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骞达紱鍧囨彁渚涙敹璨讳笅杓�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
绗� 1 闋�锛屽叡 7 闋� 2018 骞村娉㈠ぇ瀛哥ⅸ澹爺绌剁敓鎷涚敓鑰冭│鍒濊│绉戠洰 鑰� 瑭� 澶� 缍� 绉戠洰浠g⒓銆佸悕绋�: 743 杈�(n贸ng)瀛稿熀绀庢暩(sh霉)瀛� 涓€銆佽€冭│褰㈠紡鑸囪│鍗风祼(ji茅)妲� 锛堜竴锛夎│鍗锋豢鍒嗗€煎強鑰冭│鏅傞枔 鏈│鍗锋豢鍒嗙偤 150 鍒�锛岃€冭│鏅傞枔鐐� 180 鍒嗛悩銆� 锛堜簩锛夌瓟椤屾柟寮� 绛旈鏂瑰紡鐐洪枆鍗�銆佺瓎瑭�銆傝│鍗风敱瑭﹂鍜岀瓟椤岀礄绲勬垚锛涚瓟妗堝繀闋堝鍦ㄧ瓟椤岀礄锛堢敱鑰冮粸鎻愪緵锛� 鐩告噳鐨勪綅缃笂銆� 锛堜笁锛夎│鍗峰収(n猫i)瀹圭祼(ji茅)妲� 鑰冭│鍏�(n猫i)瀹逛富瑕佸寘鎷€婂井绌嶅垎銆嬨€併€婄窔鎬т唬鏁�(sh霉)銆嬪拰銆婃鐜囪珫鑸囨暩(sh霉)鐞嗙当(t菕ng)瑷堛€�銆� 锛堝洓锛夎│鍗烽鍨嬬祼(ji茅)妲� 1.鍠爡閬告搰椤岋紱 2.濉┖椤�锛� 3.瑙g瓟椤岋紙鍖呮嫭璀夋槑椤岋級銆� 浜�銆佽€冩煡鐩 杈�(n贸ng)瀛搁杸椤炴暩(sh霉)瀛歌€冭│娑佃搵楂樼瓑鏁�(sh霉)瀛搞€佺窔鎬т唬鏁�(sh霉)銆佹鐜囪珫鑸囨暩(sh霉)鐞嗙当(t菕ng)瑷堢瓑鍏叡鍩虹瑾茬▼銆傝姹� 鑰冪敓姣旇純绯荤当(t菕ng)鍦扮悊瑙f暩(sh霉)瀛哥殑鍩烘湰姒傚康鍜屽熀鏈悊璜栵紝鎺屾彙鏁�(sh霉)瀛哥殑鍩烘湰鏂规硶锛屽叿鍌欐娊璞℃€濈董鑳藉姏銆� 閭忚集鎺ㄧ悊鑳藉姏銆佺┖闁撴兂璞¤兘鍔�銆侀亱绠楄兘鍔涗互鍙婄稖鍚堥亱鐢ㄦ墍瀛哥殑鐭ヨ瓨鍒嗘瀽鍟忛鍜岃В姹哄晱椤岀殑鑳� 鍔�銆� 涓�銆佽€冩煡鑼冨湇鎴栬€冭│鍏�(n猫i)瀹规瑕� 鑰冭│绉戠洰鍖呮嫭銆婂井绌嶅垎銆�銆併€婄窔鎬т唬鏁�(sh霉)銆嬪拰銆婃鐜囪珫鑸囨暩(sh霉)鐞嗙当(t菕ng)瑷堛€嬶紟 寰� 绌� 鍒� 1) 鍑芥暩(sh霉)銆佹サ闄�銆侀€g簩(x霉) 鑰冭│鍏�(n猫i)瀹� 绗� 2 闋侊紝鍏� 7 闋� 鍑芥暩(sh霉)鐨勬蹇靛強琛ㄧず娉� 鍑芥暩(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� 寰╁悎鍑芥暩(sh霉)銆佸弽鍑芥暩(sh霉)銆� 鍒嗘鍑芥暩(sh霉)鍜岄毐鍑芥暩(sh霉) 鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍙婂叾鍦栧舰 鍒濈瓑鍑芥暩(sh霉) 鍑芥暩(sh霉)闂滅郴鐨勫缓绔� 鏁�(sh霉)鍒楁サ闄愯垏鍑芥暩(sh霉)妤甸檺鐨勫畾缇╁強鍏舵€ц唱(zh矛) 鍑芥暩(sh霉)鐨勫乏妤甸檺鍜屽彸妤甸檺 鐒$灏忛噺鍜岀劇绐ぇ閲忕殑 姒傚康鍙婂叾闂滅郴 鐒$灏忛噺鐨勬€ц唱(zh矛)鍙婄劇绐皬閲忕殑姣旇純 妤甸檺鐨勫洓鍓囬亱绠� 妤甸檺瀛樺湪鐨勫叐鍊嬫簴 鍓囷細鍠(di脿o)鏈夌晫婧栧墖鍜屽ぞ閫兼簴鍓� 鍏╁€嬮噸瑕佹サ闄愶細 0 sin lim 1 x x x? ? 