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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�锛�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
601 鏁�(sh霉)瀛稿垎鏋� 鑰冭│鍩烘湰瑕佹眰
涓€ 瀵︽暩(sh霉)闆嗚垏鍑芥暩(sh霉)
锛�1锛夋帉鎻″鏁�(sh霉)鐨勫熀鏈€ц唱(zh矛)鍜岀⒑鐣屽師鐞嗭紝寤虹珛瀵︽暩(sh霉)闆嗙⒑鐣屾蹇�锛涳紙2锛夌悊瑙ｅ嚱鏁�(sh霉)鐨勬蹇�锛岀啛鎮夎垏鍑芥暩(sh霉)鎬ф厠(t脿i)
鏈夐棞(gu膩n)鐨勪竴浜涘父瑕嬭(sh霉)瑾炪€�
浜� 鏁�(sh霉)鍒楁サ闄�
锛�1锛夌悊瑙ｆ暩(sh霉)鍒楁サ闄愮殑姒傚康 锛�2锛変簡瑙ｆ敹鏂傛暩(sh霉)鍒楃殑鎬ц唱(zh矛)锛岀悊瑙ｆ暩(sh霉)鍒楁敹鏂傛€х殑鍒ゅ垾娉曘€傛帉鎻″苟鏈冭瓑鏄庢敹鏂�
鏁�(sh霉)鍒楁€ц唱(zh矛)銆佹サ闄愮殑鍞竴鎬с€佸柈瑾�(di脿o)鎬�銆佷繚铏熸€у強涓嶇瓑寮忔€ц唱(zh矛)锛涳紙3锛夋帉鎻″苟鏈冭瓑鏄庢敹鏂傛暩(sh霉)鍒楃殑鍥涘墖閬嬬畻瀹氱悊銆�
杩杺鎬у畾鐞嗗強鍠(di脿o)鎬у畾鐞嗭紝骞舵渻鐢ㄩ€欎簺瀹氱悊姹傛煇浜涙敹鏂傛暩(sh霉)鍒楃殑妤甸檺銆�
涓� 鍑芥暩(sh霉)妤甸檺
锛�1锛夋簴纰哄缓绔嬪嚱鏁�(sh霉)妤甸檺(鍖呮嫭鍠伌(c猫)妤甸檺)姒傚康锛岀悊瑙ｅ嚱鏁�(sh霉)妤甸檺鐨勎� 锛嵨� 锛屛� 锛峂 瀹氱京锛涳紙2锛夋帉鎻″嚱鏁�(sh霉)妤�
闄愮殑鍩烘湰鎬ц唱(zh矛)锛氬敮涓€鎬�銆佸眬閮ㄤ繚铏熸€�銆佷笉绛夊紡鎬ц唱(zh矛)浠ュ強鏈夌悊閬嬬畻鎬ц唱(zh矛)绛夛紱(3)鎺屾彙 Heine 瀹氱悊鑸� Cauchy 婧�
鍓�锛�(4)鎺屾彙鍏╁€嬮噸瑕佹サ闄�锛�(5) 鎺屾彙鐒＄灏忥紙澶э級閲忓強鍏堕殠鐨勬蹇�锛屽苟鐢辨姹傚嚭鏌愪簺鍑芥暩(sh霉)鐨勬サ闄�銆�
鍥� 鍑芥暩(sh霉)鐨勯€ｇ簩(x霉)鎬�
锛�1锛夌悊瑙ｅ嚱鏁�(sh霉)鍦ㄤ竴榛為€ｇ簩(x霉)锛堝惈鍠伌(c猫)閫ｇ簩(x霉)锛夌殑瀹氱京锛涳紙2锛夋帉鎻￠€ｇ簩(x霉)鍑芥暩(sh霉)鐨勫眬閮ㄦ€ц唱(zh矛)锛岄€ｇ簩(x霉)鍑芥暩(sh霉)鐨勬湁鐞嗛亱
