂傚煙銆佸拰鍑芥暩(sh霉)銆佷竴鑷存敹鏂傛蹇�锛屽嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鐨勪竴鑷存敹鏂傚垽鍒ユ硶銆佸拰鍑芥暩(sh霉)鐨勫垎鏋愭€ц唱(zh矛)(閫ｇ簩(x霉)鎬�銆佸彲寰€у拰鍙⿳鎬�锛涢€愰爡姹傛サ闄�銆佹眰寰垎鍜岄€愰爡姹傜⿳鍒�),锛堜笁锛夊啰绱氭暩(sh霉)锛氬啰绱氭暩(sh霉)鍙婂叾鏀舵杺鍗婂緫銆佹敹鏂傚崁(q奴)闁擄紙鎸囬枊鍗€(q奴)闁擄級鍜屾敹鏂傚煙锛屽啰绱氭暩(sh霉)鐨勫拰鍑芥暩(sh霉)锛屽啰绱氭暩(sh霉)鍦ㄥ叾鏀舵杺鍗€(q奴)闁撳収(n猫i)鐨勫熀鏈€ц唱(zh矛)锛岀啊鍠啰绱氭暩(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勬眰娉�锛�鍒濈瓑鍑芥暩(sh霉)鐨勫啰绱氭暩(sh霉)灞曢枊寮�.锛堝洓锛変笁瑙掔礆鏁�(sh霉)鑸囧嚱鏁�(sh霉)鐨勫倕閲岃憠锛團ourier锛夌礆鏁�(sh霉)锛�2谢-鍛ㄦ湡鍑芥暩(sh霉)鐨勫倕閲岃憠绯绘暩(sh霉)鑸囧倕閲岃憠绱氭暩(sh霉)锛岄粠鏇煎紩鐞�锛岃矟濉炵埦涓嶇瓑寮�锛屽倕閲岃憠绱氭暩(sh霉)鏀舵杺鐨勭媱灏�(Dini)鍒ゅ垾娉�銆佺媱鍒╁厠闆�(Dirichlet)鍒ゅ垾娉�锛屽倕閲岃憠绱氭暩(sh霉)鐨勬敹鏂傚畾鐞�锛�2l(l>0)-鍛ㄦ湡鍑芥暩(sh霉)鍑芥暩(sh霉)鐨勫倕閲岃憠绱氭暩(sh霉)锛屾寮︾礆鏁�(sh霉)鍜屼綑寮︾礆鏁�(sh霉).

鑰冭│瑕佹眰锛�

1锛庣悊瑙ｅ父鏁�(sh霉)闋呯礆鏁�(sh霉)鏀舵杺銆佺櫦(f膩)鏁ｄ互鍙婃敹鏂傜礆鏁�(sh霉)鐨勫拰鐨勬蹇�锛屾帉鎻＄礆鏁�(sh霉)鐨勫熀鏈€ц唱(zh矛)鍙婃敹鏂傜殑蹇呰姊濅欢.

2锛庢帉鎻″咕浣曠礆鏁�(sh霉)鑸嘰,$p$绱氭暩(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁ｇ殑姊濅欢.

3锛庢帉鎻℃闋呯礆鏁�(sh霉)鏀舵杺鎬х殑鏌タ鍒ゅ垾婧�(zh菙n)鍓囥€佹瘮杓冨垽鍒ユ硶銆佹瘮鍊煎垽鍒ユ硶銆佹牴鍊煎垽鍒ユ硶銆佹媺姣�(Raabe)鍒ゅ垾娉�銆�绌嶅垎鍒ゅ垾娉曠瓑.

4锛庢帉鎻′氦閷礆鏁�(sh霉)鐨勮悐甯冨凹鑼ㄥ垽鍒ユ硶.

5锛�鎺屾彙浠绘剰闋呯礆鏁�(sh霉)绲曞皪鏀舵杺鑸囨浠舵敹鏂傜殑姒傚康銆佺禃灏嶆敹鏂傝垏鏀舵杺鐨勯棞(gu膩n)绯诲拰绲曞皪鏀舵杺绱氭暩(sh霉)鐨勪箻绌�.

6锛�鎺屾彙鐙勫埄鍏嬮浄鍒ゅ垾娉曞拰闃胯矟鐖惧垽鍒ユ硶.

