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鍙嬫儏鎻愮ず锛氭湰绔欐彁渚涘叏鍦�(gu贸)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€冨崥鐪熼銆佺瓟妗堬紝閮ㄥ垎瀛�(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�(k霉)鈥� 涓嬭級
1
鏁�(sh霉)瀛�(xu茅)(鐞�)澶х侗
鑰冭│绉戠洰锛氶珮绛夋暩(sh霉)瀛�(xu茅)銆佺窔鎬т唬鏁�(sh霉)銆佹鐜囪珫鑸囨暩(sh霉)鐞嗙当(t菕ng)瑷�(j矛)
1銆佽│鍗峰収(n猫i)瀹圭祼(ji茅)妲�(g貌u)
楂樼瓑鏁欏(xu茅) 56%
绶氭€т唬鏁�(sh霉) 22%
姒傜巼璜栬垏鏁�(sh霉)鐞嗙当(t菕ng)瑷�(j矛) 22%
2銆佽│鍗烽鍨嬬祼(ji茅)妲�(g貌u)
瑭﹀嵎椤屽瀷绲�(ji茅)妲�(g貌u)鐐猴細
鍠伕椤� 8 灏忛锛屾瘡椤� 4 鍒�锛屽叡 32 鍒�
濉┖椤� 6 灏忛锛屾瘡椤� 4 鍒�锛屽叡 24 鍒�
瑙ｇ瓟椤�(鍖呮嫭璀夋槑椤�) 9 灏忛锛屽叡 94 鍒�
楂樼瓑鏁�(sh霉)瀛�(xu茅)
涓€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� 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� 寰�(f霉)鍚堝嚱鏁�(sh霉)銆�
鍙嶅嚱鏁�(sh霉)銆佸垎娈靛嚱鏁�(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�(gu膩n)
绯荤殑寤虹珛
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)鐨勫乏妤甸檺鑸囧彸妤甸檺 鐒�(w煤)绐皬閲�
鍜岀劇(w煤)绐ぇ閲忕殑姒傚康鍙婂叾闂�(gu膩n)绯� 鐒�(w煤)绐皬閲忕殑鎬ц唱(zh矛)鍙婄劇(w煤)绐皬閲忕殑姣旇純 妤甸檺鐨勫洓鍓�
閬�(y霉n)绠� 妤甸檺瀛樺湪鐨勫叐鍊�(g猫)婧�(zh菙n)鍓囷細?ji菐n)鎻(di脿o)鏈夌晫婧�(zh菙n)鍓囧拰澶鹃€兼簴(zh菙n)鍓� 鍏╁€�(g猫)閲嶈妤甸檺:
鍑芥暩(sh霉)閫ｇ簩(x霉)鐨勬蹇� 鍑芥暩(sh霉)闁撴柗榛�(di菐n)鐨勯鍨� 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(hu矛)寤虹珛鎳�(y墨ng)鐢ㄥ晱椤岀殑鍑芥暩(sh霉)闂�(gu膩n)绯�.
2.浜嗚В鍑芥暩(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�.
3.鐞嗚В寰�(f霉)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�.
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�.
5.鐞嗚В妤甸檺鐨勬蹇碉紝鐞嗚В鍑芥暩(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�
宸�銆佸彸妤甸檺涔嬮枔鐨勯棞(gu膩n)绯�.
6.鎺屾彙妤甸檺鐨勬€ц唱(zh矛)鍙婂洓鍓囬亱(y霉n)绠楁硶鍓�.
7.鎺屾彙妤甸檺瀛樺湪鐨勫叐鍊�(g猫)婧�(zh菙n)鍓�锛屽苟鏈�(hu矛)鍒╃敤瀹冨€戞眰妤甸檺锛屾帉鎻″埄鐢ㄥ叐鍊�(g猫)閲嶈妤甸檺
姹傛サ闄愮殑鏂规硶.
8.鐞嗚В鐒�(w煤)绐皬閲忋€佺劇(w煤)绐ぇ閲忕殑姒傚康锛屾帉鎻＄劇(w煤)绐皬閲忕殑姣旇純鏂规硶锛屾渻(hu矛)鐢ㄧ瓑鍍�(ji脿)鐒�(w煤)
绐皬閲忔眰妤甸檺.