锛� 1 lim 1 x x e x? ? ? ? ? ? ? ? ? ? 鍑芥暩(sh霉)閫g簩(x霉)鐨勬蹇� 鍑芥暩(sh霉)闁撴柗榛炵殑椤炲瀷 鍒濈瓑鍑芥暩(sh霉)鐨勯€g簩(x霉)鎬� 闁夊崁(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 1. 鐞嗚В鍑芥暩(sh霉)鐨勬蹇�锛屾帉鎻″嚱鏁�(sh霉)鐨勮〃绀烘硶锛屾渻寤虹珛鎳夌敤鍟忛涓殑鍑芥暩(sh霉)闂滅郴锛� 2. 浜嗚В鍑芥暩(sh霉)鐨勬湁鐣屾€�銆佸柈瑾�(di脿o)鎬�銆佸懆鏈熸€у拰濂囧伓鎬э紟 3. 鐞嗚В寰╁悎鍑芥暩(sh霉)鍙婂垎娈靛嚱鏁�(sh霉)鐨勬蹇�锛屼簡瑙e弽鍑芥暩(sh霉)鍙婇毐鍑芥暩(sh霉)鐨勬蹇碉紟 4. 鎺屾彙鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍙婂叾鍦栧舰锛屼簡瑙e垵绛夊嚱鏁�(sh霉)鐨勬蹇碉紟 5. 浜嗚В鏁�(sh霉)鍒楁サ闄愬拰鍑芥暩(sh霉)妤甸檺锛堝寘鎷乏妤甸檺鍜屽彸妤甸檺锛夌殑姒傚康锛� 6. 浜嗚В妤甸檺鐨勬€ц唱(zh矛)鑸囨サ闄愬瓨鍦ㄧ殑鍏╁€嬫簴鍓�锛屾帉鎻℃サ闄愬洓鍓囬亱绠楁硶鍓�锛屾帉鎻″埄鐢ㄥ叐鍊嬮噸瑕� 妤甸檺姹傛サ闄愮殑鏂规硶锛� 7. 鐞嗚В鐒$灏忛噺鐨勬蹇靛拰鍩烘湰鎬ц唱(zh矛)锛屾帉鎻$劇绐皬閲忕殑姣旇純鏂规硶锛屼簡瑙g劇绐ぇ閲忕殑姒傚康鍙� 鍏惰垏鐒$灏忛噺鐨勯棞绯伙紟 8. 鐞嗚В鍑芥暩(sh霉)閫g簩(x霉)鎬х殑姒傚康锛堝惈宸﹂€g簩(x霉)鑸囧彸閫g簩(x霉)锛夛紝鏈冨垽鍒ュ嚱鏁�(sh霉)闁撴柗榛炵殑椤炲瀷锛� 9. 浜嗚В閫g簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍜屽垵绛夊嚱鏁�(sh霉)鐨勯€g簩(x霉)鎬�锛岀悊瑙i枆鍗€(q奴)闁撲笂閫g簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛堟湁鐣屾€�銆� 鏈€澶у€煎拰鏈€灏忓€煎畾鐞�銆佷粙鍊煎畾鐞嗭級锛屽苟鏈冩噳鐢ㄩ€欎簺鎬ц唱(zh矛)锛� 2) 涓€鍏冨嚱鏁�(sh霉)寰垎瀛� 鑰冭│鍏�(n猫i)瀹� 灏庢暩(sh霉)鍜屽井鍒嗙殑姒傚康 灏庢暩(sh霉)鐨勫咕浣曟剰缇� 鍑芥暩(sh霉)鐨勫彲灏庢€ц垏閫g簩(x霉)鎬т箣闁撶殑闂滅郴 