绠楁€ц唱(zh矛)骞惰兘鍔犱互璀夋槑锛岀啛鎮夊京鍚堝嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬у拰鍙嶅嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�锛�(3) 鐞嗚В鍒濈瓑鍑芥暩(sh霉)鍦ㄥ叾鏈夊畾缇╃殑鍗€(q奴)闁撲笂
閮芥槸閫ｇ簩(x霉)鐨�锛屽苟鑳介亱鐢ㄩ€ｇ簩(x霉)鎬х殑姒傚康浠ュ強閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍔犱互璀夋槑锛岃兘鐔熺反閬嬬敤閫欎竴绲�(ji茅)璜栨眰鍒濈瓑鍑芥暩(sh霉)鐨勬サ
闄�锛�(4)鎺屾彙闁夊崁(q奴)闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勯噸瑕佹€ц唱(zh矛)锛岀悊瑙ｅ叾骞句綍鎰忕京锛屽苟鑳藉湪鍚勭ó鏈夐棞(gu膩n)鐨勫叿楂斿晱椤屼腑鍔犱互閬嬬敤銆�
浜� 灏庢暩(sh霉)鍜屽井鍒�
锛�1锛夋帉鎻″皫鏁�(sh霉)鑸囧井鍒嗘蹇�锛屼簡瑙ｅ畠鍊戠殑骞句綍鎰忕京锛涳紙2锛夎兘鐔熺反閬嬬敤灏庢暩(sh霉)鐨勯亱绠楁€ц唱(zh矛)鍜屾眰灏庢硶鍓囨眰鍑芥暩(sh霉)
鐨勫皫鏁�(sh霉)锛堢壒鍒ユ槸姹傚京鍚堝嚱鏁�(sh霉)鐨勫皫鏁�(sh霉)锛�锛涳紙3锛夌悊瑙ｅ柈鍋�(c猫)灏庢暩(sh霉)锛屽彲灏庢€у拰閫ｇ簩(x霉)鎬х殑闂�(gu膩n)绯伙紝楂橀殠灏庢暩(sh霉)鐨勬眰娉�锛涳紙4锛�
浜嗚В灏庢暩(sh霉)鐨勫咕浣曟剰缇�锛屽井鍒嗗湪杩戜技瑷堢畻涓殑鎳�(y墨ng)鐢�銆�
鍏� 寰垎涓€煎畾鐞嗗強鍏舵噳(y墨ng)鐢�
锛�1锛夌悊瑙ｅ苟鎺屾彙涓€煎畾鐞嗙殑骞句綍鎰忕京銆傦紙2锛夋帉鎻″父鐢ㄧ殑涓€浜� Taylor 鍏紡锛涙帉鎻� Taylor 鍏紡涓殑 Lagrange
浣欓爡鍜� Peano 浣欓爡銆傦紙3锛夎兘闈堟椿閬嬬敤 L鈥橦ospital 娉曞墖铏曠悊涓嶅畾寮忔サ闄�銆傦紙4锛夋帉鎻″埄鐢ㄥ皫鏁�(sh霉)鎬ц唱(zh矛)瑷庤珫鍑芥暩(sh霉)
