2021骞�婀栧崡甯寖澶у纰╁＋鐮旂┒鐢熷叆瀛歌€冭│鑷懡椤岀鐩€冭│澶х侗

鑰冭│绉戠洰浠ｇ⒓锛歔958]               鑰冭│绉戠洰鍚嶇ū锛氭暩(sh霉)瀛稿熀绀庣稖鍚�

涓€銆佽€冭│鍏�(n猫i)瀹瑰強瑕侀粸

锛堜竴锛夋暩(sh霉)瀛稿垎鏋愰儴鍒�

1銆佸嚱鏁�(sh霉)銆佹サ闄�銆侀€ｇ簩(x霉)

鑰冭│鍏�(n猫i)瀹�

鍑芥暩(sh霉)鐨勬蹇靛強琛ㄧず娉曘€€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с€€寰╁悎鍑芥暩(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)銆€鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍙婂叾鍦栧舰銆€鍒濈瓑鍑芥暩(sh霉)銆€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)銆€鍑芥暩(sh霉)鐨勫乏妤甸檺鍜屽彸妤甸檺銆€鐒＄灏忛噺鍜岀劇绐ぇ閲忕殑姒傚康鍙婂叾闂滅郴銆€鐒＄灏忛噺鐨勬€ц唱(zh矛)鍙婄劇绐皬閲忕殑姣旇純銆€妤甸檺鐨勫洓鍓囬亱绠椼€€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囥€€鍏╁€嬮噸瑕佹サ闄�  

鍑芥暩(sh霉)閫ｇ簩(x霉)鐨勬蹇点€€鍑芥暩(sh霉)闁撴柗榛炵殑椤炲瀷銆€鍒濈瓑鍑芥暩(sh霉)鐨勯€ｇ簩(x霉)鎬с€€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│瑕侀粸

锛�1锛夌悊瑙ｅ嚱鏁�(sh霉)鐨勬蹇碉紝鎺屾彙鍑芥暩(sh霉)鐨勮〃绀烘硶锛屾渻寤虹珛鎳夌敤鍟忛鐨勫嚱鏁�(sh霉)闂滅郴.

锛�2锛変簡瑙ｅ嚱鏁�(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

锛�3锛夌悊瑙ｅ京鍚堝嚱鏁�(sh霉)鍙婂垎娈靛嚱鏁�(sh霉)鐨勬蹇碉紝浜嗚В鍙嶅嚱鏁�(sh霉)鍙婇毐鍑芥暩(sh霉)鐨勬蹇碉紟

锛�4锛夋帉鎻″熀鏈垵绛夊嚱鏁�(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�.

锛�5锛夌悊瑙ｆサ闄愮殑姒傚康锛岀悊瑙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绯伙紟

锛�6锛夋帉鎻℃サ闄愮殑鎬ц唱(zh矛)鍙婂洓鍓囬亱绠楁硶鍓�.

锛�7锛夋帉鎻℃サ闄愬瓨鍦ㄧ殑鍏╁€嬫簴鍓�锛屽苟鏈冨埄鐢ㄥ畠鍊戞眰妤甸檺锛屾帉鎻″埄鐢ㄥ叐鍊嬮噸瑕佹サ闄愭眰妤甸檺鐨勬柟娉曪紟

锛�8锛夌悊瑙ｇ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�

锛�9锛夌悊瑙ｅ嚱鏁�(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�锛屾渻鍒ゅ垾鍑芥暩(sh霉)闁撴柗榛炵殑椤炲瀷锛�

锛�10锛変簡瑙ｉ€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€�銆佹渶澶у€煎拰鏈€灏忓€煎畾鐞嗐€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銆佷竴鍏冨嚱鏁�(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銆€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箣闁撶殑闂滅郴銆€骞抽潰鏇茬窔鐨勫垏绶氬拰娉曠窔銆€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)銆€寰╁悎鍑芥暩(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)鐨勫井鍒嗘硶銆€楂橀殠灏庢暩(sh霉) 涓€闅庡井鍒嗗舰寮忕殑涓嶈畩鎬с€€寰垎涓€煎畾鐞嗐€€娲涘繀閬旓紙L鈥橦ospital锛夋硶鍓囥€€鍑芥暩(sh霉)鍠(di脿o)鎬х殑鍒ゅ垾  鍑芥暩(sh霉)鐨勬サ鍊笺€€鍑芥暩(sh霉)鍦栧舰鐨勫嚬鍑告€�銆佹嫄榛炲強婕歌繎绶氥€€鍑芥暩(sh霉)鍦栧舰鐨勬弿绻€€鍑芥暩(sh霉)鐨勬渶澶у€艰垏鏈€灏忓€笺€€

鑰冭│瑕侀粸

锛�1锛夌悊瑙ｅ皫鏁�(sh霉)鍜屽井鍒嗙殑姒傚康锛岀悊瑙ｅ皫鏁�(sh霉)鑸囧井鍒嗙殑闂滅郴锛岀悊瑙ｅ皫鏁�(sh霉)鐨勫咕浣曟剰缇�锛屾渻姹傚钩闈㈡洸绶氱殑鍒囩窔鏂圭▼鍜屾硶绶氭柟绋�锛岀悊瑙ｅ嚱鏁�(sh霉)鐨勫彲灏庢€ц垏閫ｇ簩(x霉)鎬т箣闁撶殑闂滅郴锛�

锛�2锛夋帉鎻″皫鏁�(sh霉)鐨勫洓鍓囬亱绠楁硶鍓囧拰寰╁悎鍑芥暩(sh霉)鐨勬眰灏庢硶鍓囷紝鎺屾彙鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨勫皫鏁�(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�锛屾渻姹傚嚱鏁�(sh霉)鐨勫井鍒嗭紟

锛�3锛変簡瑙ｉ珮闅庡皫鏁�(sh霉)鐨勬蹇�锛屾渻姹傜啊鍠嚱鏁�(sh霉)鐨勯珮闅庡皫鏁�(sh霉)锛�

锛�4锛夋渻姹傚垎娈靛嚱鏁�(sh霉)鐨勫皫鏁�(sh霉)锛屾渻姹傞毐鍑芥暩(sh霉)鍜岀敱鍙冩暩(sh霉)鏂圭▼鎵€纰哄畾鐨勫嚱鏁�(sh霉)浠ュ強鍙嶅嚱鏁�(sh霉)鐨勫皫鏁�(sh霉).

锛�5锛夌悊瑙ｅ苟鏈冪敤缇呯埦(Rolle)瀹氱悊銆佹媺鏍兼湕鏃�(Lagrange)涓€煎畾鐞嗗拰娉板嫆(Taylor)瀹氱悊锛屼簡瑙ｅ苟鏈冪敤鏌タ(Cauchy)涓€煎畾鐞嗭紟

锛�6锛夋帉鎻＄敤娲涘繀閬旀硶鍓囨眰鏈畾寮忔サ闄愮殑鏂规硶锛�

锛�7锛夌悊瑙ｅ嚱鏁�(sh霉)鐨勬サ鍊兼蹇碉紝鎺屾彙鐢ㄥ皫鏁�(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夌敤锛�

锛�8锛夋渻鐢ㄥ皫鏁�(sh霉)鍒ゆ柗鍑芥暩(sh霉)鍦栧舰鐨勫嚬鍑告€э紝鏈冩眰鍑芥暩(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

3銆佷竴鍏冨嚱鏁�(sh霉)绌嶅垎瀛�

鑰冭│鍏�(n猫i)瀹�

鍘熷嚱鏁�(sh霉)鍜屼笉瀹氱⿳鍒嗙殑姒傚康銆€涓嶅畾绌嶅垎鐨勫熀鏈€ц唱(zh矛)銆€鍩烘湰绌嶅垎鍏紡銆€瀹氱⿳鍒嗙殑姒傚康鍜屽熀鏈€ц唱(zh矛)銆€瀹氱⿳鍒嗕腑鍊煎畾鐞嗐€€绌嶅垎涓婇檺鐨勫嚱鏁�(sh霉)鍙婂叾灏庢暩(sh霉)銆€鐗涢爴-钀婂竷灏艰尐锛圢ewton-Leibniz锛夊叕寮忋€€涓嶅畾绌嶅垎鍜屽畾绌嶅垎鐨勬彌鍏冪⿳鍒嗘硶鑸囧垎閮ㄧ⿳鍒嗘硶銆€鏈夌悊鍑芥暩(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⿳鍒嗐€€鍙嶅父锛堝唬缇╋級绌嶅垎銆€瀹氱⿳鍒嗙殑鎳夌敤

鑰冭│瑕侀粸

锛�1锛夌悊瑙ｅ師鍑芥暩(sh霉)鐨勬蹇碉紝鐞嗚В涓嶅畾绌嶅垎鍜屽畾绌嶅垎鐨勬蹇碉紟

锛�2锛夋帉鎻′笉瀹氱⿳鍒嗙殑鍩烘湰鍏紡锛屾帉鎻′笉瀹氱⿳鍒嗗拰瀹氱⿳鍒嗙殑鎬ц唱(zh矛)鍙婂畾绌嶅垎涓€煎畾鐞嗭紝鎺屾彙鎻涘厓绌嶅垎娉曡垏鍒嗛儴绌嶅垎娉曪紟

锛�3锛夋渻姹傛湁鐞嗗嚱鏁�(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

锛�4锛夌悊瑙ｇ⿳鍒嗕笂闄愮殑鍑芥暩(sh霉)锛屾渻姹傚畠鐨勫皫鏁�(sh霉)锛屾帉鎻＄墰闋�-钀婂竷灏艰尐鍏紡锛�

锛�5锛変簡瑙ｅ弽甯哥⿳鍒嗙殑姒傚康锛屾渻瑷堢畻鍙嶅父绌嶅垎锛�

锛�6锛夋帉鎻＄敤瀹氱⿳鍒嗚〃閬斿拰瑷堢畻骞抽潰鍦栧舰鐨勯潰绌�銆佸钩闈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�.