骞抽潰鏇茬窔鐨� 鍒囩窔鍜屾硶绶� 灏庢暩(sh霉)鍜屽井鍒嗙殑鍥涘墖閬嬬畻 鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨勫皫鏁�(sh霉) 寰╁悎鍑芥暩(sh霉)鍜岄毐鍑芥暩(sh霉)鐨勫井鍒嗘硶 楂橀殠灏庢暩(sh霉) 寰垎涓€煎畾鐞� 娲涘繀閬�(L鈥橦ospital)娉曞墖 鍑芥暩(sh霉)鍠(di脿o)鎬х殑鍒ゅ垾 鍑芥暩(sh霉)鐨勬サ鍊� 鍑芥暩(sh霉) 鍦栧舰鐨勫嚬鍑告€�銆佹嫄榛炲強婕歌繎绶� 鍑芥暩(sh霉)鐨勬渶澶у€艰垏鏈€灏忓€� 鑰冭│瑕佹眰 1锛庣悊瑙e皫鏁�(sh霉)鐨勬蹇靛強鍙皫鎬ц垏閫g簩(x霉)鎬т箣闁撶殑闂滅郴锛屼簡瑙e皫鏁�(sh霉)鐨勫咕浣曟剰缇╋紝鏈冩眰骞抽潰鏇茬窔 鐨勫垏绶氭柟绋嬪拰娉曠窔鏂圭▼锛� 2锛庢帉鎻″熀鏈垵绛夊嚱鏁�(sh霉)鐨勫皫鏁�(sh霉)鍏紡銆佸皫鏁�(sh霉)鐨勫洓鍓囬亱绠楁硶鍓囧強寰╁悎鍑芥暩(sh霉)鐨勬眰灏庢硶鍓囷紝鏈冩眰闅� 鍑芥暩(sh霉)鐨勫皫鏁�(sh霉)锛� 3锛庝簡瑙i珮闅庡皫鏁�(sh霉)鐨勬蹇�锛屾帉鎻′簩闅庡皫鏁�(sh霉)鐨勬眰娉曪紟 4锛庝簡瑙e井鍒嗙殑姒傚康浠ュ強灏庢暩(sh霉)鑸囧井鍒嗕箣闁撶殑闂滅郴锛屾渻姹傚嚱鏁�(sh霉)鐨勫井鍒嗭紟 5锛庣悊瑙g緟鐖撅紙Rolle锛夊畾鐞嗗拰鎷夋牸鏈楁棩锛圠agrange锛変腑鍊煎畾鐞�锛屾帉鎻¢€欏叐鍊嬪畾鐞嗙殑绨″柈鎳� 鐢紟 6锛庢渻鐢ㄦ礇蹇呴仈娉曞墖姹傛サ闄愶紟 7锛庢帉鎻″嚱鏁�(sh霉)鍠(di脿o)鎬х殑鍒ゅ垾鏂规硶锛屼簡瑙e嚱鏁�(sh霉)妤靛€肩殑姒傚康锛屾帉鎻″嚱鏁�(sh霉)妤靛€�銆佹渶澶у€煎拰鏈€灏忓€� 鐨勬眰娉曞強鎳夌敤锛� 绗� 3 闋侊紝鍏� 7 闋� 8锛庢渻鐢ㄥ皫鏁�(sh霉)鍒ゆ柗鍑芥暩(sh霉)鍦栧舰鐨勫嚬鍑告€�锛屾渻姹傚嚱鏁�(sh霉)鍦栧舰鐨勬嫄榛炲拰婕歌繎绶氾紙姘村钩銆侀墰鐩存几杩戠窔锛夛紟 3) 涓€鍏冨嚱鏁�(sh霉)绌嶅垎瀛� 鑰冭│鍏�(n猫i)瀹� 鍘熷嚱鏁�(sh霉)鍜屼笉瀹氱⿳鍒嗙殑姒傚康 涓嶅畾绌嶅垎鐨勫熀鏈€ц唱(zh矛) 鍩烘湰绌嶅垎鍏紡 瀹氱⿳鍒嗙殑姒傚康鍜屽熀鏈� 鎬ц唱(zh矛) 瀹氱⿳鍒嗕腑鍊煎畾鐞� 绌嶅垎涓婇檺鐨勫嚱鏁�(sh霉)鑸囧叾灏庢暩(sh霉) 鐗涢爴-钀婂竷灏艰尐锛圢ewton-Leibniz锛夊叕寮� 涓嶅畾绌嶅垎鍜屽畾绌嶅垎鐨勬彌鍏冪⿳鍒嗘柟娉曡垏鍒嗛儴绌嶅垎娉� 鍙嶅父锛堝唬缇╋級绌嶅垎 瀹氱⿳鍒嗙殑鎳夌敤 鑰冭│瑕佹眰 1锛庣悊瑙e師鍑芥暩(sh霉)鑸囦笉瀹氱⿳鍒嗙殑姒傚康锛屾帉鎻′笉瀹氱⿳鍒嗙殑鍩烘湰鎬ц唱(zh矛)鍜屽熀鏈⿳鍒嗗叕寮�锛屾帉鎻′笉瀹� 绌嶅垎鐨勬彌鍏冪⿳鍒嗘硶鍜屽垎閮ㄧ⿳鍒嗘硶锛� 