7锛�鐞嗚В鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勬敹鏂傚煙銆佸拰鍑芥暩(sh霉)鐨勬蹇靛強鎬ц唱(zh矛).

8锛�鎺屾彙鍒ゅ垾鍑芥暩(sh霉)鍒楀強鍑芥暩(sh霉)闋呯礆鏁�(sh霉)涓€鑷存敹鏂傝垏鍚︾殑鏂规硶(鏌タ婧�(zh菙n)鍓�銆佸劒(y艒u)绱氭暩(sh霉)鍒ゅ垾娉�銆佺媱鍒╁厠闆峰垽鍒ユ硶銆侀樋璨�鐖惧垽鍒ユ硶鍜岃开灏煎垽鍒ユ硶绛�)锛屾帉鎻″嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勫垎鏋愭€ц唱(zh矛).

9锛庣悊瑙ｅ啰绱氭暩(sh霉)鏀舵杺鍗婂緫鐨勬蹇�銆佸苟鎺屾彙鍐礆鏁�(sh霉)鐨勬敹鏂傚崐寰�銆佹敹鏂傚崁(q奴)闁撳強鏀舵杺鍩熺殑姹傛硶.

10锛庣悊瑙ｅ啰绱氭暩(sh霉)鍦ㄥ叾鏀舵杺鍗€(q奴)闁撳収(n猫i)鐨勫熀鏈€ц唱(zh矛)(鍜屽嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�銆侀€愰爡姹傚皫(d菐o)鍜岄€愰爡绌嶅垎)锛屾渻姹備竴浜涘啰绱氭暩(sh霉)鍦�鏀舵杺鍗€(q奴)闁撳収(n猫i)鐨勫拰鍑芥暩(sh霉)锛屽苟鏈冪敱姝ゆ眰鍑烘煇浜涙暩(sh霉)闋呯礆鏁�(sh霉)鐨勫拰.

11锛庣悊瑙ｅ嚱鏁�(sh霉)灞曢枊鐐烘嘲鍕掔礆鏁�(sh霉)鐨勫厖鍒嗗繀瑕佹浠�.

12锛庢帉鎻″咕鍊嬪熀鏈垵绛夊嚱鏁�(sh霉)ex,ln(1+x),sinx,cosx,(1+x)伪鐨勯亥鍏嬪嫗鏋�(Maclaurin)灞曢枊寮�锛�鏈冪敤瀹冨€戝皣涓€浜涚啊鍠嚱鏁�(sh霉)闁撴帴灞曢枊鎴愬啰绱氭暩(sh霉).

13锛庣悊瑙ｆ浜ゅ嚱鏁�(sh霉)绯汇€佸倕閲岃憠绯绘暩(sh霉)鍙婂倕閲岃憠绱氭暩(sh霉)鐨勬蹇�.鎺屾彙榛庢浖寮曠悊锛屽眬閮ㄥ寲瀹氱悊锛岃矟濉炵埦涓嶇瓑寮�.鎺屾彙鍌呴噷钁夌礆鏁�(sh霉)鐨勭媱灏�(Dini)鍒ゅ垾娉�銆佺媱鍒╁厠闆峰垽鍒ユ硶鍙婃敹鏂傚畾鐞�.

14.鏈冨皣瀹氱京鍦ㄩ枆鍗€(q奴)闁揫-l,l)涓婄殑榛庢浖鍙⿳鍑芥暩(sh霉)寤舵嫇鎴愬懆鏈熺偤2l鐨勫嚱鏁�(sh霉)骞跺睍闁嬪叾鍌呴噷钁夌礆鏁�(sh霉)锛屾渻灏囧畾缇�鍦�[0,l)涓婄殑鍑芥暩(sh霉)灞曢枊鐐烘寮︾礆鏁�(sh霉)鑸囦綑寮︾礆鏁�(sh霉)锛屾渻瀵嚭鍌呴噷钁夌礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勮〃閬�(d谩)寮�.