4銆佸鍏冨嚱鏁�(sh霉)寰垎瀛�

鑰冭│鍏�(n猫i)瀹�

澶氬厓鍑芥暩(sh霉)鐨勬蹇点€€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� 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)銆€澶氬厓鍑芥暩(sh霉)鐨勫亸灏庢暩(sh霉)鍜屽叏寰垎銆€鍏ㄥ井鍒嗗瓨鍦ㄧ殑蹇呰姊濅欢鍜屽厖鍒嗘浠� 澶氬厓寰╁悎鍑芥暩(sh霉)銆侀毐鍑芥暩(sh霉)鐨勬眰灏庢硶  浜岄殠鍋忓皫鏁�(sh霉)銆€鏂瑰悜?q奴)顫�?sh霉)鍜屾搴︺€€绌洪枔鏇茬窔鐨勫垏绶氬拰娉曞钩闈€€€鏇查潰鐨勫垏骞抽潰鍜屾硶绶氥€€浜屽厓鍑芥暩(sh霉)鐨勪簩闅庢嘲鍕掑叕寮忋€€澶氬厓鍑芥暩(sh霉)鐨勬サ鍊煎拰姊濅欢妤靛€笺€€澶氬厓鍑芥暩(sh霉)鐨勬渶澶у€�銆佹渶灏忓€煎強鍏剁啊鍠噳鐢�

鑰冭│瑕侀粸

锛�1锛夌悊瑙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�.

锛�2锛変簡瑙ｄ簩鍏冨嚱鏁�(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).

锛�3锛夌悊瑙ｅ鍏冨嚱鏁�(sh霉)鍋忓皫鏁�(sh霉)鍜屽叏寰垎鐨勬蹇碉紝鏈冩眰鍏ㄥ井鍒�锛屼簡瑙ｅ叏寰垎瀛樺湪鐨勫繀瑕佹浠跺拰鍏呭垎姊濅欢锛屼簡瑙ｅ叏寰垎褰㈠紡鐨勪笉璁婃€�.

锛�4锛夌悊瑙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�.

锛�5锛夋帉鎻″鍏冨京鍚堝嚱鏁�(sh霉)涓€闅�銆佷簩闅庡亸灏庢暩(sh霉)鐨勬眰娉�.

锛�6锛変簡瑙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)鐨勫亸灏庢暩(sh霉).

锛�7锛変簡瑙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�锛屾渻姹傚畠鍊戠殑鏂圭▼.

锛�8锛変簡瑙ｄ簩鍏冨嚱鏁�(sh霉)鐨勪簩闅庢嘲鍕掑叕寮�.

锛�9锛夌悊瑙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姊濅欢锛屼簡瑙ｄ簩鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑鍏呭垎姊濅欢锛屾渻姹備簩鍏冨嚱鏁�(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€�锛屽苟鏈冭В姹轰竴浜涚啊鍠殑鎳夌敤鍟忛.

5銆佸鍏冨嚱鏁�(sh霉)绌嶅垎瀛�

鑰冭│鍏�(n猫i)瀹�

浜岄噸绌嶅垎鐨勬蹇�銆佹€ц唱(zh矛)銆佽▓绠楀拰鎳夌敤銆€

鑰冭│瑕侀粸

锛�1锛夌悊瑙ｄ簩閲嶇⿳鍒嗙殑姒傚康锛屼簡瑙ｄ簩閲嶇⿳鍒嗙殑鎬ц唱(zh矛)锛屼簡瑙ｄ簩閲嶇⿳鍒嗙殑涓€煎畾鐞�.

锛�2锛夋帉鎻′簩閲嶇⿳鍒嗙殑瑷堢畻鏂规硶锛堢洿瑙掑潗妯�銆佹サ鍧愭锛�.

6銆佺劇绐礆鏁�(sh霉)

鑰冭│鍏�(n猫i)瀹�

甯告暩(sh霉)闋呯礆鏁�(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁ｇ殑姒傚康銆€鏀舵杺绱氭暩(sh霉)鐨勫拰鐨勬蹇点€€绱氭暩(sh霉)鐨勫熀鏈€ц唱(zh矛)鑸囨敹鏂傜殑蹇呰姊濅欢銆€骞句綍绱氭暩(sh霉)鑸噋绱氭暩(sh霉)鍙婂叾鏀舵杺鎬с€€姝ｉ爡绱氭暩(sh霉)鏀舵杺鎬х殑鍒ゅ垾娉曘€€浜ら尟绱氭暩(sh霉)鑸囪悐甯冨凹鑼ㄥ畾鐞嗐€€浠绘剰闋呯礆鏁�(sh霉)鐨勭禃灏嶆敹鏂傝垏姊濅欢鏀舵杺銆€鍐礆鏁�(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銆€鍐礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)銆€鍐礆鏁�(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) 绨″柈鍐礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勬眰娉曘€€鍒濈瓑鍑芥暩(sh霉)鐨勫啰绱氭暩(sh霉)灞曢枊寮�

鑰冭│瑕侀粸

锛�1锛夌悊瑙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蹇碉紝鎺屾彙绱氭暩(sh霉)鐨勫熀鏈€ц唱(zh矛)鍙婃敹鏂傜殑蹇呰姊濅欢.