鎬ц唱(zh矛)鐨勬柟娉�銆傦紙5锛夋帉鎻＄敤寰垎瀛哥煡璀樿В姹烘噳(y墨ng)鐢ㄥ晱椤岀殑鍩烘湰鑳藉姏锛屽鍑芥暩(sh霉)鍠(di脿o)鎬х殑鍒ゅ畾锛屼笉绛夊紡鐨勮瓑鏄�锛�
妤甸檺鍟忛绛夈€�
涓� 瀵︽暩(sh霉)鐨勫畬鍌欐€�
锛�1锛夌悊瑙ｅ埢鍔冨鏁�(sh霉)瀹屽倷鎬х殑纰虹晫瀹氱悊銆佸柈瑾�(di脿o)鏈夌晫瀹氱悊銆侀枆鍗€(q奴)闁撳瀹氱悊銆佽嚧瀵嗘€у畾鐞�銆佹湁鐣岃钃嬪畾鐞�銆�
Cauchy 鏀舵杺鍘熺悊绛夊咕鍊嬬瓑鍍瑰懡椤岋紝骞朵笖鏈冪敤纰虹晫瀹氱悊璀夋槑涓€浜涘晱椤�锛�(2)鏈冪敤鈥滈枆鍗€(q奴)闁撳瀹氱悊鈥濈殑浜屽垎娉�
璀夋槑锛涒€滆嚧瀵嗘€у畾鐞嗏€濈殑鎶藉瓙鍒楁硶璀夋槑锛屽苟鑳借瓑鏄庡叾瀹冪殑涓€浜涘畾鐞�锛�(3)鏈冪敤鍠(di脿o)鏈夌晫瀹氱悊鑸囨暩(sh霉)鍒楁サ闄愮殑
Cauchy 鏀舵杺鍘熺悊渚嗚瓑鏄庝竴浜涙サ闄愬瓨鍦ㄨ垏涓嶅瓨鍦紱(4)鎺屾彙閬嬬敤鍩烘湰瀹氱悊璀夋槑闁夊崁(q奴)闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛岀悊
瑙ｅ叾璀夋槑鐨勬€濇兂鏂规硶锛�(5)浜嗚В鏁�(sh霉)鍒楃殑涓婃サ闄愬拰涓嬫サ闄愮殑姒傚康鍙婂叾鑸囨暩(sh霉)鍒楁サ闄愮殑闂�(gu膩n)绯�銆�
鍏� 涓嶅畾绌嶅垎
(1) 鎺屾彙鍘熷嚱鏁�(sh霉)鑸囦笉瀹氱⿳鍒嗙殑姒傚康锛�(2) 鐔熺反鎺屾彙骞惰兘闈堟椿鎳�(y墨ng)鐢ㄥ熀鏈⿳鍒嗗叕寮�锛�(3) 鐔熺反鎺屾彙婀婂井鍒�
娉曪紱锛�4锛夋帉鎻℃彌鍏冪⿳鍒嗘硶锛岀壒鍒ヨ兘杓冪啛绶村湴浣跨敤涓夎浠ｆ彌銆佹牴寮忎唬鎻涳紱锛�5锛夋帉鎻＄敤鍒嗛儴绌嶅垎娉曞寲涓嶅畾绌�
鍒嗘垚浠ｆ暩(sh霉)鏂圭▼锛屽緸鑰屾眰瑙ｄ笉瀹氱⿳鍒嗙殑鏂规硶锛涳紙7锛夋帉鎻￠儴鍒嗗垎寮忔硶瑙ｆ湁鐞嗗嚱鏁�(sh霉)鐨勪笉瀹氱⿳鍒嗙殑鏂规硶锛涳紙8锛夎兘
闈堟椿鍦拌檿鐞嗕笁瑙掑嚱鏁�(sh霉)鐨勪笉瀹氱⿳鍒�銆�
涔� 瀹氱⿳鍒�
(1)鐞嗚В瀹氱⿳鍒嗙殑瀹氱京鍙婂叾骞句綍鎰忕京鍜岀墿鐞嗘剰缇�锛涳紙2锛変簡瑙ｉ仈 Darboux 涓�銆佷笅鍜岀殑鎬ц唱(zh矛)锛涳紙3锛夋帉鎻�
鍙⿳鐨勫厖瑕佹浠讹紝骞惰兘鐢ㄤ互璀夋槑涓夐鍑芥暩(sh霉)鐨勫彲绌嶆€э紱锛�4锛夋帉鎻″畾绌嶅垎鐨勬€ц唱(zh矛)锛屽苟鑳介€茶绨″柈鐨勬帹鐞嗚珫璀�
鍜岃▓绠楋紱锛�5锛夋帉鎻＄⿳鍒嗕笂闄愬嚱鏁�(sh霉)鐨勬€ц唱(zh矛)锛屽苟鑳藉湪瑙ｉ涓噳(y墨ng)鐢ㄩ€欏€嬫€ц唱(zh矛)锛涳紙6锛夋帉鎻� Newton锛峀eibniz 鍏紡锛�
鑳界啛绶村湴閫茶绌嶅垎瑷堢畻锛涳紙7锛夎兘缍滃悎閬嬬敤鎻涘厓娉�銆佸垎閮ㄧ⿳鍒嗘硶鍜屽畾绌嶅垎鐨勬€ц唱(zh矛)閫茶瀹氱⿳鍒嗙殑瑷堢畻銆�
鍗� 瀹氱⿳鍒嗙殑鎳�(y墨ng)鐢�
锛�1锛夋帉鎻″钩闈㈠湒褰㈢殑闈㈢⿳銆佸钩闈㈡洸绶氱殑寮ч暦锛�(2) 鎺屾彙宸茬煡骞宠鎴潰闈㈢⿳鐨勭珛楂旂殑楂旂⿳銆佹棆杞�(zhu菐n)鏇查潰鐨勯潰
绌�锛�(3) 鐞嗚В寰厓娉�锛�(4) 浜嗚В绌嶅垎鍦ㄧ墿鐞嗕腑鐨勬煇浜涙噳(y墨ng)鐢ㄣ€佸畾绌嶅垎鐨勮繎浼艰▓绠�銆�
鍗佷竴 鍙嶅父绌嶅垎
锛�1锛夌悊瑙ｅ叐绋鍨嬪弽甯哥⿳鍒嗙殑瀹氱京銆佹€ц唱(zh矛)锛涳紙2锛夋渻鐢ㄥ畾缇╄垏鎬ц唱(zh矛)瑷堢畻鍏╃ó鍙嶅父绌嶅垎鍊�锛涳紙3锛夋帉鎻�
鍏╃ó鍙嶅父绌嶅垎鏀舵杺鐨勫垽鏂锋硶锛氭瘮杓冨垽鍒ユ硶銆丆auchy 鍒ゅ垾娉�銆丄bel 鍒ゅ垾娉曞拰 Dirichlet 鍒ゅ垾娉曚締鍒ゅ垾绌嶅垎
鏀舵杺锛涳紙4锛夎兘鐢ㄦ瘮杓冨垽鍒ユ硶銆丆auchy 鍒ゅ垾娉曘€丆auchy 鏀舵杺鍘熺悊鍒ゅ垾鍙嶅父绌嶅垎鐨勬杺鏁ｆ€�锛涳紙5锛夋帉鎻″叐椤�
绌嶅垎绲曞皪鏀舵杺鍜屾浠舵敹鏂傛蹇�銆�
鍗佷簩 鏁�(sh霉)闋呯礆鏁�(sh霉)
锛�1锛夌悊瑙ｆ暩(sh霉)闋呯礆鏁�(sh霉)鍜屾暩(sh霉)鍒楁サ闄愮殑闂�(gu膩n)绯�锛屾渻鐢ㄢ€� -N鈥濊獮瑷€琛ㄨ堪绱氭暩(sh霉)鏀舵杺鎴栫櫦(f膩)鏁�銆傦紙2锛夋帉鎻� Cauchy 鏀�
鏂傚師鐞�锛岃兘鐢� Cauchy 鍘熺悊璀夋槑绱氭暩(sh霉)鏀舵杺鑸囩櫦(f膩)鏁�锛岀啛绶存帉鎻＄礆鏁�(sh霉)鐨勫繀瑕佹浠躲€傦紙3锛夋帉鎻℃闋呯礆鏁�(sh霉)鏂傛暎鐨勬瘮
杓冨師鍓�锛孋auchy 鍒ゅ垾娉�锛岄仈鏈楄矟鐖惧垽鍒ユ硶锛孋auchy 绌嶅垎鍒ゅ垾娉�銆傦紙4锛夋帉鎻� Leibniz 鍒ゅ垾娉�锛孉bel 鍒ゅ垾娉�
鍜� Dirichlet 鍒ゅ垾娉�锛屽垽鏂风礆鏁�(sh霉)鐨勬浠舵敹鏂�銆傦紙5锛夌悊瑙ｇ礆鏁�(sh霉)鏀舵杺銆佺禃灏嶆敹鏂�銆佹浠舵敹鏂備箣闁撶殑闂�(gu膩n)绯�锛屼簡