2锛庝簡瑙e畾绌嶅垎鐨勬蹇靛拰鍩烘湰鎬ц唱(zh矛)锛屼簡瑙e畾绌嶅垎涓€煎畾鐞�锛岀悊瑙g⿳鍒嗕笂闄愮殑鍑芥暩(sh霉)骞舵渻姹傚畠 鐨勫皫鏁�(sh霉)锛屾帉鎻$墰闋�-钀婂竷灏艰尐鍏紡浠ュ強瀹氱⿳鍒嗙殑鎻涘厓绌嶅垎娉曡垏鍒嗛儴绌嶅垎娉曪紟 3锛庢渻鍒╃敤瀹氱⿳鍒嗚▓绠楀钩闈㈠湒褰㈢殑闈㈢⿳鍜屾棆杞�(zhu菐n)楂旂殑楂旂⿳锛� 4锛庝簡瑙g劇绐崁(q奴)闁撲笂鐨勫弽甯哥⿳鍒嗙殑姒傚康锛屾渻瑷堢畻鐒$鍗€(q奴)闁撲笂鐨勫弽甯哥⿳鍒嗭紟 4) 澶氬厓鍑芥暩(sh霉)寰⿳鍒嗗 鑰冭│鍏�(n猫i)瀹� 澶氬厓鍑芥暩(sh霉)鐨勬蹇� 浜屽厓鍑芥暩(sh霉)鐨勫咕浣曟剰缇� 浜屽厓鍑芥暩(sh霉)鐨勬サ闄愯垏閫g簩(x霉)鐨勬蹇� 澶氬厓鍑芥暩(sh霉)鍋忓皫 鏁�(sh霉)鐨勬蹇佃垏瑷堢畻 澶氬厓寰╁悎鍑芥暩(sh霉)鐨勬眰灏庢硶鑸囬毐鍑芥暩(sh霉)姹傚皫娉� 浜岄殠鍋忓皫鏁�(sh霉) 鍏ㄥ井鍒� 澶氬厓鍑芥暩(sh霉) 鐨勬サ鍊煎拰姊濅欢妤靛€� 浜岄噸绌嶅垎鐨勬蹇点€佸熀鏈€ц唱(zh矛)鍜岃▓绠� 鑰冭│瑕佹眰 1锛庝簡瑙e鍏冨嚱鏁�(sh霉)鐨勬蹇�锛屼簡瑙d簩鍏冨嚱鏁�(sh霉)鐨勫咕浣曟剰缇╋紟 2锛庝簡瑙d簩鍏冨嚱鏁�(sh霉)鐨勬サ闄愯垏閫g簩(x霉)鐨勬蹇碉紟 3锛庝簡瑙e鍏冨嚱鏁�(sh霉)鍋忓皫鏁�(sh霉)鑸囧叏寰垎鐨勬蹇�锛屾渻姹傚鍏冨京鍚堝嚱鏁�(sh霉)涓€闅庛€佷簩闅庡亸灏庢暩(sh霉)锛屾渻姹傚叏 寰垎锛屾渻姹傚鍏冮毐鍑芥暩(sh霉)鐨勫亸灏庢暩(sh霉)锛� 4锛庝簡瑙e鍏冨嚱鏁�(sh霉)妤靛€煎拰姊濅欢妤靛€肩殑姒傚康锛屾帉鎻″鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑蹇呰姊濅欢锛屼簡瑙d簩鍏� 鍑芥暩(sh霉)妤靛€煎瓨鍦ㄧ殑鍏呭垎姊濅欢锛� 5锛庝簡瑙d簩閲嶇⿳鍒嗙殑姒傚康鑸囧熀鏈€ц唱(zh矛)锛屾渻鐢ㄧ洿瑙掑潗妯欑郴瑷堢畻浜岄噸绌嶅垎锛� 5) 甯稿井鍒嗘柟绋� 鑰冭│鍏�(n猫i)瀹� 甯稿井鍒嗘柟绋嬬殑鍩烘湰姒傚康 璁婇噺鍙垎闆㈢殑寰垎鏂圭▼ 涓€闅庣窔鎬у井鍒嗘柟绋� 鑰冭│瑕佹眰 1锛庝簡瑙e井鍒嗘柟绋嬪強鍏堕殠銆佽В銆侀€氳В銆佸垵濮嬫浠跺拰鐗硅В绛夋蹇碉紟 2锛庢帉鎻¤畩閲忓彲鍒嗛洟鐨勫井鍒嗘柟绋嬪拰涓€闅庣窔鎬у井鍒嗘柟绋嬬殑姹傝В鏂规硶锛� 绶� 鎬� 浠� 鏁�(sh霉) 1) 琛屽垪寮� 鑰冭│鍏�(n猫i)瀹� 琛屽垪寮忕殑姒傚康鍜屽熀鏈€ц唱(zh矛) 琛屽垪寮忔寜琛岋紙鍒楋級灞曢枊瀹氱悊 绗� 4 闋�锛屽叡 7 闋� 鑰冭│瑕佹眰 1锛庝簡瑙h鍒楀紡鐨勬蹇�锛屾帉鎻¤鍒楀紡鐨勬€ц唱(zh矛)锛� 2锛庢渻鎳夌敤琛屽垪寮忕殑鎬ц唱(zh矛)鍜岃鍒楀紡鎸夎锛堝垪锛夊睍闁嬪畾鐞嗚▓绠楄鍒楀紡锛� 