涓�銆佸鍏冨嚱鏁�(sh霉)寰垎瀛�(xu茅)

鑰冭│鍏�(n猫i)瀹�锛氬鍏冨嚱鏁�(sh霉)鐨勬蹇�锛屼簩鍏冨嚱鏁�(sh霉)鐨勫咕浣曟剰缇�锛屽鍏冨嚱鏁�(sh霉)鐨勬サ闄愯垏閫ｇ簩(x霉)鐨勬蹇�锛屽鍏冨嚱鏁�(sh霉)妤甸檺瀛樺湪鑸囧惁鐨勫垽鏂�锛屼簩鍏冨嚱鏁�(sh霉)鐨勭疮娆℃サ闄愶紝鏈夌晫闁夊崁(q奴)鍩熶笂澶氬厓閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛屽鍏冨嚱鏁�(sh霉)鐨勫亸灏�(d菐o)鏁�(sh霉)鍜屽叏寰垎銆佷簩闅庝箖鑷虫洿楂橀殠鍋忓皫(d菐o)鏁�(sh霉)锛屽叏寰垎瀛樺湪鐨勫繀瑕佹浠跺拰鍏呭垎姊濅欢锛岄毐鍑芥暩(sh霉)瀛樺湪瀹氱悊锛屽弽鍑芥暩(sh霉)瀛樺湪瀹氱悊锛屽鍏冨京(f霉)鍚堝嚱鏁�(sh霉)銆侀毐鍑芥暩(sh霉)鐨勬眰灏�(d菐o)娉�銆佷簩闅庡皫(d菐o)鏁�(sh霉)锛屾柟鍚�?q奴)顫�?sh霉)鍜屾搴�锛岀┖闁撴洸绶氱殑鍒囩窔鍜屾硶骞抽潰锛屾洸闈㈢殑鍒囧钩闈㈠拰娉曠窔锛屼簩鍏�鍑芥暩(sh霉)鐨勪簩闅庢嘲鍕掑叕寮�锛屽鍏冨嚱鏁�(sh霉)鐨勬サ鍊煎拰姊濅欢妤靛€硷紝澶氬厓鍑芥暩(sh霉)鐨勬渶澶у€�銆佹渶灏忓€煎強鍏剁啊鍠噳(y墨ng)鐢�.

鑰冭│瑕佹眰锛�

1锛庣悊瑙ｅ鍏冨嚱鏁�(sh霉)鐨勬蹇�锛岀悊瑙ｄ簩鍏冨嚱鏁�(sh霉)鐨勫咕浣曟剰缇�.

2锛庣悊瑙ｅ鍏冨嚱鏁�(sh霉)鐨勬サ闄愯垏閫ｇ簩(x霉)鐨勬蹇典互鍙婃湁鐣岄枆鍗€(q奴)鍩熶笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛).

3锛庣悊瑙ｅ鍏冨嚱鏁�(sh霉)鍋忓皫(d菐o)鏁�(sh霉)鍜屽叏寰垎鐨勬蹇�锛屾渻姹傚叏寰垎锛岀悊瑙ｅ叏寰垎瀛樺湪鐨勫繀瑕佹浠跺拰鍏呭垎姊濅欢锛岀悊瑙ｅ叏寰�鍒嗗舰寮忕殑涓嶈畩鎬�.

4锛庣悊瑙ｆ柟鍚�?q奴)顫�?sh霉)鑸囨搴︾殑姒傚康锛屽苟鎺屾彙鍏惰▓绠楁柟娉�.

5锛庢帉鎻″鍏冨京(f霉)鍚堝嚱鏁�(sh霉)涓€闅庛€佷簩闅庡亸灏�(d菐o)鏁�(sh霉)鐨勬眰娉�锛屼互鍙婁竴浜涚啊鍠嚱鏁�(sh霉)鐨勯珮闅庡亸灏�(d菐o)鏁�(sh霉)鐨勬眰娉�.

6锛庣悊瑙ｉ毐鍑芥暩(sh霉)瀛樺湪瀹氱悊锛屾渻姹傚鍏冮毐鍑芥暩(sh霉)鐨勪竴闅庛€佷簩闅庡亸灏�(d菐o)鏁�(sh霉)浠ュ強涓€浜涚啊鍠嚱鏁�(sh霉)鐨勯珮闅庡亸灏�(d菐o)鏁�(sh霉).

7锛庣悊瑙ｇ┖闁撴洸绶氱殑鍒囩窔鍜屾硶骞抽潰鍙婃洸闈㈢殑鍒囧钩闈㈠拰娉曠窔鐨勬蹇碉紝鏈冩眰瀹冨€戠殑鏂圭▼.