9.鐞嗚В鍑芥暩(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(hu矛)鍒ゅ垾鍑芥暩(sh霉)闁撴柗榛�(di菐n)鐨勯鍨�.
10.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€�
璩�(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�)锛屽苟鏈�(hu矛)鎳�(y墨ng)鐢ㄩ€欎簺鎬ц唱(zh矛).
浜�銆佷竴鍏冨嚱鏁�(sh霉)寰垎瀛�(xu茅)
鑰冭│鍏�(n猫i)瀹�
灏�(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑姒傚康 灏�(d菐o)鏁�(sh霉)鐨勫咕浣曟剰缇╁拰鐗╃悊鎰忕京 鍑芥暩(sh霉)鐨勫彲灏�(d菐o)鎬ц垏閫ｇ簩(x霉)鎬�
涔嬮枔鐨勯棞(gu膩n)绯� 骞抽潰鏇茬窔鐨勫垏绶氬拰娉曠窔 灏�(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑鍥涘墖閬�(y霉n)绠� 鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨�
2
灏�(d菐o)鏁�(sh霉) 寰�(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 楂橀殠灏�(d菐o)
鏁�(sh霉) 涓€闅庡井鍒嗗舰寮忕殑涓嶈畩鎬� 寰垎涓€煎畾鐞� 娲涘繀閬�(d谩)(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�(di菐n)鍙婃几杩戠窔 鍑芥暩(sh霉)鍦栧舰鐨勬弿绻�
鍑芥暩(sh霉)鐨勬渶澶у€煎拰鏈€灏忓€� 寮у井鍒� 鏇茬巼鐨勬蹇� 鏇茬巼鍦撹垏鏇茬巼鍗婂緫
鑰冭│瑕佹眰
1.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)绯伙紝鐞嗚В灏�(d菐o)鏁�(sh霉)鐨勫咕浣曟剰缇�锛�
鏈�(hu矛)姹傚钩闈㈡洸绶氱殑鍒囩窔鏂圭▼鍜屾硶绶氭柟绋�锛屼簡瑙ｅ皫(d菐o)鏁�(sh霉)鐨勭墿鐞嗘剰缇╋紝鏈�(hu矛)鐢ㄥ皫(d菐o)鏁�(sh霉)鎻忚堪涓€浜�
鐗╃悊閲�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�.
2.鎺屾彙灏�(d菐o)鏁�(sh霉)鐨勫洓鍓囬亱(y霉n)绠楁硶鍓囧拰寰�(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.浜嗚В寰垎鐨勫洓鍓囬亱(y霉n)绠楁硶鍓囧拰涓€闅庡井鍒嗗舰寮忕殑涓嶈畩鎬�锛屾渻(hu矛)姹傚嚱鏁�(sh霉)鐨勫井鍒�.
3.浜嗚В楂橀殠灏�(d菐o)鏁�(sh霉)鐨勬蹇�锛屾渻(hu矛)姹傜啊(ji菐n)鍠嚱鏁�(sh霉)鐨勯珮闅庡皫(d菐o)鏁�(sh霉).
4.鏈�(hu矛)姹傚垎娈靛嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)锛屾渻(hu矛)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(d菐o)鏁�(sh霉).
5.鐞嗚В骞舵渻(hu矛)鐢ㄧ緟鐖�(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�(hu矛)鐢ㄦ煰瑗�(Cauchy)涓€煎畾鐞�.
6.鎺屾彙鐢ㄦ礇蹇呴仈(d谩)娉曞墖姹傛湭瀹氬紡妤甸檺鐨勬柟娉�.
7.鐞嗚В鍑芥暩(sh霉)鐨勬サ鍊兼蹇碉紝鎺屾彙鐢ㄥ皫(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�
娉�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�.