瑙ｇ禃灏嶆敹鏂傚拰姊濅欢鏀舵杺绱氭暩(sh霉)鐨勪富瑕佹€ц唱(zh矛)锛屾渻灏嶅惈鏈変竴鍊嬪弮鏁�(sh霉)鐨勭礆鏁�(sh霉)纰哄畾鍏剁禃灏嶆敹鏂傚煙鍜屾浠舵敹鏂傚煙銆�
鍗佷笁 鍑芥暩(sh霉)鍒楄垏鍑芥暩(sh霉)闋呯礆鏁�(sh霉)
锛�1锛夎兘鐢ㄦ暩(sh霉)闋呯礆鏁�(sh霉)鏀舵杺鍒ゅ垾娉曡◣璜栧嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鐨勬敹鏂傛€э紝鐮旂┒鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鑸囧嚱鏁�(sh霉)鍒楁敹鏂傚煙锛涳紙2锛夌悊
瑙ｄ竴鑷存敹鏂傛蹇碉紝鑳藉緸瀹氱京鍑虹櫦(f膩)璀夋槑鍑芥暩(sh霉)鍒楁垨鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勪竴鑷存敹鏂傚拰闈炰竴鑷存敹鏂�锛涳紙3锛夋帉鎻� Cauchy 鏀�
鏂傚師鐞�锛屽苟鑳芥噳(y墨ng)鐢ㄤ簬鍒ゅ垾涓€鑷存敹鏂傝垏闈炰竴鑷存敹鏂�锛涳紙4锛夋帉鎻″悇绋垽鍒ユ硶锛岀爺绌跺嚱鏁�(sh霉)鍒楁垨鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勪竴
鑷存敹鏂傛€э紱锛�5锛夊埄鐢ㄤ竴鑷存敹鏂傛€ц瓑鏄庢サ闄愬嚱鏁�(sh霉)鍜屽嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�銆佸彲寰€ц垏鍙⿳鎬�銆傚弽閬庝締锛屽緸鍜屽嚱鏁�(sh霉)鎴�
妤甸檺鍑芥暩(sh霉)鐨勫垎鏋愭€ц唱(zh矛)鐮旂┒鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鎴栧嚱鏁�(sh霉)鍒楃殑涓€鑷存敹鏂傛€э紙Dini 瀹氱悊锛�銆�
鍗佸洓 鍐礆鏁�(sh霉)
锛�1锛夋帉鎻℃眰鍐礆鏁�(sh霉)鐨勬敹鏂傚崐寰戠殑鏂规硶锛岀⒑瀹氭敹鏂傚崁(q奴)闁撶榛炵殑鏂傛暎鎬�锛涳紙2锛夋帉鎻″啰绱氭暩(sh霉)鍦ㄦ敹鏂傚崁(q奴)闁撳収(n猫i)鐨�
鍏�(n猫i)闁変竴鑷存敹鏂傛€�锛屽啰绱氭暩(sh霉)鍜屽嚱鏁�(sh霉)鐨勫垎鏋愭€ц唱(zh矛)锛涳紙3锛夌敤绛夋瘮鏁�(sh霉)鍒楁眰鍜屽叕寮�锛屾垨閫氶亷鍒╃敤鍐礆鏁�(sh霉)閫愰爡姹傚皫閫�
闋呮眰绌嶇殑鎬ц唱(zh矛)锛屽彲鍖栫偤绛夋瘮鏁�(sh霉)鍒楁眰鍜屾眰鍑烘煇浜涘啰绱氭暩(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勫垵绛夊舰寮忋€�
鍗佷簲 Fourier 绱氭暩(sh霉)
锛�1锛変簡瑙ｄ笁瑙掔礆鏁�(sh霉)鐨勬浜ゆ€�锛屽苟鑳藉湪鏌愪簺绌嶅垎瑷堢畻涓姞浠ユ噳(y墨ng)鐢�锛涳紙2锛夋渻瑷堢畻鍙⿳鍑芥暩(sh霉)鐨� Fourier 绯绘暩(sh霉)锛�
锛�3锛夋帉鎻℃敹鏂傚畾鐞嗙殑姊濅欢鑸囩祼(ji茅)璜�锛屾渻鐢ㄦ敹鏂傚畾鐞嗗皣浠� 2 鐐哄懆鏈熺殑鍑芥暩(sh霉)灞曟垚 Fourier 绱氭暩(sh霉)锛涳紙4锛夋帉鎻″銆�
鍋跺嚱鏁�(sh霉)鐨� Fourier 绱氭暩(sh霉)灞曢枊鐨勭壒榛�锛屾渻灏囧畾缇╁湪鏌愬崁(q奴)闁撲笂鐨勫嚱鏁�(sh霉)鎸夎姹傚睍鎴愭寮︾礆鏁�(sh霉)鎴栦綑寮︾礆鏁�(sh霉)锛涳紙5锛�
鑳藉埄鐢� Fourier 灞曢枊姹備竴浜涚啊鍠礆鏁�(sh霉)鐨勫拰锛涳紙6锛変簡瑙ｉ粠鏇硷紞鍕掕矟鏍煎紩鐞嗙殑鍏�(n猫i)瀹瑰強瀹冪殑涓€浜涚啊鍠噳(y墨ng)鐢�銆�
鍗佸叚 澶氬厓鍑芥暩(sh霉)鐨勬サ闄愬拰閫ｇ簩(x霉)
锛�1锛夋帉鎻″钩闈㈤粸闆�銆侀劙鍩熴€佷腑蹇冮劙鍩熺殑琛ㄧず娉�锛涳紙2锛夋渻鍒ゅ垾涓€鑸钩闈㈤粸闆嗘槸闁嬮泦閭勬槸闁夐泦锛屾湁鐣岄倓鏄�
鐒＄晫锛屾槸鍚︽槸鍗€(q奴)鍩熴€侀枊鍗€(q奴)鍩�銆侀枆鍗€(q奴)鍩燂紝鏈冨鍑哄叾閭婄晫锛涳紙3锛変簡瑙ｅ钩闈㈤粸闆嗙殑鐭╁舰濂楀畾鐞�銆佽仛榛炲畾鐞�銆佹湁
闄愯钃嬪畾鐞嗭紝鐞嗚В瀹冨€戣垏鐩寸窔涓婃湁闂�(gu膩n)瀹氱悊鐩镐簰闂�(gu膩n)绯�锛涳紙4锛夋帉鎻″钩闈㈤粸鍒楁敹鏂傜殑蔚 -N 瀹氱京鍙婃煰瑗挎敹鏂傚師鐞�锛�
锛�5锛夌悊瑙ｄ簩鍏冨嚱鏁�(sh霉)鐨勬蹇靛強骞句綍鎰忕京锛屽苟鑳芥帹寤ｅ埌澶氬厓鍑芥暩(sh霉)锛涙渻纰哄畾涓€鑸簩鍏冨嚱鏁�(sh霉)鐨勫畾缇╁煙鍙婇€ｇ簩(x霉)鑼冨湇锛�
锛�6锛夌悊瑙ｄ簩鍏冨嚱鏁�(sh霉)妤甸檺蔚 -N 瀹氱京锛屾渻渚濆畾缇╄瓑鏄庝笉澶京闆滅殑浜岄噸妤甸檺锛涳紙7锛夋帉鎻＄疮娆℃サ闄愭蹇�锛岃兘閫氶亷