2) 鐭╅櫍 鑰冭│鍏�(n猫i)瀹� 鐭╅櫍鐨勬蹇� 鐭╅櫍鐨勭窔鎬ч亱绠� 鐭╅櫍鐨勪箻娉� 鏂归櫍鐨勫啰 鏂归櫍涔樼⿳鐨勮鍒楀紡 鐭╅櫍鐨勮綁(zhu菐n) 缃� 閫嗙煩闄g殑姒傚康鍜屾€ц唱(zh矛) 鐭╅櫍鍙€嗙殑鍏呭垎蹇呰姊濅欢 浼撮毃鐭╅櫍 鐭╅櫍鐨勫垵绛夎畩鎻� 鍒濈瓑鐭� 闄� 鐭╅櫍鐨勭З 鐭╅櫍鐨勭瓑鍍� 鑰冭│瑕佹眰 1锛庣悊瑙g煩闄g殑姒傚康锛屼簡瑙e柈浣嶇煩闄�銆佸皪瑙掔煩闄c€佷笁瑙掔煩闄g殑瀹氱京鍙婃€ц唱(zh矛)锛屼簡瑙e皪绋辩煩闄c€� 鍙嶅皪绋辩煩闄e強姝d氦鐭╅櫍绛夌殑瀹氱京鍜屾€ц唱(zh矛)锛� 2锛庢帉鎻$煩闄g殑绶氭€ч亱绠�銆佷箻娉曘€佽綁(zhu菐n)缃互鍙婂畠鍊戠殑閬嬬畻瑕�(gu墨)寰�锛屼簡瑙f柟闄g殑鍐垏鏂归櫍涔樼⿳鐨� 琛屽垪寮忕殑鎬ц唱(zh矛)锛� 3锛庣悊瑙i€嗙煩闄g殑姒傚康锛屾帉鎻¢€嗙煩闄g殑鎬ц唱(zh矛)浠ュ強鐭╅櫍鍙€嗙殑鍏呭垎蹇呰姊濅欢锛屼簡瑙d即闅ㄧ煩闄� 鐨勬蹇�锛屾渻鐢ㄤ即闅ㄧ煩闄f眰閫嗙煩闄o紟 4锛庝簡瑙g煩闄g殑鍒濈瓑璁婃彌鍜屽垵绛夌煩闄e強鐭╅櫍绛夊児鐨勬蹇碉紝鐞嗚В鐭╅櫍鐨勭З鐨勬蹇�锛屾帉鎻$敤鍒� 绛夎畩鎻涙眰鐭╅櫍鐨勯€嗙煩闄e拰绉╃殑鏂规硶锛� 3) 鍚戦噺 鑰冭│鍏�(n猫i)瀹� 鍚戦噺鐨勬蹇� 鍚戦噺鐨勭窔鎬х祫鍚堣垏绶氭€ц〃绀� 鍚戦噺绲勭殑绶氭€х浉闂滆垏绶氭€х劇闂� 鍚戦噺绲勭殑妤� 澶х窔鎬х劇闂滅祫 绛夊児鍚戦噺绲� 鍚戦噺绲勭殑绉� 鍚戦噺绲勭殑绉╄垏鐭╅櫍鐨勭З涔嬮枔鐨勯棞绯� 鑰冭│瑕佹眰 1锛庝簡瑙e悜閲忕殑姒傚康锛屾帉鎻″悜閲忕殑鍔犳硶鍜屾暩(sh霉)涔橀亱绠楁硶鍓囷紟 2锛庣悊瑙e悜閲忕殑绶氭€х祫鍚堣垏绶氭€ц〃绀�銆佸悜閲忕祫绶氭€х浉闂�銆佺窔鎬х劇闂滅瓑姒傚康锛屾帉鎻″悜閲忕祫绶� 鎬х浉闂�銆佺窔鎬х劇闂滅殑鏈夐棞鎬ц唱(zh矛)鍙婂垽鍒ユ硶锛� 3锛庣悊瑙e悜閲忕祫鐨勬サ澶х窔鎬х劇闂滅祫鍜岀З鐨勬蹇�锛屾渻姹傚悜閲忕祫鐨勬サ澶х窔鎬х劇闂滅祫鍙婄З锛� 4锛庝簡瑙e悜閲忕祫绛夊児鐨勬蹇�锛屼簡瑙g煩闄g殑绉╄垏鍏惰锛堝垪锛夊悜閲忕祫鐨勭З涔嬮枔鐨勯棞绯伙紟 4) 绶氭€ф柟绋嬬祫 鑰冭│鍏�(n猫i)瀹� 绶氭€ф柟绋嬬祫鐨勫厠钀婂锛圕ramer锛夋硶鍓� 绶氭€ф柟绋嬬祫鏈夎В鍜岀劇瑙g殑鍒ゅ畾 榻婃绶氭€ф柟绋嬬祫 鐨勫熀绀庤В绯诲拰閫氳В 闈為綂娆$窔鎬ф柟绋嬬祫鐨勮В鑸囩浉鎳夌殑榻婃绶氭€ф柟绋嬬祫鐨勮В涔嬮枔鐨勯棞绯� 闈為綂 娆$窔鎬ф柟绋嬬祫鐨勯€氳В 鑰冭│瑕佹眰 1锛庢渻鐢ㄥ厠钀婂娉曞墖瑙g窔鎬ф柟绋嬬祫锛� 2锛庢帉鎻¢潪榻婃绶氭€ф柟绋嬬祫鏈夎В鍜岀劇瑙g殑鍒ゅ畾鏂规硶锛� 