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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(xu茅)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(xu茅)鏍℃洿鏂拌嚦2012骞�锛�2013骞达紱鍧囨彁渚涙敹璨�(f猫i)涓嬭級銆� 涓嬭級娴佺▼锛� 鑰冪爺鐪熼 榛�(di菐n)鎿娾€�鑰冪爺瑭﹀嵎鈥濃€濅笅杓�; 鑰冨崥鐪熼 榛�(di菐n)鎿娾€�鑰冨崥瑭﹀嵎搴�鈥� 涓嬭級
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2015骞磋泊宸炲斧鑼冨ぇ瀛�(xu茅)纰╁＋鐮旂┒鐢熷叆瀛�(xu茅)鑰冭│澶х侗
銆婇珮绛夋暩(sh霉)瀛�(xu茅)銆嬶紙绉戠洰浠ｇ⒓锛�601锛�
涓€銆佽€冭│褰㈠紡鑸囪│鍗风祼(ji茅)妲�(g貌u)
1. 瑭﹀嵎婊垮垎 鍙� 鑰冭│鏅�(sh铆)闁�
鏈│鍗锋豢鍒嗙偤 150 鍒�锛岃€冭│鏅�(sh铆)闁撶偤 180 鍒嗛悩銆�
2. 绛旈鏂瑰紡
绛旈鏂瑰紡鐐洪枆鍗�銆佺瓎瑭︺€�
瑭﹀嵎鐢辫│椤屽拰绛旈绱欑祫鎴�锛涚瓟妗堝繀闋堝鍦ㄧ瓟椤岀礄锛堢敱鑰冮粸(di菐n)鎻愪緵锛夌浉鎳�(y墨ng)鐨勪綅缃笂銆�
浜�銆佸京(f霉)缈�(x铆)瑕佹眰
鍏ㄦ棩鍒舵敾璁€纰╁＋瀛�(xu茅)浣嶇爺绌剁敓鍏ュ(xu茅)鑰冭│楂樼瓑鏁�(sh霉)瀛�(xu茅)绉戠洰鑰冭│鍏�(n猫i)瀹瑰寘鎷珮绛夋暩(sh霉)瀛�(xu茅)涓娿€佷笅鍐�(c猫)鍩虹(ch菙)瑾�
绋�锛岃姹傝€冪敓绯荤当(t菕ng)鎺屾彙鐩搁棞(gu膩n)瀛�(xu茅)绉戠殑鍩烘湰鐭ヨ瓨(sh铆)銆佸熀绀�(ch菙)鐞嗚珫鍜屽熀鏈柟娉�锛屽苟鑳介亱(y霉n)鐢ㄧ浉闂�(gu膩n)鐞嗚珫鍜屾柟娉�
鍒嗘瀽銆佽В姹虹浉闂�(gu膩n)鐨勪竴浜涘(sh铆)闅涘晱椤�銆�
涓�銆佽€冭│鍏�(n猫i)瀹硅垏瑕佹眰
绗竴閮ㄥ垎 妤甸檺鑸囬€ｇ簩(x霉)
1銆� 鑰冭│鍏�(n猫i)瀹�
鍑芥暩(sh霉)姒傚康鍙婂叾琛ㄧず娉�锛屽嚱鏁�(sh霉)鐨勫咕绋壒鎬э紝鍙嶅嚱鏁�(sh霉)锛屽京(f霉)鍚堝嚱鏁�(sh霉)锛屽垵绛夊嚱鏁�(sh霉)锛岄洐鏇插嚱鏁�(sh霉)鑸囧弽闆�
鏇插嚱鏁�(sh霉)锛涙暩(sh霉)鍒楁サ闄�锛屽嚱鏁�(sh霉)妤甸檺锛屾サ闄愰亱(y霉n)绠楁硶鍓�锛岀劇绐皬鑸囩劇绐ぇ閲�锛岀劇绐皬鐨勬瘮杓冿紝妤甸檺瀛樺湪
婧�(zh菙n)鍓囧強鍏╁€�(g猫)閲嶈妤甸檺锛屽嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�锛屽嚱鏁�(sh霉)鐨勯枔鏂烽粸(di菐n)锛屽垵绛夊嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬э紝闁夊崁(q奴)闁撲笂鍑芥暩(sh霉)閫ｇ簩(x霉)
鐨勬€ц唱(zh矛)銆�
2銆� 鑰冭│瑕佹眰
2.1 鐞嗚В鍑芥暩(sh霉)鐨勬蹇�;浜嗚В鍑芥暩(sh霉)鐨勫柈瑾�(di脿o)鎬�銆佸懆鏈熸€�銆佸鍋舵€х瓑銆�
2.2. 鐞嗚В鍙嶅嚱鏁�(sh霉)鍜屽京(f霉)鍚堝嚱鏁�(sh霉)鐨勬蹇�銆�
2.3. 鐞嗚В鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍙婂湒褰�銆�
2.4. 鑳藉垪鍑虹啊鍠(sh铆)闅涘晱椤屼腑鐨勫嚱鏁�(sh霉)闂�(gu膩n)绯�銆�
2.5.浜嗚В妤甸檺鐨� 蔚 -N,蔚 -未 瀹氱京 锛屽苟鑳藉湪瀛�(xu茅)缈�(x铆)閬庣▼涓€愭鍔犳繁灏�(du矛)妤甸檺鎬濇兂鐨勭悊瑙�銆�
2
2.6 鎺屾彙妤甸檺鐨勫洓鍓囬亱(y霉n)绠�銆�
2.7 鐞嗚В鍏╁€�(g猫)妤甸檺瀛樺湪婧�(zh菙n)鍓�(澶鹃€兼簴(zh菙n)鍓囧拰鍠(di脿o)鏈夌晫婧�(zh菙n)鍓�),鏈�(hu矛)鐢ㄥ叐鍊�(g猫)閲嶈妤甸檺姹傛サ闄愩€�
2.8 鐞嗚В鐒＄灏�,鐒＄澶х殑姒傚康,鎺屾彙鐒＄灏忕殑姣旇純銆�
2.9 鐞嗚В鍑芥暩(sh霉)鍦ㄤ竴榛�(di菐n)閫ｇ簩(x霉)鐨勬蹇�,鏈�(hu矛)鍒ゆ柗闁撴柗榛�(di菐n)鐨勯鍨�銆�
2.10 浜嗚В鍒濈瓑鍑芥暩(sh霉)鐨勯€ｇ簩(x霉)鎬�,鐭ラ亾閫ｇ簩(x霉)鍑芥暩(sh霉)鍦ㄩ枆鍗€(q奴)闁撲笂鐨勯€ｇ簩(x霉)鎬�(浠嬪€煎畾鐞嗗拰鏈€鍊煎畾鐞�) 绛夈€�
绗簩閮ㄥ垎 涓€鍏冨嚱寰垎瀛�(xu茅)
1銆佽€冭│鍏�(n猫i)瀹�
灏�(d菐o)鏁�(sh霉)姒傚康锛屽嚱鏁�(sh霉)姹傚皫(d菐o)娉曞墖锛屽熀鏈垵绛夊嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)鍙婂垵绛夊嚱鏁�(sh霉)鐨勬眰灏�(d菐o)鍟忛锛岄珮闅庡皫(d菐o)鏁�(sh霉)锛岄毐鍑�
鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)锛岀敱鍙冩暩(sh霉)鏂圭▼鎵€纰哄畾鐨勫嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)锛屽嚱鏁�(sh霉)寰垎鐨勬蹇�锛屽熀鏈垵绛夌殑寰垎鍙婂井鍒嗛亱(y霉n)绠楁硶
鍓�锛屽井鍒嗗湪杩戜技瑷�(j矛)绠楀強瑾ゅ樊浼拌▓(j矛)涓殑鎳�(y墨ng)鐢�锛涗腑鍊煎畾鐞�锛岀緟蹇呭娉曞墖锛屾嘲鍕掑叕寮�锛屽嚱鏁�(sh霉)鍠(di脿o)鎬х殑
鍒ゅ畾娉�锛屽嚱鏁�(sh霉)妤靛€煎強鍏舵眰娉曘€佹渶澶у€�銆佹渶灏忓€肩殑姹傛硶锛屾洸绶氱殑鍑瑰嚫鑸囨嫄榛�(di菐n)锛屽嚱鏁�(sh霉)鍦栧舰鐨勪綔娉�銆�
2銆� 鑰冭│瑕佹眰
2.1 鐞嗚В灏�(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑姒傚康,浜嗚В灏�(d菐o)鏁�(sh霉)鐨勫咕浣曟剰缇╁強鍑芥暩(sh霉)鐨勫彲灏�(d菐o)鎬у拰閫ｇ簩(x霉)鎬т箣闁撶殑闂�(gu膩n)绯�,鑳界敤
灏�(d菐o)鏁�(sh霉)鎻忚堪涓€浜涚墿鐞嗛噺銆�
2.2 鐞嗚В灏�(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑閬�(y霉n)绠楁硶鍓�(鍖呮嫭寰垎褰㈠紡涓嶈畩鎬�)鍜屽皫(d菐o)鏁�(sh霉)鐨勫熀鏈叕寮�,浜嗚В楂橀殠灏�(d菐o)鏁�(sh霉)鐨勬
蹇�,鑳界啛绶寸殑姹傚垵绛夊嚱鏁�(sh霉)鐨勪竴闅�,浜岄殠灏�(d菐o)鏁�(sh霉)銆�
2.3 鎺屾彙闅卞嚱鏁�(sh霉)鍜屽弮鏁�(sh霉)寮忔墍纰哄畾鐨勫嚱鏁�(sh霉)鐨勪竴闅庡拰浜岄殠灏�(d菐o)鏁�(sh霉)銆�
2.4 鐞嗚В娲涚埦(Rolle)瀹氱悊,鎷夋牸鏈楁棩(Lagrange)瀹氱悊,浜嗚В鏌タ(Cauchy)瀹氱悊鍜屾嘲鍕�(Taylor)
瀹氱悊,鏈�(hu矛)鐢ㄦ媺鏍兼湕鏃ュ畾鐞�銆�
2.5 鎺屾彙娲涘繀閬�(d谩)(L'Hospital)娉曞墖绛�銆�
2.6 鐞嗚В鍑芥暩(sh霉)妤靛€肩殑姒傚康,鎺屾彙姹傚嚱鏁�(sh霉)鐨勬サ鍊�,鍒ゆ柗鍑芥暩(sh霉)鐨勫娓涙€ц垏鍑芥暩(sh霉)鍦栧舰鐨勫嚬鍑告€�,姹傚嚱鏁�(sh霉)
鍦栧舰鐨勬嫄榛�(di菐n)绛夋柟娉�,鑳芥弿绻嚱鏁�(sh霉)鐨勫湒褰�(鍖呮嫭姘村钩鍜岄墰鐩存几杩戠窔),鏈�(hu矛)姹傜啊鍠殑鏈€澶у€煎拰鏈€