鍏烽珨鍙嶄緥鍒嗘瀽浜岄噸妤甸檺鑸囩疮娆℃サ闄愮殑闂�(gu膩n)绯�锛涳紙8锛夌悊瑙ｄ簩鍏冨嚱鏁�(sh霉)閫ｇ簩(x霉)鎬у強涓€鑷撮€ｇ簩(x霉)鎬х殑瀹氱京锛屾渻渚濆畾缇╄◣
璜栭€ｇ簩(x霉)鎬у強鏈夐棞(gu膩n)鐨勭啊鍠懡椤岋紝鐞嗚В鏈夌晫闁夊煙涓婇€ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)銆�
鍗佷竷 澶氬厓鍑芥暩(sh霉)寰垎瀛�
锛�1锛夋帉鎻″亸灏庢暩(sh霉)鑸囧叏寰垎鐨勫畾缇�銆佸京鍚堝嚱鏁�(sh霉)鐨勬眰灏庢硶鍓囷紱锛�2锛夋帉鎻″彲寰殑姊濅欢銆佸京鍚堝嚱鏁�(sh霉)鐨勫叏寰垎銆�
涓€闅庡叏寰垎褰㈠紡涓嶈畩鎬�銆侀珮闅庡亸灏庢暩(sh霉)銆佷腑鍊煎畾鐞嗐€乀aylor 鍏紡锛涳紙3锛夌悊瑙ｅ彲寰€у咕浣曟剰缇╁強鎳�(y墨ng)鐢ㄣ€佹サ鍊煎晱
椤�锛涳紙4锛変簡瑙ｆ柟鍚�?q奴)顫�?sh霉)鑸囨搴︺€�
鍗佸叓 闅卞嚱鏁�(sh霉)瀹氱悊鍙婂叾鎳�(y墨ng)鐢�
锛�1锛夌悊瑙ｉ毐鍑芥暩(sh霉)瀹氱悊鐨勬湁闂�(gu膩n)姒傚康锛屽強闅卞嚱鏁�(sh霉)瀛樺湪鐨勬浠�锛涳紙2锛変簡瑙ｉ毐鍑芥暩(sh霉)绲勶紝鍙嶅嚱鏁�(sh霉)绲勭殑鏈夐棞(gu膩n)姒傚康锛�
鐞嗚В浜屽厓闅卞嚱鏁�(sh霉)绲勫瓨鍦ㄧ殑姊濅欢锛屼簡瑙ｅ弽鍑芥暩(sh霉)绲勫瓨鍦ㄧ殑姊濅欢锛涳紙3锛夋帉鎻￠毐鍑芥暩(sh霉)鐨勫井鍒嗘硶鍦ㄥ咕浣曟柟闈㈢殑鎳�(y墨ng)鐢紝
鏈冩妸瀵﹂殯鍟忛鎶借薄鐐烘浠舵サ鍊煎苟浜堜互瑙ｆ焙銆�
鍗佷節 鍚弮閲忕⿳鍒�
锛�1锛夌悊瑙ｅ惈鍙冭畩閲忓父瑕嬬⿳鍒嗕綔鐐哄弮閲忕殑鍑芥暩(sh霉)锛屾帉鎻″畠鐨勯€ｇ簩(x霉)鎬�銆佸彲寰€у拰鍙⿳鎬х殑姊濅欢锛屽苟鑳芥噳(y墨ng)鐢ㄩ€�
浜涙浠惰◣璜栦竴浜涘惈鍙冮噺甯歌绌嶅垎鐨勬湁闂�(gu膩n)鎬ц唱(zh矛)锛涳紙2锛夌悊瑙ｅ惈鍙冮噺寤ｇ京绌嶅垎鍙婁竴鑷存敹鏂傛蹇�锛屾渻寰炲畾缇╂垨 Cauchy
鏀舵杺鍘熺悊鍑虹櫦(f膩)璀夋槑绌嶅垎鐨勪竴鑷存敹鏂傛€ф垨闈炰竴鑷存敹鏂傛€э紱锛�3锛夋帉鎻″拰鍒╃敤 M锛嶅垽鍒ユ硶銆丏irichlet 鍒ゅ垾娉�銆�
Abel 鍒ゅ垾娉�锛屽垽鍒ヤ竴浜涘父瑕嬬⿳鍒嗙殑涓€鑷存敹鏂傛€�锛涳紙4锛夋帉鎻″惈鍙冮噺寤ｇ京绌嶅垎鐨勫垎鏋愭€ц唱(zh矛)锛氶€ｇ簩(x霉)鎬�銆佸彲寰€�銆�
鍙⿳鎬�锛涳紙5锛夋帉鎻� Euler 绌嶅垎鐨勫畾缇�銆佹€ц唱(zh矛)銆侀仦鎺ㄥ叕寮忓強瀹冨€戜箣闁撶殑闂�(gu膩n)绯�锛屽苟鐢ㄤ簬瑷堢畻绌嶅垎銆�
浜屽崄 鏇茬窔绌嶅垎
锛�1锛夋帉鎻＄涓€鍨嬫洸绶氱⿳鍒嗙殑瀹氱京銆佺涓€鍨嬫洸绶氱⿳鍒嗙殑瑷堢畻銆佺浜屽瀷鏇茬窔绌嶅垎鐨勫畾缇�銆佺浜屽瀷鏇茬窔绌嶅垎
鐨勮▓绠�锛涳紙2锛変簡瑙ｇ涓€鍨嬫洸绶氱⿳鍒嗙殑鎰忕京銆佺浜屽瀷 鏇茬窔绌嶅垎鐨勬剰缇┿€佸叐椤炴洸绶氱⿳鍒嗙殑闂�(gu膩n)绯�銆�
浜屽崄涓€ 閲嶇⿳鍒�
锛�1锛夋帉鎻″皣閲嶇⿳鍒嗗寲鐐虹疮娆＄⿳鍒嗙殑瑷堢畻鏂规硶锛屽苟鏈冧氦鎻涚⿳鍒嗛爢搴�锛涳紙2锛夋帉鎻′簩閲嶇⿳鍒嗙殑妤靛潗妯欒畩鎻涳紝
涓夐噸绌嶅垎鐨勬煴鍧愭銆佺悆鍧愭銆佸唬缇╃悆鍧愭璁婃彌锛屾帉鎻′竴浜涚啊鍠殑涓€鑸畩鎻�锛屼互閬斿埌绨″寲閲嶇⿳鍒嗚▓绠楃殑鐩殑锛�
锛�3锛夎兘姝ｇ⒑鍦颁娇鐢ㄥ皪绋辨€�锛涙纰哄湴铏曠悊琚⿳鍑芥暩(sh霉)涓惈鏈夌禃灏嶅€肩铏熷強涓€鑸垎娈靛嚱鏁�(sh霉)鐨勯噸绌嶅垎瑷堢畻锛涳紙4锛�
鑳界敤閲嶇⿳鍒嗚▓绠楀钩闈㈠湒褰㈢殑闈㈢⿳锛岀┖闁撶珛楂旂殑楂旂⿳銆佺墿楂旂殑璩�(zh矛)閲忋€侀噸蹇�銆佽綁(zhu菐n)鍕曟叄閲忕瓑銆傦紙5锛変簡瑙� 閲嶇⿳
鍒�銆�
浜屽崄浜� 鏇查潰绌嶅垎
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瀹氱京銆佺墿鐞嗘剰缇╁拰瑷堢畻锛屼簡瑙ｅ叐椤炴洸闈㈢⿳鍒嗙殑鑱�(li谩n)绯伙紙3锛夋帉鎻� Gauss 鍏紡鑸� Stokes 鍏紡锛涳紙4锛変簡瑙ｅ牬璜栧垵
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鍏嶈铂鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)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�(gu膩n)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�(gu膩n)鍏�(n猫i)瀹�銆�
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