3锛庣悊瑙i綂娆$窔鎬ф柟绋嬬祫鐨勫熀绀庤В绯荤殑姒傚康锛屾帉鎻¢綂娆$窔鎬ф柟绋嬬祫鐨勫熀绀庤В绯诲拰閫氳В鐨勬眰 娉曪紟 4锛庝簡瑙i潪榻婃绶氭€ф柟绋嬬祫鐨勭祼(ji茅)妲嬪強閫氳В鐨勬蹇碉紟 5锛庢帉鎻$敤鍒濈瓑琛岃畩鎻涙眰瑙g窔鎬ф柟绋嬬祫鐨勬柟娉曪紟 绗� 5 闋�锛屽叡 7 闋� 5) 鐭╅櫍鐨勭壒寰佸€煎拰鐗瑰緛鍚戦噺 鑰冭│鍏�(n猫i)瀹� 鐭╅櫍鐨勭壒寰佸€煎拰鐗瑰緛鍚戦噺鐨勬蹇�銆佹€ц唱(zh矛) 鐩镐技鐭╅櫍鐨勬蹇靛強鎬ц唱(zh矛) 鐭╅櫍鍙浉浼煎皪瑙掑寲鐨� 鍏呭垎蹇呰姊濅欢鍙婄浉浼煎皪瑙掔煩闄� 瀵﹀皪绋辩煩闄g殑鐗瑰緛鍊笺€佺壒寰佸悜閲忓強鍏剁浉浼煎皪瑙掔煩闄� 鑰冭│瑕佹眰 1锛庣悊瑙g煩闄g殑鐗瑰緛鍊�銆佺壒寰佸悜閲忕殑姒傚康锛屾帉鎻$煩闄g壒寰佸€肩殑鎬ц唱(zh矛)锛屾帉鎻℃眰鐭╅櫍鐗瑰緛鍊煎拰 鐗瑰緛鍚戦噺鐨勬柟娉曪紟 2锛庝簡瑙g煩闄g浉浼肩殑姒傚康鍜岀浉浼肩煩闄g殑鎬ц唱(zh矛)锛屼簡瑙g煩闄e彲鐩镐技灏嶈鍖栫殑鍏呭垎蹇呰姊濅欢锛屾渻 灏囩煩闄e寲鐐虹浉浼煎皪瑙掔煩闄o紟 3锛庝簡瑙e灏嶇ū鐭╅櫍鐨勭壒寰佸€煎拰鐗瑰緛鍚戦噺鐨勬€ц唱(zh矛)锛� 姒傜巼璜栬垏鏁�(sh霉)鐞嗙当(t菕ng)瑷� 1) 闅ㄦ浜嬩欢鍜屾鐜� 鑰冭│鍏�(n猫i)瀹� 闅ㄦ浜嬩欢鑸囨ǎ鏈┖闁� 浜嬩欢鐨勯棞绯昏垏閬嬬畻 姒傜巼鐨勫熀鏈€ц唱(zh矛) 鍙ゅ吀鍨嬫鐜� 姊濅欢姒傜巼 姒傜巼 鐨勫熀鏈叕寮� 浜嬩欢鐨勭崹绔嬫€� 鐛ㄧ珛閲嶅京瑭﹂ 鑰冭│瑕佹眰 1锛庝簡瑙fǎ鏈┖闁撶殑姒傚康锛岀悊瑙i毃姗熶簨浠剁殑姒傚康锛屾帉鎻′簨浠剁殑闂滅郴鑸囬亱绠楋紟 2锛庣悊瑙f鐜�銆佹浠舵鐜囩殑姒傚康锛屾帉鎻℃鐜囩殑鍩烘湰鎬ц唱(zh矛)锛屾渻瑷堢畻鍙ゅ吀鍨嬫鐜囷紝鎺屾彙姒傜巼鐨� 鍔犳硶鍏紡銆佹笡娉曞叕寮�銆佷箻娉曞叕寮�銆佸叏姒傜巼鍏紡浠ュ強璨濊憠鏂�(Bayes)鍏紡锛� 3锛庣悊瑙d簨浠剁殑鐛ㄧ珛鎬х殑姒傚康锛屾帉鎻$敤浜嬩欢鐛ㄧ珛鎬ч€茶姒傜巼瑷堢畻锛涚悊瑙g崹绔嬮噸寰╄│椹楃殑姒� 蹇�锛屾帉鎻¤▓绠楁湁闂滀簨浠舵鐜囩殑鏂规硶锛� 2) 闅ㄦ璁婇噺鍙婂叾鍒嗗竷 鑰冭│鍏�(n猫i)瀹� 闅ㄦ璁婇噺 闅ㄦ璁婇噺鍒嗗竷鍑芥暩(sh霉)鐨勬蹇靛強鍏舵€ц唱(zh矛) 闆㈡暎鍨嬮毃姗熻畩閲忕殑姒傜巼鍒嗗竷 閫g簩(x霉)鍨嬮毃姗� 璁婇噺鐨勬鐜囧瘑搴� 甯歌闅ㄦ璁婇噺鐨勫垎甯� 闅ㄦ璁婇噺鍑芥暩(sh霉)鐨勫垎甯� 鑰冭│瑕佹眰 1锛庣悊瑙i毃姗熻畩閲忕殑姒傚康锛庣悊瑙e垎甯冨嚱鏁�(sh霉) ( ) { } ( )F x P X x x? ? ??? ?? ? ? ? 鐨勬蹇靛強鎬ц唱(zh矛)锛庢渻瑷堢畻鑸囬毃姗熻畩閲忕浉鑱�(li谩n)绯荤殑浜嬩欢鐨勬鐜囷紟 2锛庣悊瑙i洟鏁e瀷闅ㄦ璁婇噺鍙婂叾姒傜巼鍒嗗竷鐨勬蹇�锛屾帉鎻� 0锛�1 鍒嗗竷銆佷簩闋呭垎甯� ( , )B n p 銆佹硦鏉� 锛圥oisson锛夊垎甯� ( )P ? 