8.鏈�(hu矛)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€�(娉細鍦ㄥ崁(q奴)闁� 鍏�(n猫i)锛岃ō(sh猫)鍑芥暩(sh霉) 鍏锋湁浜岄殠灏�(d菐o)鏁�(sh霉)銆�
鐣�(d膩ng) 鏅�(sh铆)锛� 鐨勫湒褰㈡槸鍑圭殑;鐣�(d膩ng) 鏅�(sh铆)锛� 鐨勫湒褰㈡槸鍑哥殑)锛屾渻(hu矛)姹傚嚱鏁�(sh霉)鍦栧舰鐨勬嫄榛�(di菐n)浠ュ強姘村钩銆�
閴涚洿鍜屾枩婕歌繎绶�锛屾渻(hu矛)鎻忕躬鍑芥暩(sh霉)鐨勫湒褰�.
9.浜嗚В鏇茬巼銆佹洸鐜囧湏鑸囨洸鐜囧崐寰戠殑姒傚康锛屾渻(hu矛)瑷�(j矛)绠楁洸鐜囧拰鏇茬巼鍗婂緫.
涓�銆佷竴鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)
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�
鐨勬蹇靛拰鍩烘湰鎬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)鍙婂叾灏�(d菐o)鏁�(sh霉) 鐗涢爴涓€钀婂竷
灏艰尐(Newton-Leibniz)鍏紡 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 鏈�
鐞嗗嚱鏁�(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)鐨勬湁鐞嗗紡鍜岀啊(ji菐n)鍠劇(w煤)鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒� 鍙嶅父(寤ｇ京)绌嶅垎 瀹氱⿳鍒嗙殑
鎳�(y墨ng)鐢�
鑰冭│瑕佹眰
1.鐞嗚В鍘熷嚱鏁�(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�.
2.鎺屾彙涓嶅畾绌嶅垎鐨勫熀鏈叕寮�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�锛屾帉鎻℃彌鍏冪⿳鍒嗘硶鑸囧垎閮ㄧ⿳鍒嗘硶.
3.鏈�(hu矛)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�(ji菐n)鍠劇(w煤)鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒�.
4.鐞嗚В绌嶅垎涓婇檺鐨勫嚱鏁�(sh霉)锛屾渻(hu矛)姹傚畠鐨勫皫(d菐o)鏁�(sh霉)锛屾帉鎻＄墰闋�-钀婂竷灏艰尐鍏紡.
5.浜嗚В鍙嶅父绌嶅垎鐨勬蹇�锛屾渻(hu矛)瑷�(j矛)绠楀弽甯哥⿳鍒�.
6.鎺屾彙鐢ㄥ畾绌嶅垎琛ㄩ仈(d谩)鍜岃▓(j矛)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�銆佸钩闈㈡洸绶�
鐨勫姬闀�(zh菐ng)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嶃€佸姛銆佸紩鍔�銆�
澹撳姏銆佽唱(zh矛)蹇�銆佸舰蹇冪瓑)鍙婂嚱鏁�(sh霉)鐨勫钩鍧囧€�.
鍥�銆佸悜閲忎唬鏁�(sh霉)鍜岀┖闁撹В鏋愬咕浣�
鑰冭│鍏�(n猫i)瀹�
鍚戦噺鐨勬蹇� 鍚戦噺鐨勭窔鎬ч亱(y霉n)绠� 鍚戦噺鐨勬暩(sh霉)閲忕⿳鍜屽悜閲忕⿳ 鍚戦噺鐨勬贩鍚堢⿳
鍏╁悜閲忓瀭鐩淬€佸钩琛岀殑姊濅欢 鍏╁悜閲忕殑澶捐 鍚戦噺鐨勫潗妯�(bi膩o)琛ㄩ仈(d谩)寮忓強鍏堕亱(y霉n)绠� 鍠綅鍚�
閲� 鏂瑰悜鏁�(sh霉)鑸囨柟鍚戜綑寮� 鏇查潰鏂圭▼鍜岀┖闁撴洸绶氭柟绋嬬殑姒傚康 骞抽潰鏂圭▼銆佺洿绶氭柟绋�
3
骞抽潰鑸囧钩闈�銆佸钩闈㈣垏鐩寸窔銆佺洿绶氳垏鐩寸窔鐨勫ぞ瑙掍互鍙婂钩琛�銆佸瀭鐩寸殑姊濅欢 榛�(di菐n)鍒板钩闈�
鍜岄粸(di菐n)鍒扮洿绶氱殑璺濋洟 鐞冮潰 鏌遍潰 鏃嬭綁(zhu菐n)鏇查潰 甯哥敤鐨勪簩娆℃洸闈㈡柟绋嬪強鍏跺湒褰�
绌洪枔鏇茬窔鐨勫弮鏁�(sh霉)鏂圭▼鍜屼竴鑸柟绋� 绌洪枔鏇茬窔鍦ㄥ潗妯�(bi膩o)闈笂鐨勬姇褰辨洸绶氭柟绋�
鑰冭│瑕佹眰
1.鐞嗚В绌洪枔鐩磋鍧愭(bi膩o)绯�锛岀悊瑙ｅ悜閲忕殑姒傚康鍙婂叾琛ㄧず.