8锛庣悊瑙ｅ鍏冨嚱鏁�(sh霉)鐨勬嘲鍕掑叕寮�.

9锛庣悊瑙ｅ鍏冨嚱鏁�(sh霉)妤靛€煎拰姊濅欢妤靛€肩殑姒傚康锛屾帉鎻″鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑蹇呰姊濅欢锛岀悊瑙ｅ鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑鍏�鍒嗘浠�锛屾渻姹傜啊鍠殑澶氬厓鍑芥暩(sh霉)鐨勬サ鍊�锛屾渻鐢ㄦ媺鏍兼湕鏃ヤ箻鏁�(sh霉)娉曟眰姊濅欢妤靛€�锛屾渻姹傜啊鍠鍏冨嚱鏁�(sh霉)鐨勬渶澶у€煎拰鏈€灏忓€硷紝骞舵渻瑙ｆ焙涓€浜涚啊鍠殑鎳�(y墨ng)鐢ㄥ晱椤�.

鍏�銆佸惈鍙冭畩閲忕殑寤ｇ京绌嶅垎

鑰冭│鍏�(n猫i)瀹�锛氬惈鍙冭畩閲忕殑寤ｇ京绌嶅垎鐨勬蹇�锛屽惈鍙冭畩閲忕殑寤ｇ京绌嶅垎涓€鑷存敹鏂傜殑姒傚康锛屽惈鍙冭畩閲忕殑寤ｇ京绌嶅垎鐨勫垎鏋愭€ц唱(zh矛)锛屼竴浜涘惈鍙冭畩閲忕殑寤ｇ京绌嶅垎鐨勮▓绠�.浼界應(Gamma)鍑芥暩(sh霉),璨濆(Beta)鍑芥暩(sh霉).

鑰冭│瑕佹眰锛�

1锛�鎺屾彙甯哥京鍚弮璁婄⿳鍒嗙殑姒傚康銆佸熀鏈€ц唱(zh矛)鍜屽畾鐞�.

2锛�鐞嗚В鍚弮璁婇噺寤ｇ京绌嶅垎鏀舵杺銆佷竴鑷存敹鏂傜殑姒傚康锛屾帉鎻″惈鍙冮噺寤ｇ京绌嶅垎鐨勯瓘鐖炬柉鐗规媺鏂垽鍒ユ硶銆佹煰瑗挎簴(zh菙n)鍓�銆�闃胯矟鐖惧垽鍒ユ硶銆佺媱鍒╁厠闆峰垽鍒ユ硶鍙婅开灏煎垽鍒ユ硶.

3锛�鎺屾彙鍚弮璁婇噺鐨勫唬缇╃⿳鍒嗙殑鍒嗘瀽鎬ц唱(zh矛)(閫ｇ簩(x霉)鎬с€佸彲寰€у拰鍙⿳鎬�)鐨勫畾鐞�.

4锛�鎺屾彙涓€浜涘唬缇╃⿳鍒嗗強鍚弮閲忓唬缇╃⿳鍒嗙殑瑷堢畻.鐞嗚В鍚弮閲忓唬缇╃⿳鍒嗘蹇靛拰鍑芥暩(sh霉)闋呯礆鏁�(sh霉)姒傚康涔嬮枔鐨勯棞(gu膩n)绯�.

5锛�鐞嗚В浼界應鍑芥暩(sh霉)銆佽矟濉斿嚱鏁�(sh霉)鍙婂叾鎬ц唱(zh矛)鍜岄棞(gu膩n)绯�,鐞嗚В鏂壒鏋楀叕寮�.