鍙婂叾鎳夌敤锛� 3锛庣悊瑙i€g簩(x霉)鍨嬮毃姗熻畩閲忓強鍏舵鐜囧瘑搴︾殑姒傚康锛屾帉鎻″潎鍕诲垎甯� ( , )U a b 銆佹鎱�(t脿i)鍒嗗竷 2 ( , )N ? ? 銆� 鎸囨暩(sh霉)鍒嗗竷鍙婂叾鎳夌敤锛屽叾涓弮鏁�(sh霉)鐐� ( 0)? ? ? 鐨勬寚鏁�(sh霉)鍒嗗竷 ( )E ? 鐨勬鐜囧瘑搴︾偤 0 ( ) 0 x e x f x x ? ? ? ??????? ? ? ?????? ???????? ? ? ? ? , 鑻� 0, 鑻� 4锛庢渻姹傞毃姗熻畩閲忕啊鍠嚱鏁�(sh霉)鐨勫垎甯冿紟 绗� 6 闋�锛屽叡 7 闋� 3) 浜岀董闅ㄦ璁婇噺鍙婂叾鍒嗗竷 鑰冭│鍏�(n猫i)瀹� 浜岀董闅ㄦ璁婇噺鍙婂叾鍒嗗竷 浜岀董闆㈡暎鍨嬮毃姗熻畩閲忕殑姒傜巼鍒嗗竷鍜岄倞绶e垎甯� 浜岀董閫g簩(x霉)鍨嬮毃姗� 璁婇噺鐨勬鐜囧瘑搴﹀拰閭婄罚姒傜巼瀵嗗害 闅ㄦ璁婇噺鐨勭崹绔嬫€у拰涓嶇浉闂滄€� 甯哥敤浜岀董闅ㄦ璁婇噺鐨勫垎甯� 鍏╁€嬮毃姗熻畩閲忕啊鍠嚱鏁�(sh霉)鐨勫垎甯� 鑰冭│瑕佹眰 1锛庣悊瑙d簩缍毃姗熻畩閲忕殑姒傚康锛岀悊瑙d簩缍毃姗熻畩閲忕殑鍒嗗竷鐨勬蹇靛拰鎬ц唱(zh矛)锛岀悊瑙d簩缍洟鏁e瀷 闅ㄦ璁婇噺鐨勬鐜囧垎甯冨拰閭婄罚鍒嗗竷锛岀悊瑙d簩缍€g簩(x霉)鍨嬮毃姗熻畩閲忕殑姒傜巼瀵嗗害鍜岄倞绶e瘑搴︼紝鏈冩眰鑸� 浜岀董闆㈡暎鍨嬭畩閲忕浉闂滀簨浠剁殑姒傜巼锛� 2锛庣悊瑙i毃姗熻畩閲忕殑鐛ㄧ珛鎬у強涓嶇浉闂滄€х殑姒傚康锛屼簡瑙i毃姗熻畩閲忕浉浜掔崹绔嬬殑姊濅欢锛� 3锛庝簡瑙d簩缍潎鍕诲垎甯冿紝浜嗚В浜岀董姝f厠(t脿i)鍒嗗竷 2 2 1 2 1 2 ( , ; , ; )N u u ? ? ? 鐨勬鐜囧瘑搴︼紝浜嗚В鍏朵腑鍙冩暩(sh霉)鐨勬鐜囨剰缇╋紟 4锛庢渻姹傚叐鍊嬬崹绔嬮毃姗熻畩閲忓拰鐨勫垎甯冿紟 4) 闅ㄦ璁婇噺鐨勬暩(sh霉)瀛楃壒寰� 鑰冭│鍏�(n猫i)瀹� 闅ㄦ璁婇噺鐨勬暩(sh霉)瀛告湡鏈涳紙鍧囧€硷級銆佹柟宸�銆佹婧栧樊鍙婂叾鎬ц唱(zh矛) 闅ㄦ璁婇噺绨″柈鍑芥暩(sh霉)鐨勬暩(sh霉)瀛告湡鏈� 鐭┿€� 鍗�(xi茅)鏂瑰樊鍜岀浉闂滅郴鏁�(sh霉)鍙婂叾鎬ц唱(zh矛) 鑰冭│瑕佹眰 1锛庣悊瑙i毃姗熻畩閲忔暩(sh霉)瀛楃壒寰侊紙鏁�(sh霉)瀛告湡鏈�銆佹柟宸�銆佹婧栧樊銆佺煩銆佸崝(xi茅)鏂瑰樊銆佺浉闂滅郴鏁�(sh霉)锛夌殑姒傚康锛� 鏈冮亱鐢ㄦ暩(sh霉)瀛楃壒寰佺殑鍩烘湰鎬ц唱(zh矛)锛屽苟鎺屾彙甯哥敤鍒嗗竷鐨勬暩(sh霉)瀛楃壒寰侊紟 2锛庢渻姹傞毃姗熻畩閲忕啊鍠嚱鏁�(sh霉)鐨勬暩(sh霉)瀛告湡鏈涳紟 5) 