2.鎺屾彙鍚戦噺鐨勯亱(y霉n)绠�(绶氭€ч亱(y霉n)绠椼€佹暩(sh霉)閲忕⿳銆佸悜閲忕⿳銆佹贩鍚堢⿳)锛屼簡瑙ｅ叐鍊�(g猫)鍚戦噺鍨�
鐩�銆佸钩琛岀殑姊濅欢.
3.鐞嗚В鍠綅鍚戦噺銆佹柟鍚戞暩(sh霉)鑸囨柟鍚戜綑寮�銆佸悜閲忕殑鍧愭(bi膩o)琛ㄩ仈(d谩)寮忥紝鎺屾彙鐢ㄥ潗妯�(bi膩o)琛ㄩ仈(d谩)
寮忛€�(j矛n)琛屽悜閲忛亱(y霉n)绠楃殑鏂规硶.
4.鎺屾彙骞抽潰鏂圭▼鍜岀洿绶氭柟绋嬪強鍏舵眰娉�.
5.鏈�(hu矛)姹傚钩闈㈣垏骞抽潰銆佸钩闈㈣垏鐩寸窔銆佺洿绶氳垏鐩寸窔涔嬮枔鐨勫ぞ瑙�锛屽苟鏈�(hu矛)鍒╃敤骞抽潰銆�
鐩寸窔鐨勭浉浜掗棞(gu膩n)绯�(骞宠銆佸瀭鐩�銆佺浉浜ょ瓑)瑙ｆ焙鏈夐棞(gu膩n)鍟忛.
6.鏈�(hu矛)姹傞粸(di菐n)鍒扮洿绶氫互鍙婇粸(di菐n)鍒板钩闈㈢殑璺濋洟.
7.浜嗚В鏇查潰鏂圭▼鍜岀┖闁撴洸绶氭柟绋嬬殑姒傚康.
8.浜嗚В甯哥敤浜屾鏇查潰鐨勬柟绋嬪強鍏跺湒褰�锛屾渻(hu矛)姹傜啊(ji菐n)鍠殑鏌遍潰鍜屾棆杞�(zhu菐n)鏇查潰鐨勬柟绋�.
9.浜嗚В绌洪枔鏇茬窔鐨勫弮鏁�(sh霉)鏂圭▼鍜屼竴鑸柟绋�.浜嗚В绌洪枔鏇茬窔鍦ㄥ潗妯�(bi膩o)骞抽潰涓婄殑鎶曞奖锛�
骞舵渻(hu矛)姹傝┎鎶曞奖鏇茬窔鐨勬柟绋�.