灏忓€肩殑鎳�(y墨ng)鐢ㄥ晱椤�銆�
2.7 浜嗚В鏇茬巼鍜屾洸鐜囧崐寰戠殑姒傚康,骞舵渻(hu矛)瑷�(j矛)绠楁洸鐜囧拰鏇茬巼鍗婂緫绛夈€�
绗笁閮ㄥ垎 涓€鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)
1銆佽€冭│鍏�(n猫i)瀹�
3
涓嶅畾绌嶅垎鐨勬蹇�銆佹€ц唱(zh矛)鑸囧熀鏈⿳鍒嗗叕寮�锛屾彌鍏冪⿳鍒嗘硶锛屽垎閮ㄧ⿳鍒嗘硶锛屽咕绋壒娈婇鍨嬪嚱鏁�(sh霉)锛堟湁
鐞嗗嚱鏁�(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)鐨勬湁鐞嗗紡锛岀啊鍠劇鐞嗗嚱鏁�(sh霉)锛夌殑绌嶅垎锛涘畾绌嶅垎姒傚康鍙婂叾鎬ц唱(zh矛)锛屽井绌嶅垎鍩烘湰鍏紡锛�
瀹氱⿳鍒嗘彌鍏冩硶锛屽畾绌嶅垎鍒嗛儴绌嶅垎娉�锛屽唬缇╃⿳鍒�锛屽畾绌嶅垎鐨勮繎浼艰▓(j矛)绠楋紱瀹氱⿳鍒嗙殑寰厓娉�锛屽畾绌嶅垎
鍦ㄨ▓(j矛)绠楅潰绌嶏紝楂旂⿳鍙婃洸绶氬姬闀蜂腑鐨勬噳(y墨ng)鐢�锛屽畾绌嶅垎鍦ㄧ墿鐞嗕腑鐨勬噳(y墨ng)鐢�锛屽钩鍧囧€笺€�
2銆佽€冭│瑕佹眰
2.1 鐞嗚В涓嶅畾绌嶅垎鐨勬蹇靛強鎬ц唱(zh矛)銆�
2.2 鐔熸倝涓嶅畾绌嶅垎鐨勫熀鏈叕寮�,鐔熺反鎺屾彙涓嶅畾绌嶅垎鍜屽畾绌嶅垎鐨勬彌鍏冪⿳鍒嗘硶,鍒嗛儴绌嶅垎娉�,鎺屾彙杓�
绨″柈鐨勬湁鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒�銆�
2.3 骞剧ó鐗规畩鍑芥暩(sh霉)鐨勭⿳鍒�
2.4 绌嶅垎琛ㄧ殑浣跨敤绛�銆�
2.5 鐞嗚В瀹氱⿳鍒嗙殑姒傚康鍙婃€ц唱(zh矛)銆�
2.6 鐞嗚В璁婁笂闄愮殑瀹氱⿳鍒嗕綔鐐哄叾涓婇檺鐨勫嚱鏁�(sh霉)鍙婂叾姹傚皫(d菐o)瀹氱悊锛岀啛鎮夌墰闋�(Newton)-- 钀婂竷灏艰尐
(Leibuniz)鍏紡銆�
2.7 鐔熺反鎺屾彙瀹氱⿳鍒嗙殑鎻涘厓绌嶅垎娉�,鍒嗛儴绌嶅垎娉�銆�
2.8 瀹氱⿳鍒嗙殑杩戜技瑷�(j矛)绠�銆�
2.9 浜嗚В瀹氱⿳鍒嗙殑鎳�(y墨ng)鐢� 锛欰 鐞嗚В寰厓娉�锛� B 姹傚钩闈㈠湒鍨嬬殑闈㈢⿳鍙婂姬闀�锛岀┖闁撶墿楂旂殑楂旂⿳锛� C
鍔熴€佹按澹撳姏銆佸紩鍔� 锛汥 骞冲潎鍊肩瓑銆�
绗洓閮ㄥ垎 鍚戦噺浠ｆ暩(sh霉)鑸囩┖闁撹В鏋愬咕浣�
1銆佽€冭│鍏�(n猫i)瀹�
绌洪枔鐩磋鍧愭(bi膩o)绯诲強鍏╅粸(di菐n)闁撶殑璺濋洟锛屽悜閲忕殑姒傚康鍙婂叾閬�(y霉n)绠楋紙鍖呮嫭鏁�(sh霉)閲忕⿳鑸囧悜閲忕⿳锛夛紝鍚戦噺鐨�
鍧愭(bi膩o)锛岀┖闁撲腑鐨勫钩闈㈠拰鐩寸窔锛屽父瑕嬩簩娆℃洸闈€€�
2銆佽€冭│瑕佹眰
2.1 鐞嗚В鍚戦噺鐨勬蹇点€�
2.2 鎺屾彙鍚戦噺鐨勯亱(y霉n)绠楋紙绶氭€ч亱(y霉n)绠�锛岄粸(di菐n)涔樻硶锛屽弶涔樻硶锛�锛屾帉鎻″叐鍊�(g猫)鍚戦噺澶捐鐨勬眰娉曚互鍙婂瀭鐩�锛屽钩
琛岀殑姊濅欢銆�
2.3 鐔熸倝鍠綅鍚戦噺,鏂瑰悜浣欏鸡鍙婂悜閲忕殑鍧愭(bi膩o)琛ㄩ仈(d谩)寮�锛屾帉鎻＄敤鍧愭(bi膩o)琛ㄩ仈(d谩)寮忛€�(j矛n)琛屽悜閲忛亱(y霉n)绠椼€�
4
2.4 鎺屾彙骞抽潰鐨勬柟绋嬪拰鐩寸窔鐨勬柟绋嬪強鍏舵眰娉�銆�
2.5 鐞嗚В鏇查潰鏂圭▼鐨勬蹇�锛屾帉鎻″父鐢ㄤ簩娆℃洸闈㈢殑鏂圭▼鍙婂叾鍦栧舰锛屼簡瑙ｄ互鍧愭(bi膩o)杌哥偤鏃嬭綁(zhu菐n)杌哥殑鏃嬭綁(zhu菐n)
鏇查潰鍙婃瘝绶氬钩琛屼簬鍧愭(bi膩o)杌哥殑鏌遍潰鏂圭▼銆�
2.6 浜嗚В绌洪枔鏇茬窔鐨勫弮鏁�(sh霉)鏂圭▼鍜屼竴鑸柟绋嬬瓑銆�
绗簲閮ㄥ垎 澶氬厓鍑芥暩(sh霉)寰垎瀛�(xu茅)
1銆佽€冭│鍏�(n猫i)瀹�
澶氬厓鍑芥暩(sh霉)鐨勬蹇�锛屽鍏冨嚱鏁�(sh霉)鐨勬サ闄愯垏閫ｇ簩(x霉)鎬�锛屽亸灏�(d菐o)鏁�(sh霉)锛屽叏寰垎锛屽鍏冨京(f霉)鍚堝嚱鏁�(sh霉)鐨勬眰灏�(d菐o)锛岄毐
鍑芥暩(sh霉)姹傚皫(d菐o)锛屽亸灏�(d菐o)鏁�(sh霉)鐨勫咕浣曟噳(y墨ng)鐢�锛屾柟鍚�?q奴)顫�?sh霉)鑸囨搴�锛屽鍏冨嚱鏁�(sh霉)鐨勬サ鍊煎強鍏舵眰娉曪紝浜屽厓鍑芥暩(sh霉)鐨勬嘲鍕�
鍏紡銆�
2銆佽€冭│瑕佹眰
2.1 鐞嗚В澶氬厓鍑芥暩(sh霉)鐨勬蹇�銆�
2.2 浜嗚В浜屽厓鍑芥暩(sh霉)鐨勬サ闄�锛岄€ｇ簩(x霉)鎬х瓑姒傚康鍙婃湁鐣岄枆鍗€(q奴)鍩熶笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)銆�
2.3 鐞嗚В鍋忓皫(d菐o)鏁�(sh霉)銆佸叏寰垎绛夋蹇碉紝浜嗚В鍏ㄥ井鍒嗗瓨鍦ㄧ殑蹇呰姊濅欢鍜屽厖鍒嗘浠�銆�
2.4 浜嗚В鏂瑰悜?q奴)顫�?sh霉)鑸囨搴︾殑姒傚康锛屽苟鎺屾彙瀹冨€戠殑瑷�(j矛)绠楁柟娉�銆�
2.5 鎺屾彙寰�(f霉)鍚堝嚱鏁�(sh霉)鐨勬眰灏�(d菐o)娉曪紝鏈�(hu矛)姹備簩闅庡亸灏�(d菐o)鏁�(sh霉)銆�
2.6 鎺屾彙闅卞嚱鏁�(sh霉)鍖呮嫭鐢辨柟绋嬬祫纰哄畾鐨勯毐鍑芥暩(sh霉)鐨勫皫(d菐o)鏁�(sh霉)姹傛硶銆�
2.7 浜嗚В鏇茬窔鐨勫垏绶氳垏娉曞钩闈㈠強鏇查潰鐨勫垏骞抽潰鑸囨硶绶�锛屽苟鎺屾彙瀹冨€戞柟绋嬬殑姹傛硶銆�
2.8 鐞嗚В澶氬厓鍑芥暩(sh霉)妤靛€肩殑姒傚康锛屾渻(hu矛)姹傚嚱鏁�(sh霉)鐨勬サ鍊�锛屼簡瑙ｆ浠舵サ鍊肩殑姒傚康锛屾渻(hu矛)鐢ㄦ媺鏍兼湕鏃ヤ箻鏁�(sh霉)娉�
姹傛浠舵サ鍊�锛屾渻(hu矛)姹備竴浜涜純绨″柈鐨勬渶澶у€煎拰鏈€灏忓€肩殑鎳�(y墨ng)鐢ㄥ晱椤岀瓑銆�
绗叚閮ㄥ垎 閲嶇⿳鍒�
1銆佽€冭│鍏�(n猫i)瀹�
浜岄噸绌嶅垎鐨勬蹇靛強鎬ц唱(zh矛)锛屼簩閲嶇⿳鍒嗙殑瑷�(j矛)绠楁硶锛屼簩閲嶇⿳鍒嗙殑鎳�(y墨ng)鐢�锛屼笁閲嶇⿳鍒嗙殑姒傚康鍙婂叾瑷�(j矛)绠�
鏂规硶銆�
2銆佽€冭│瑕佹眰
2.1 鐞嗚В浜岄噸绌嶅垎銆佷簩閲嶇⿳鍒嗙殑鎬ц唱(zh矛)銆�
5
2.2 鎺屾彙浜岄噸绌嶅垎鐨勮▓(j矛)绠楁柟娉曪紙鐩磋鍧愭(bi膩o)绯伙紝妤靛潗妯�(bi膩o)绯伙級銆�
2.3 鐞嗚В涓夐噸绌嶅垎鐨勬蹇碉紝浜嗚В涓夐噸绌嶅垎鐨勬€ц唱(zh矛)銆�
2.4 鎺屾彙涓夐噸绌嶅垎鐨勮▓(j矛)绠楁柟娉曪紙鐩磋鍧愭(bi膩o)锛屾煴闈㈠潗妯�(bi膩o)锛岀悆闈㈠潗妯�(bi膩o)锛夌瓑銆�
绗竷閮ㄥ垎 鏇茬窔绌嶅垎鑸囨洸闈㈢⿳鍒�
1銆佽€冭│鍏�(n猫i)瀹�
鏇茬窔绌嶅垎鐨勬蹇靛強鎬ц唱(zh矛)锛屾洸绶氱⿳鍒嗙殑瑷�(j矛)绠楋紝鏍兼灄鍏紡鍙婂叾鎳�(y墨ng)鐢�锛屾洸闈㈢⿳鍒嗙殑姒傚康鍙婃€ц唱(zh矛)锛�
鏇查潰绌嶅垎鐨勮▓(j矛)绠�锛岄珮鏂叕寮�
2銆佽€冭│瑕佹眰锛�
2.1 鎺屾彙绗竴鍨嬫洸绶氱⿳鍒嗚垏鏇查潰绌嶅垎銆�
2.2 鎺屾彙绗簩鍨嬫洸绶氱⿳鍒�锛涗簡瑙ｆ牸鏋楀叕寮�銆�
2.3 浜嗚В绗簩鍨嬫洸闈㈢⿳鍒嗚垏楂樻柉鍏紡銆�
2.4 浜嗚В鏂墭鍏嬫柉鍏紡銆�
绗叓閮ㄥ垎 鐒＄绱�(j铆)鏁�(sh霉)
1銆佽€冭│鍏�(n猫i)瀹�
甯告暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬蹇靛強鎬ц唱(zh矛)锛屽父鏁�(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鍜屾敹鏂傛硶锛屽啰绱�(j铆)鏁�(sh霉)锛屽嚱鏁�(sh霉)灞曟垚鍐礆(j铆)鏁�(sh霉)锛屽嚱鏁�(sh霉)鐨勫啰