涔濄€佸鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)

鑰冭│鍏�(n猫i)瀹癸細浜岄噸绌嶅垎鑸囦笁閲嶇⿳鍒嗙殑姒傚康銆佹€ц唱(zh矛)銆佽▓绠楀拰鎳�(y墨ng)鐢�,鍏╅鏇茬窔绌嶅垎鐨勬蹇�銆佹€ц唱(zh矛)鍙婅▓绠楋紝鍏╅鏇茬窔绌嶅垎鐨勯棞(gu膩n)绯伙紝鏍兼灄锛圙reen锛夊叕寮�,骞抽潰鏇茬窔绌嶅垎鑸囪矾寰戠劇闂�(gu膩n)鐨勬浠�锛屼簩鍏冨嚱鏁�(sh霉)鍏ㄥ井鍒嗙殑鍘熷嚱鏁�(sh霉)锛屽叐椤炴洸闈㈢⿳鍒嗙殑姒傚康銆佹€ц唱(zh矛)鍙婅▓绠�锛屽叐椤炴洸闈㈢⿳鍒嗙殑闂�(gu膩n)绯�锛岄珮鏂紙Gauss锛夊叕寮�,鏂墭鍏嬫柉锛圫tokes)鍏紡,鏁ｅ害銆�鏃嬪害鐨勬蹇靛強瑷堢畻,鏇茬窔绌嶅垎鍜屾洸闈㈢⿳鍒嗙殑鎳�(y墨ng)鐢�.

鑰冭│瑕佹眰锛�

1锛庣悊瑙ｉ噸绌嶅垎鐨勬蹇点€佹€ц唱(zh矛).

2锛庢帉鎻′簩銆佷笁閲嶇⿳鍒嗙殑瑷堢畻鏂规硶锛岀壒鍒ユ槸绌嶅垎璁婃彌锛堢洿瑙掑潗妯�(bi膩o)銆佹サ鍧愭(bi膩o)銆佹煴闈㈠潗妯�(bi膩o)銆佺悆闈㈠潗妯�(bi膩o)浠ュ強鍏朵粬绨�鍠殑璁婃彌锛�,鏈冭▓绠椾竴浜涚啊鍠殑閲嶆暩(sh霉)楂樹簬涓夌殑閲嶇⿳鍒�.

3锛庢帉鎻″叐椤炴洸绶氱⿳鍒嗙殑姒傚康銆佹€ц唱(zh矛)鍙婂叐椤炴洸绶氱⿳鍒嗕箣闁撶殑闂�(gu膩n)绯�.

4锛庢帉鎻¤▓绠楀叐椤炴洸绶氱⿳鍒嗙殑鏂规硶.

5锛庢帉鎻℃牸鏋楀叕寮忓苟鏈冮亱鐢ㄥ钩闈㈡洸绶氱⿳鍒嗚垏璺緫鐒￠棞(gu膩n)鐨勬浠�锛屾渻姹備簩鍏冨嚱鏁�(sh霉)鍏ㄥ井鍒嗙殑鍘熷嚱鏁�(sh霉).鎺屾彙鏂墭鍏嬫柉鍏紡骞舵渻閬嬬敤鍏惰▓绠楁洸绶氱⿳鍒�,鏈冮亱鐢ㄦ洸绶氱⿳鍒嗚垏璺緫鐒￠棞(gu膩n)鐨勬浠舵眰涓夊厓鍑芥暩(sh霉)鍏ㄥ井鍒嗙殑鍘熷嚱鏁�(sh霉).

6锛庣悊瑙ｅ叐椤炴洸闈㈢⿳鍒嗙殑姒傚康銆佹€ц唱(zh矛)鍙婂叐椤炴洸闈㈢⿳鍒嗙殑闂�(gu膩n)绯�锛屾帉鎻¤▓绠楀叐椤炴洸闈㈢⿳鍒嗙殑鏂规硶锛屾帉鎻￠珮鏂叕寮�骞舵渻閬嬬敤鍏惰▓绠楁洸闈㈢⿳鍒嗙殑鏂规硶.

7锛庣悊瑙ｆ暎搴﹁垏鏃嬪害鐨勬蹇�锛屽苟鏈冭▓绠�.

8锛庢渻鐢ㄩ噸绌嶅垎銆佹洸绶氱⿳鍒嗗強鏇查潰绌嶅垎姹備竴浜涘咕浣曢噺鑸囩墿鐞嗛噺锛堝钩闈㈠湒褰㈢殑闈㈢⿳銆侀珨绌�銆佹洸闈㈤潰绌�銆佸姬闀�銆�璩�(zh矛)閲忋€佽唱(zh矛)蹇�銆佸舰蹇冦€佽綁(zhu菐n)鍕曟叄閲�銆佸紩鍔涖€佸姛鍙婃祦閲忕瓑锛�.