澶ф暩(sh霉)瀹氬緥鍜屼腑蹇冩サ闄愬畾鐞� 鑰冭│鍏�(n猫i)瀹� 鍒囨瘮闆か(Chebyshev)涓嶇瓑寮� 鍒囨瘮闆か澶ф暩(sh霉)瀹氬緥 浼姫鍒�(Bernoulli)澶ф暩(sh霉)瀹氬緥 妫h帿寮椾竴 鎷夋櫘鎷夋柉(De Moivre-Laplace)瀹氱悊 鍒楃董涓€鏋楀痉浼牸(Levy-Lindberg)瀹氱悊锛� 鑰冭│瑕佹眰 1锛庝簡瑙e垏姣旈洩澶笉绛夊紡锛� 2锛庝簡瑙e垏姣旈洩澶ぇ鏁�(sh霉)瀹氬緥鍜屼集鍔埄澶ф暩(sh霉)瀹氬緥锛� 3锛庝簡瑙f#鑾紬鈥旀媺鏅媺鏂畾鐞嗭紙浜岄爡鍒嗗竷浠ユ鎱�(t脿i)鍒嗗竷鐐烘サ闄愬垎甯冿級鍜屽垪缍€旀灄寰蜂集鏍煎畾 鐞嗭紙鐛ㄧ珛鍚屽垎甯冮毃姗熻畩閲忓簭鍒楃殑涓績妤甸檺瀹氱悊锛夛紟 6) 鏁�(sh霉)鐞嗙当(t菕ng)瑷堢殑鍩烘湰姒傚康 鑰冭│鍏�(n猫i)瀹� 绺介珨 鍊嬮珨 绨″柈闅ㄦ妯f湰 绲�(t菕ng)瑷堥噺 妯f湰鍧囧€� 妯f湰鏂瑰樊鍜屾ǎ鏈煩 2 ? 鍒嗗竷 t 鍒嗗竷 F 鍒嗗竷 鍒嗕綅鏁�(sh霉) 姝f厠(t脿i)绺介珨鐨勫父鐢ㄦ娊妯e垎甯冿紟 鑰冭│瑕佹眰 1锛庝簡瑙g附楂斻€佺啊鍠毃姗熸ǎ鏈�銆佺当(t菕ng)瑷堥噺銆佹ǎ鏈潎鍊�銆佹ǎ鏈柟宸強妯f湰鐭╃殑姒傚康锛屽叾涓ǎ鏈� 鏂瑰樊瀹氱京鐐� 绗� 7 闋侊紝鍏� 7 闋� 2 2 1 1 ( ) 1 n i i S X X n ? ? ? ? ? 2锛庝簡瑙� 2 ? 鍒嗗竷銆乼 鍒嗗竷鍜� F 鍒嗗竷鐨勬蹇靛拰鎬ц唱(zh矛)锛屼簡瑙e垎浣嶆暩(sh霉)鐨勬蹇靛苟鏈冩煡琛ㄨ▓绠楋紟 3锛庝簡瑙f鎱�(t脿i)绺介珨鐨勫父鐢ㄦ娊妯e垎甯冿紟 鍙冭€冩暀鏉愭垨涓昏鍙冭€冩浉锛� 銆婇珮绛夋暩(sh霉)瀛搞€嬶紙绗竷鐗堬級鍚屾繜澶у鏁�(sh霉)瀛哥郴绶�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�2014锛� 銆婂伐绋嬫暩(sh霉)瀛哥窔鎬т唬鏁�(sh霉)銆嬶紙绗叚鐗堬級鍚屾繜澶у鏁�(sh霉)瀛哥郴绶紝楂樼瓑鏁欒偛鍑虹増绀�锛�2014锛� 銆婃柊绶ㄦ鐜囪珫鑸囨暩(sh霉)鐞嗙当(t菕ng)瑷堛€嬶紙绗簩鐗堬級鑲栫鍗楃瓑绶�锛屽寳浜ぇ瀛稿嚭鐗堢ぞ锛�2013..
鍏嶈铂鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(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わ紝鍙︼細鏈枃鍍呬唬琛ㄤ綔鑰呭€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с€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�
|