绱�(j铆)鏁�(sh霉)灞曢枊寮忕殑鎳�(y墨ng)鐢�锛屽倕閲岃憠绱�(j铆)鏁�(sh霉)锛屾寮︾礆(j铆)鏁�(sh霉)鑸囦綑寮︾礆(j铆)鏁�(sh霉)銆�
2銆佽€冭│瑕佹眰
2.1 鐞嗚В鐒＄绱�(j铆)鏁�(sh霉)鏀舵杺锛岀櫦(f膩)鏁ｄ互鍙婂拰鐨勬蹇碉紱浜嗚В鐒＄绱�(j铆)鏁�(sh霉)鏀舵杺鐨勫繀瑕佹浠�锛岀煡閬撶劇绐礆(j铆)鏁�(sh霉)
鐨勫熀鏈€ц唱(zh矛)銆�
2.2 浜嗚В骞句綍绱�(j铆)鏁�(sh霉)鍜� P 绱�(j铆)鏁�(sh霉)鐨勬敹鏂傛€�銆�
2.3 鎺屾彙姝ｉ爡(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬瘮杓冨鏂傛硶锛屾帉鎻℃闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬瘮鍊煎鏂傛硶銆�
2.4 鎺屾彙浜ら尟(cu貌)绱�(j铆)鏁�(sh霉)鐨勮悐甯冨凹鑼插畾鐞�锛屽苟鑳戒及瑷�(j矛)瀹冪殑鎴�?c谩i)鍡綻宸�銆�
2.5 浜嗚В鐒＄绱�(j铆)鏁�(sh霉)绲曞皪(du矛)鏀舵杺鑸囨浠舵敹鏂傜殑闂�(gu膩n)绯�銆�
2.6 浜嗚В鍑芥暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬敹鏂傚煙鍙婂拰鍑芥暩(sh霉)鐨勬蹇点€�
6
2.7 鎺屾彙杓冪啊鍠殑鍐礆(j铆)鏁�(sh霉)鐨勬敹鏂傚崁(q奴)闁撶殑姹傛硶锛堝彲涓嶈€冩叜绔粸(di菐n)鐨勯€ｇ簩(x霉)鎬э級銆傜煡閬撳啰绱�(j铆)鏁�(sh霉)鍦ㄥ叾鏀舵杺
鍗€(q奴)闁撶殑涓€浜涙€ц唱(zh矛)銆�
2.8 鎺屾彙鍑芥暩(sh霉)灞曢枊鎴愭嘲鍕掔礆(j铆)鏁�(sh霉)鐨勯噸瑕佹浠�銆�
2.9 鎺屾彙 e
x
,sinx,cosx,Ln(1+x)鍜�(1+x)
n
鐨勯亥鍏嬪嫗鏋楋紙Maclaurin锛夊睍闁嬪紡锛屽苟鑳界敤閫欎簺灞�
闁嬪紡灏囦竴浜涚啊鍠殑鍑芥暩(sh霉)灞曢枊鎴愬啰绱�(j铆)鏁�(sh霉)銆�
2.10 浜嗚В鍐礆(j铆)鏁�(sh霉)閫�(j矛n)琛屼竴浜涜繎浼艰▓(j矛)绠楃殑鏂规硶銆�
2.11 浜嗚В鍑芥暩(sh霉)灞曢枊鎴愬倕绔嬭憠锛團ourier锛夌礆(j铆)鏁�(sh霉)鐨勫厖鍒嗘浠�锛屽苟鑳藉皣瀹氱京鍦╗-蟺 ,蟺 ]鍜孾-l,l]