锛�2锛夋帉鎻″咕浣曠礆鏁�(sh霉)鑸� 绱氭暩(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁ｇ殑姊濅欢.

锛�3锛夋帉鎻℃闋呯礆鏁�(sh霉)鏀舵杺鎬х殑姣旇純鍒ゅ垾娉曞拰姣斿€煎垽鍒ユ硶锛屾渻鐢ㄦ牴鍊煎垽鍒ユ硶鍜屾煰瑗匡紙Caucy锛夌⿳鍒嗗垽鍒ユ硶.

锛�4锛夋帉鎻′氦閷礆鏁�(sh霉)鐨勮悐甯冨凹鑼ㄥ垽鍒ユ硶.

锛�5锛変簡瑙ｄ换鎰忛爡绱氭暩(sh霉)绲曞皪鏀舵杺鑸囨浠舵敹鏂傜殑姒傚康浠ュ強绲曞皪鏀舵杺鑸囨敹鏂傜殑闂滅郴.

锛�6锛夌悊瑙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.

锛�7锛変簡瑙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)锛堝拰鍑芥暩(sh霉)鐨勯€ｇ簩(x霉)鎬�銆侀€愰爡姹傚皫鍜岄€愰爡绌嶅垎锛�锛屾渻姹備竴浜涘啰绱氭暩(sh霉)鍦ㄦ敹鏂傚崁(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.

锛�8锛変簡瑙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�.

锛�9锛夋帉鎻x锛宻inx锛�(1+x)c锛屽強鐨勯亥鍏嬪嫗鏋楋紙Maclaurin锛夊睍闁嬪紡锛屾渻鐢ㄥ畠鍊戝皣涓€浜涚啊鍠嚱鏁�(sh霉)闁撴帴灞曢枊鐐哄啰绱氭暩(sh霉).

锛堜簩锛夐珮绛変唬鏁�(sh霉)

   1銆佸闋呭紡

鑰冭│鍏�(n猫i)瀹�

鏁�(sh霉)鍩�锛屼竴鍏冨闋呭紡锛屾暣闄ょ殑姒傚康锛屾渶澶у叕鍥犲紡锛屽洜寮忓垎瑙ｅ畾鐞�锛岄噸鍥犲紡锛屽闋呭紡鍑芥暩(sh霉)锛屽京绯绘暩(sh霉)鑸囧绯绘暩(sh霉)澶氶爡寮忕殑鍥犲紡鍒嗚В锛屾湁鐞嗙郴鏁�(sh霉)澶氶爡寮忋€�

鑰冭│瑕侀粸

锛�1锛夋帉鎻℃暩(sh霉)鍩熺殑瀹氱京锛屽苟鏈冨垽鏂蜂竴鍊嬩唬鏁�(sh霉)绯荤当(t菕ng)鏄惁鏄暩(sh霉)鍩�銆�

锛�2锛夌悊瑙ｆ暩(sh霉)鍩烶涓婁竴鍏冨闋呭紡鐨勫畾缇�锛屽闋呭紡鐩镐箻锛屾鏁�(sh霉)锛屼竴鍏冨闋呭紡鐠�(hu谩n)绛夋蹇�銆傛帉鎻″闋呭紡鐨勯亱绠楀強閬嬬畻寰�銆�

锛�3锛夌悊瑙ｆ暣闄ょ殑瀹氱京锛岀啛绶存帉鎻″付浣欓櫎娉曞強鏁撮櫎鐨勬€ц唱(zh矛)銆�

锛�4锛夌悊瑙ｅ拰鎺屾彙鍏╁€嬶紙鎴栬嫢骞插€嬶級澶氶爡寮忕殑鏈€澶у叕鍥犲紡锛屼簰绱犵瓑姒傚康鍙婃€ц唱(zh矛)銆傝兘鐢ㄨ季杞�(zhu菐n)鐩搁櫎娉曟眰鍏╁€嬪闋呭紡鐨勬渶澶у叕鍥犲紡銆�

锛�5锛夋帉鎻′笉鍙磩澶氶爡寮忕殑瀹氱京鍙婃€ц唱(zh矛)銆備簡瑙ｅ洜寮忓垎瑙ｅ畾鐞嗐€�

锛�6锛夋帉鎻閲嶅洜寮忕殑瀹氱京銆�

锛�7锛夋帉鎻″闋呭紡鍑芥暩(sh霉)鐨勬蹇�锛屼綑鏁�(sh霉)瀹氱悊锛屽闋呭紡鐨勬牴鍙婃€ц唱(zh矛)銆傜悊瑙ｄ唬鏁�(sh霉)鍩烘湰瀹氱悊銆傜啛绶存帉鎻″京锛堝锛夌郴鏁�(sh霉)澶氶爡寮忓垎瑙ｅ畾鐞嗗強妯欐簴鍒嗚В寮�銆�

锛�8锛夋帉鎻℃湰鍘熷闋呭紡鐨勫畾缇╁強鎬ц唱(zh矛)銆� 鎺屾彙鏁寸郴鏁�(sh霉)澶氶爡寮忕殑鏈夌悊鏍圭殑瑷堢畻銆�

2銆佽鍒楀紡

鑰冭│鍏�(n猫i)瀹�

鎺掑垪锛宯绱氳鍒楀紡鐨勫畾缇╋紝n绱氳鍒楀紡鐨勬€ц唱(zh矛)锛宯绱氳鍒楀紡鐨勫睍闁�锛岃鍒楀紡鐨勮▓绠楋紝鍏嬫媺榛�(Cramer)娉曞墖锛岃鍒楀紡鐨勪箻娉曡(gu墨)鍓囥€�

    鑰冭│瑕侀粸

锛�1锛夋帉鎻℃帓鍒�銆侀€嗗簭銆侀€嗗簭鏁�(sh霉)銆佸鍋舵帓鍒楃殑瀹氱京銆傛帉鎻℃帓鍒楃殑濂囧伓鎬ц垏灏嶆彌鐨勯棞绯�銆�

锛�2锛夌悊瑙绱氳鍒楀紡鐨勫畾缇╋紝骞惰兘鐢ㄥ畾缇╄▓绠椾竴浜涚壒娈婅鍒楀紡銆�

锛�3锛夋帉鎻¤鍒楀紡鐨勫熀鏈€ц唱(zh矛)銆�

锛�4锛夌悊瑙ｇ煩闄�銆佺煩闄ｇ殑琛屽垪寮忋€佺煩闄ｇ殑鍒濈瓑璁婃彌绛夋蹇�锛岃兘鍒╃敤琛屽垪寮忔€ц唱(zh矛)瑷堢畻涓€浜涚啊鍠鍒楀紡銆�

锛�5锛夌悊瑙ｅ厓绱犵殑浣欏瓙寮�銆佷唬鏁�(sh霉)浣欏瓙寮忕瓑姒傚康銆傜啛绶存帉鎻¤鍒楀紡鎸変竴琛岋紙鍒楋級灞曢枊鐨勫叕寮�銆傛帉鎻¤▓绠楄鍒楀紡鐨勫熀鏈柟娉曡垏鎶€宸с€�

锛�6锛夌啛绶存帉鎻″厠鎷夐粯(Cramer)娉曞墖锛�

    3銆佺窔鎬ф柟绋嬬祫

鑰冭│鍏�(n猫i)瀹�

娑堝厓娉�锛宯缍悜閲忕┖闁�锛岀窔鎬х浉闂滄€э紝鐭╅櫍鐨勭З锛岀窔鎬ф柟绋嬬祫鏈夎В鍒ゅ垾瀹氱悊锛岀窔鎬ф柟绋嬬祫瑙ｇ殑绲�(ji茅)妲�(g貌u)銆�

鑰冭│瑕侀粸

锛�1锛夋帉鎻′竴鑸窔鎬ф柟绋嬬祫锛屾柟绋嬬祫鐨勮В锛屽寤ｇ煩闄�锛岀窔鎬ф柟绋嬬祫鐨勫垵绛夎畩鎻涚瓑姒傚康鍙婃€ц唱(zh矛)銆傛帉鎻￠殠姊舰鏂圭▼绲勭殑鐗瑰緛鍙婁綔鐢ㄣ€傛渻姹傜窔鎬ф柟绋嬬祫鐨勪竴鑸В銆�

锛�2锛夋帉鎻缍悜閲忓強鍏╁€媙缍悜閲忕浉绛夌殑瀹氱京銆傜啛绶存帉鎻″悜閲忕殑閬嬬畻瑕�(gu墨)寰嬪拰鎬ц唱(zh矛)銆�

锛�3锛夌悊瑙ｇ窔鎬х祫鍚�銆佺窔鎬х浉闂�銆佺窔鎬х劇闂滅殑瀹氱京鍙婃€ц唱(zh矛)銆傛帉鎻″叐鍊嬪悜閲忕祫绛夊児鐨勫畾缇╁強绛夊児鎬ц唱(zh矛)瀹氱悊銆傜悊瑙ｅ悜閲忕祫鐨勬サ澶х劇闂滅祫銆佺З鐨勫畾缇�锛屽苟鏈冩眰鍚戦噺绲勭殑涓€鍊嬫サ澶х劇闂滅祫銆�

锛�4锛夋帉鎻＄煩闄ｇ殑琛岀З銆佸垪绉╋紝浠ュ強鐭╅櫍鐨勭З鐨勫畾缇�銆傛帉鎻＄煩闄ｇ殑绉╄垏鍏跺瓙寮忕殑闂滅郴銆�

锛�5锛夋帉鎻＄窔鎬ф柟绋嬬祫鐨勬湁瑙ｅ垽鍒ュ畾鐞�锛屾帉鎻＄窔鎬ф柟绋嬬祫鐨勫叕寮忚В銆�

锛�6锛夌悊瑙ｉ綂娆＄窔鎬ф柟绋嬬祫鐨勫熀绀庤В绯�銆傛帉鎻″熀绀庤В绯荤殑姹傛硶銆佺窔鎬ф柟绋嬬祫鐨勭祼(ji茅)妲�(g貌u)瀹氱悊銆傚苟灏嶆湁瑙ｇ殑涓€鑸窔鎬ф柟绋嬬祫锛屾渻姹傚叾鍏ㄩ儴瑙�銆�

4銆佺煩闄�

鑰冭│鍏�(n猫i)瀹�

鐭╅櫍鐨勬蹇碉紝鐭╅櫍鐨勯亱绠�锛岀煩闄ｄ箻绌嶇殑琛屽垪寮忚垏绉�锛岀煩闄ｇ殑閫�锛岀煩闄ｇ殑鍒嗗锛屽垵绛夌煩闄ｏ紝鍒嗗涔樻硶鐨勫垵绛夎畩鎻涘強鎳夌敤銆�

鑰冭│瑕侀粸

锛�1锛夋帉鎻＄煩闄ｇ殑鐨勫姞娉�銆佹暩(sh霉)涔�銆佷箻娉�銆佽綁(zhu菐n)缃瓑閬嬬畻鍙婂叾瑷堢畻瑕�(gu墨)寰�銆�

锛�2锛夋帉鎻＄煩闄ｄ箻绌嶇殑琛屽垪寮忓畾鐞�锛岀煩闄ｄ箻绌嶇殑绉╄垏瀹冪殑鍥犲瓙鐨勭З鐨勯棞绯汇€�

锛�3锛夋帉鎻″彲閫嗙煩闄�銆侀€嗙煩闄ｃ€佷即闅ㄧ煩闄ｇ瓑姒傚康锛屾帉鎻′竴鍊媙闅庢柟闄ｅ彲閫嗙殑鍏呰姊濅欢鍜岀敤鍏紡娉曟眰涓€鍊嬬煩闄ｇ殑閫嗙煩闄�銆�

锛�4锛夌悊瑙ｅ垎濉婄煩闄ｇ殑鎰忕京锛屾帉鎻″垎濉婄煩闄ｇ殑鍔犳硶銆佷箻娉曠殑閬嬬畻鍙婃€ц唱(zh矛)銆�

锛�5锛夋帉鎻″垵绛夌煩闄�銆佸垵绛夎畩鎻涚瓑姒傚康鍙婂畠鍊戜箣闁撶殑闂滅郴锛屾帉鎻′竴鍊嬬煩闄ｇ殑绛夊児妯欐簴褰㈠拰鐭╅櫍鍙€嗙殑鍏呰姊濅欢锛涙渻鐢ㄥ垵绛夎畩鎻涚殑鏂规硶姹備竴鍊嬫柟闄ｇ殑閫嗙煩闄ｃ€�

锛�6锛夌悊瑙ｅ垎濉婁箻娉曠殑鍒濈瓑璁婃彌鍜屽唬缇╁垵绛夌煩闄ｇ殑闂滅郴锛屾渻姹傚垎濉婄煩闄ｇ殑閫嗐€�

5銆佷簩娆″瀷

鑰冭│鍏�(n猫i)瀹�

浜屾鍨嬬殑鐭╅櫍琛ㄧず锛屾婧栧瀷锛屽敮涓€鎬�锛屾瀹氾紙鍗婃瀹氾級浜屾鍨嬨€�

鑰冭│瑕侀粸

锛�1锛夋纰虹悊瑙ｄ簩娆″舰鍜岄潪閫€鍖栫窔鎬ф浛鎻涚殑姒傚康锛屾帉鎻′簩娆″瀷鐨勭煩闄ｈ〃绀哄強浜屾鍨嬭垏灏嶇ū鐭╅櫍鐨勪竴涓€灏嶆噳闂滅郴锛屾帉鎻＄煩闄ｇ殑鍚堝悓姒傚康鍙婃€ц唱(zh矛)銆�

锛�2锛夌悊瑙ｄ簩娆″瀷鐨勬婧栧舰锛屾帉鎻″寲浜屾鍨嬬偤妯欐簴褰㈢殑鍏╃ó鍩烘湰鏂规硶銆�

锛�3锛夌悊瑙ｅ京鏁�(sh霉)鍩熷拰瀵︽暩(sh霉)鍩熶笂浜屾鍨嬬殑瑕�(gu墨)鑼冩€х殑鍞竴鎬�锛屼簡瑙ｇ铏熷樊銆佹叄鎬ф寚鏁�(sh霉)绛夋蹇�锛屾帉鎻℃叄鎬у畾鐞嗙殑璀夋槑鎬濇兂銆�

锛�4锛夌悊瑙ｆ瀹�銆佸崐姝ｅ畾銆佽矤瀹氫簩娆″瀷鍙婃瀹�銆佸崐姝ｅ畾鐭╅櫍绛夋蹇碉紝鐔熺反鎺屾彙姝ｅ畾浜屾鍨嬶紙鍗婃瀹氫簩娆″瀷锛夌殑鑻ュ共绛夊児姊濅欢銆�

   6銆佺窔鎬х┖闁�

鑰冭│鍏�(n猫i)瀹�

闆嗗悎銆佹槧灏�锛岀窔鎬х┖闁撶殑瀹氱京鑸囩啊鍠€ц唱(zh矛)锛岀董鏁�(sh霉)銆佸熀鑸囧潗妯欙紝鍩鸿畩鎻涜垏鍧愭璁婃彌锛岀窔鎬у瓙绌洪枔锛屽瓙绌洪枔鐨勪氦鑸囧拰锛屽瓙绌洪枔鐨勭洿鍜�锛岀窔鎬х┖闁撶殑鍚屾(g貌u)銆�

鑰冭│瑕侀粸

锛�1锛夋帉鎻＄窔鎬х┖闁撶殑瀹氱京鍙婃€ц唱(zh矛)锛屾渻鍒ゆ柗涓€鍊嬩唬鏁�(sh霉)绯荤当(t菕ng)鏄惁鐐虹窔鎬х┖闁�銆�

锛�2锛夌悊瑙ｇ窔鎬х祫鍚堛€佺窔鎬ц〃绀�銆佺窔鎬х浉闂溿€佺窔鎬х劇闂滅瓑姒傚康锛屾纰虹悊瑙ｅ拰鎺屾彙n缍窔鎬х┖闁撶殑姒傚康鍙婃€ц唱(zh矛)銆�

锛�3锛夊熀璁婃彌鑸囧潗妯欒畩鎻涚殑闂滅郴銆�

锛�4锛夋帉鎻″熀涔嬮枔鐨勯亷娓＄煩闄ｅ強鍏舵€ц唱(zh矛)銆�

锛�5锛夌悊瑙ｇ窔鎬у瓙绌洪枔鐨勫畾缇╁強鍒ゅ垾瀹氱悊锛屾帉鎻＄窔鎬ф柟绋嬬祫鐨勮В绌洪枔鐨勬蹇靛拰鎬ц唱(zh矛)锛屾帉鎻″悜閲忕祫鐢熸垚瀛愮┖闁撶殑瀹氱京鍙婄瓑鍍规浠�銆�

锛�6锛夋帉鎻″瓙绌洪枔鐨勪氦鑸囧拰鐨勫畾缇╁強鎬ц唱(zh矛)锛屾帉鎻＄董鏁�(sh霉)鍏紡骞惰兘鐔熺反閬嬬敤銆�

锛�7锛夌悊瑙ｅ瓙绌洪枔鐨勭洿鍜岀殑姒傚康锛屼互鍙婂垽鏂风洿鍜岀殑鑻ュ共鍏呰姊濅欢銆�

   7銆佺窔鎬ц畩鎻�

鑰冭│鍏�(n猫i)瀹�

绶氭€ц畩鎻涚殑瀹氱京锛岀窔鎬ц畩鎻涚殑閬嬬畻锛岀窔鎬ц畩鎻涚殑鐭╅櫍锛岀壒寰佸€艰垏鐗瑰緛鍚戦噺锛屽皪瑙掔煩闄ｏ紝绶氭€ц畩鎻涚殑鍊煎煙鑸囨牳锛屼笉璁婂瓙绌洪枔锛岃嫢鐖剧暥(Jordan)妯欐簴褰粙绱广€�

鑰冭│瑕侀粸

锛�1锛夋帉鎻＄窔鎬ц畩鎻涚殑瀹氱京鍙婃€ц唱(zh矛)銆�

锛�2锛夋帉鎻＄窔鎬ц畩鎻涚殑閬嬬畻鍙婇亱绠楄(gu墨)寰嬶紝鐞嗚В绶氭€ц畩鎻涚殑澶氶爡寮�銆�

锛�3锛夋帉鎻＄窔鎬ц畩鎻涜垏鐭╅櫍鐨勮伅(li谩n)绯�锛屾帉鎻＄煩闄ｇ浉浼肩殑姒傚康鍜岀窔鎬ц畩鎻涘湪涓嶅悓鍩轰笅鐨勭煩闄ｇ浉浼肩瓑鎬ц唱(zh矛)銆�

锛�4锛夌悊瑙ｇ煩闄ｇ殑鐗瑰緛鍊�銆佺壒寰佸悜閲�銆佺壒寰佸闋呭紡鐨勬蹇靛拰鎬ц唱(zh矛)锛屾渻姹備竴鍊嬬煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚戦噺锛屾帉鎻＄浉浼肩煩闄ｈ垏瀹冨€戠殑鐗瑰緛澶氶爡寮忕殑闂滅郴鍙婂搱瀵嗛爴-鍑辫悐瀹氱悊銆�

锛�5锛夋帉鎻缍窔鎬х┖闁撲腑涓€鍊嬬窔鎬ц畩鎻涘湪鏌愪竴绲勫熀涓嬬殑鐭╅櫍鐐哄皪瑙掔煩闄ｇ殑鍏呰姊濅欢銆�

锛�6锛夋帉鎻＄窔鎬ц畩鎻涚殑鍊煎煙銆佹牳銆佺З銆侀浂搴︾瓑姒傚康锛屾帉鎻＄窔鎬ц畩鎻涚殑鍊煎煙鑸囧畠灏嶆噳鐨勭煩闄ｇ殑绉╃殑闂滅郴鍙婄窔鎬ц畩鎻涚殑绉╁拰闆跺害闁撶殑闂滅郴銆�

锛�7锛夋帉鎻′笉璁婂瓙绌洪枔鐨勫畾缇�锛屾渻鍒ゅ畾涓€鍊嬪瓙绌洪枔鏄惁鏄疉-瀛愮┖闁�锛岀悊瑙ｄ笉璁婂瓙绌洪枔鑸囩窔鎬ц畩鎻涚煩闄ｅ寲绨′箣闁撶殑闂滅郴锛屾帉鎻″皣绌洪枔V鎸夌壒寰佸€煎垎瑙ｆ垚涓嶈畩瀛愮┖闁撳拰鐩村拰琛ㄩ仈寮�銆�

锛�8锛変簡瑙ｈ嫢鐖剧暥(Jordan)妯欐簴褰㈠強鍏剁浉闂滄€ц唱(zh矛)銆�

    8銆佹瓙骞鹃噷寰风┖闁�

鑰冭│鍏�(n猫i)瀹�

瀹氱京鑸囧熀鏈€ц唱(zh矛)锛屾婧栨浜ゅ熀锛屽悓妲�(g貌u)锛屾浜よ畩鎻�锛屽瓙绌洪枔锛屽灏嶇ū鐭╅櫍鐨勭浉浼兼婧栧舰锛屽悜閲忓埌瀛愮┖闁撶殑璺濋洟銆�

鑰冭│瑕侀粸

锛�1锛夌悊瑙ｆ瓙姘忕┖闁撶殑瀹氱京鍙婃€ц唱(zh矛)锛岀悊瑙ｅ収(n猫i)绌嶇殑鏈唱(zh矛)锛屾帉鎻″悜閲忕殑闀峰害锛屽叐鍊嬪悜閲忕殑澶捐銆佸柈浣嶅悜閲�銆佹浜ゅ強搴﹂噺鐭╅櫍绛夋蹇靛拰鍩烘湰鎬ц唱(zh矛)锛屾帉鎻″悇绋蹇典箣闁撶殑鑱�(li谩n)绯诲拰鍗€(q奴)鍒�銆�

锛�2锛夌悊瑙ｆ浜ゅ悜閲忕祫銆佹婧栨浜ゅ熀鐨勬蹇�锛屾帉鎻℃柦瀵嗙壒姝ｄ氦鍖栭亷绋嬶紝骞惰兘鎶婁竴绲勭窔鎬х劇闂滅殑鍚戦噺鍖栫偤鍠綅姝ｄ氦鐨勫悜閲�銆�

锛�3锛夌悊瑙ｆ浜よ畩鎻涚殑姒傚康鍙婂咕鍊嬬瓑鍍归棞绯�锛屾帉鎻℃浜よ畩鎻涜垏鍚戦噺鐨勯暦搴�锛屾婧栨浜ゅ熀锛屾浜ょ煩闄ｉ枔鐨勯棞绯�銆�

锛�4锛夌悊瑙ｅ叐鍊嬪瓙绌洪枔姝ｄ氦鐨勬蹇�锛屾帉鎻℃浜よ垏鐩村拰鐨勯棞绯�锛屽強鏈夐檺缍瓙姘忕┖闁撲腑鐨勬瘡涓€鍊嬪瓙绌洪枔閮芥湁鍞竴鐨勬浜よ鐨勬€ц唱(zh矛)銆�

锛�5锛夌悊瑙ｅ苟鎺屾彙浠讳竴鍊嬪灏嶇ū鐭╅櫍鍧囧彲姝ｄ氦鐩镐技浜庝竴鍊嬪皪瑙掗櫍锛屽苟鎺屾彙姹傛浜ら櫍鐨勬柟娉�銆傝兘鐢ㄦ浜よ畩鎻涘寲瀵︿簩娆″瀷鐐烘婧栧瀷銆�

浜�銆佸弮鑰冩浉鐩�

1銆佸京鏃﹀ぇ瀛告暩(sh霉)瀛哥郴绶�.鏁�(sh霉)瀛稿垎鏋愶紙绗笁鐗堬級. 楂樼瓑鏁欒偛鍑虹増绀�, 2007

2銆佸寳浜ぇ瀛告暩(sh霉)瀛哥郴绶� 锛岄珮绛変唬鏁�(sh霉) (绗笁鐗�)锛岄珮绛夋暀鑲插嚭鐗堢ぞ, 鍖椾含锛�2003锛夛紱