涓婄殑鍑芥暩(sh霉)灞曢枊鐐哄倕绔嬭憠绱�(j铆)鏁�(sh霉)锛岃兘灏囧畾缇╁湪[0,l]涓婄殑鍑芥暩(sh霉)灞曢枊鐐烘寮︽垨浣欏鸡绱�(j铆)鏁�(sh霉)绛�銆�
绗節閮ㄥ垎 寰垎鏂圭▼
1銆佽€冭│鍏�(n猫i)瀹�
甯稿井鍒嗘柟绋嬬殑鍩烘湰姒傚康锛屽彲鍒嗛洟璁婇噺鐨勫井鍒嗘柟绋�锛岄綂娆℃柟绋�锛岄殠绶氭€ф柟绋嬭垏璨濆姫鍒╂柟绋�锛�
鍙檷闅庣殑楂橀殠寰垎鏂圭▼锛岄珮闅庣窔鎬у井鍒嗘柟绋嬪強鍏惰В鐨勭祼(ji茅)妲�(g貌u)锛屼簩闅庡父绯绘暩(sh霉)绶氭€у井鍒嗘柟绋�锛屾瓙鎷夋柟
绋�銆�
2銆佽€冭│瑕佹眰
2.1 . 鎺屾彙寰垎鏂圭▼銆佽В銆侀€氳В銆佸垵濮嬫浠跺拰鐗硅В绛夋蹇�銆�
2.2 璀�(sh铆)鍒ヤ笅鍒楀咕绋竴闅庡井鍒嗘柟绋嬶細璁婇噺鍙垎闆㈡柟绋�锛岄綂娆℃柟绋�锛屼竴闅庣窔鎬ф柟绋嬪拰鍏ㄥ井鍒嗘柟绋嬨€�
2.3 鎺屾彙璁婇噺鍙垎闆㈡柟绋嬪強涓€闅庣窔鎬ф柟绋嬬殑瑙ｆ硶銆�
2.4 浜嗚В榻婃鏂圭▼鍜屼集鍔埄鏂圭▼骞跺緸涓牁(l菒ng)鏈�(hu矛)鐢ㄨ畩閲忎唬鎻涙眰瑙ｆ柟绋嬬殑鎬濇兂銆�
2.5 鎺屾彙杓冪啊鍠殑鍏ㄥ井鍒嗘柟绋�銆�
2.6 鎺屾彙涓嬪垪骞剧ó鐗规畩鐨勯珮闅庢柟绋嬶細y(n)=f(x),y"=f(x,y),y"=(y,y鈥�)鐨勯檷闅庢硶銆�
2.7 浜嗚В浜岄殠绶氭€у井鍒嗘柟绋嬬殑绲�(ji茅)妲�(g貌u)銆�
2.8 鎺屾彙浜岄殠甯哥郴鏁�(sh霉)榻婃寰垎鏂圭▼鐨勮В娉�锛屽苟鐭ラ亾楂橀殠甯哥郴鏁�(sh霉)榻婃绶氭€у井鍒嗘柟绋嬬殑瑙ｆ硶銆�
2.9 鎺屾彙鑷敱闋�(xi脿ng)鐐哄闋�(xi脿ng)寮�銆佹寚鏁�(sh霉)鍑芥暩(sh霉)銆佹寮﹀嚱鏁�(sh霉)銆佷綑寮﹀嚱鏁�(sh霉)浠ュ強瀹冨€戠殑鍜岃垏涔樼⿳鐨勪簩闅庡父绯�
鏁�(sh霉)闈為綂娆＄窔鎬у井鍒嗘柟绋嬬殑瑙ｆ硶銆�
2.10 鎺屾彙寰垎鏂圭▼鐨勫啰绱�(j铆)鏁�(sh霉)瑙ｆ硶銆�
2.11 浜嗚В寰垎鏂圭▼瑙ｄ竴浜涚啊鍠殑骞句綍鍜岀墿鐞嗗晱椤�銆�
7
鍙冭€冩浉鐩�
銆婇珮绛夋暩(sh霉)瀛�(xu茅)銆嬩笂銆佷笅鍐�(c猫)锛屽悓婵�(j矛)澶у(xu茅)鏁�(sh霉)瀛�(xu茅)鏁欑爺瀹や富绶�锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛�2010 骞翠互
鍚庣増鏈潎鍙級銆�
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