浜斻€佸鍏冨嚱鏁�(sh霉)寰垎瀛�(xu茅)
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� 鏈�
鐣岄枆鍗€(q奴)鍩熶笂澶氬厓閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛) 澶氬厓鍑芥暩(sh霉)鐨勫亸灏�(d菐o)鏁�(sh霉)鍜屽叏寰垎 鍏ㄥ井鍒嗗瓨鍦ㄧ殑
蹇呰姊濅欢鍜屽厖鍒嗘浠� 澶氬厓寰�(f霉)鍚堝嚱鏁�(sh霉)銆侀毐鍑芥暩(sh霉)鐨勬眰灏�(d菐o)娉� 浜岄殠鍋忓皫(d菐o)鏁�(sh霉) 鏂瑰悜?q奴)顫�?sh霉)鍜�
姊害 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� 浜屽厓鍑芥暩(sh霉)鐨勪簩闅庢嘲鍕�
鍏紡 澶氬厓鍑芥暩(sh霉)鐨勬サ鍊煎拰姊濅欢妤靛€� 澶氬厓鍑芥暩(sh霉)鐨勬渶澶у€笺€佹渶灏忓€煎強鍏剁啊(ji菐n)鍠噳(y墨ng)鐢�
鑰冭│瑕佹眰
1.鐞嗚В澶氬厓鍑芥暩(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.浜嗚В浜屽厓鍑芥暩(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.鐞嗚В澶氬厓鍑芥暩(sh霉)鍋忓皫(d菐o)鏁�(sh霉)鍜屽叏寰垎鐨勬蹇�锛屾渻(hu矛)姹傚叏寰垎锛屼簡瑙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€�.
4.鐞嗚В鏂瑰悜?q奴)顫�?sh霉)鑸囨搴︾殑姒傚康锛屽苟鎺屾彙鍏惰▓(j矛)绠楁柟娉�.
5.鎺屾彙澶氬厓寰�(f霉)鍚堝嚱鏁�(sh霉)涓€闅�銆佷簩闅庡亸灏�(d菐o)鏁�(sh霉)鐨勬眰娉�.
6.浜嗚В闅卞嚱鏁�(sh霉)瀛樺湪瀹氱悊锛屾渻(hu矛)姹傚鍏冮毐鍑芥暩(sh霉)鐨勫亸灏�(d菐o)鏁�(sh霉).
7.浜嗚В绌洪枔鏇茬窔鐨勫垏绶氬拰娉曞钩闈㈠強鏇查潰鐨勫垏骞抽潰鍜屾硶绶氱殑姒傚康锛屾渻(hu矛)姹傚畠鍊戠殑
鏂圭▼.
8.浜嗚В浜屽厓鍑芥暩(sh霉)鐨勪簩闅庢嘲鍕掑叕寮�.
9.鐞嗚В澶氬厓鍑芥暩(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�
浠�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(hu矛)姹備簩鍏冨嚱鏁�(sh霉)鐨勬サ鍊�锛屾渻(hu矛)鐢ㄦ媺鏍兼湕鏃ヤ箻
鏁�(sh霉)娉曟眰姊濅欢妤靛€硷紝鏈�(hu矛)姹傜啊(ji菐n)鍠鍏冨嚱鏁�(sh霉)鐨勬渶澶у€煎拰鏈€灏忓€�锛屽苟鏈�(hu矛)瑙ｆ焙涓€浜涚啊(ji菐n)鍠殑鎳�(y墨ng)
鐢ㄥ晱椤�.
鍏€佸鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)
鑰冭│鍏�(n猫i)瀹�
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▓(j矛)绠楀拰鎳�(y墨ng)鐢� 鍏╅鏇茬窔绌嶅垎鐨勬蹇点€佹€�
璩�(zh矛)鍙婅▓(j矛)绠� 鍏╅鏇茬窔绌嶅垎鐨勯棞(gu膩n)绯� 鏍兼灄(Green)鍏紡 骞抽潰鏇茬窔绌嶅垎鑸囪矾寰戠劇(w煤)闂�(gu膩n)
鐨勬浠� 浜屽厓鍑芥暩(sh霉)鍏ㄥ井鍒嗙殑鍘熷嚱鏁�(sh霉) 鍏╅鏇查潰绌嶅垎鐨勬蹇�銆佹€ц唱(zh矛)鍙婅▓(j矛)绠� 鍏╅鏇�
4
闈㈢⿳鍒嗙殑闂�(gu膩n)绯� 楂樻柉(Gauss)鍏紡 鏂墭鍏嬫柉(Stokes)鍏紡 鏁ｅ害銆佹棆搴︾殑姒傚康鍙�
瑷�(j矛)绠� 鏇茬窔绌嶅垎鍜屾洸闈㈢⿳鍒嗙殑鎳�(y墨ng)鐢�
鑰冭│瑕佹眰
1.鐞嗚В浜岄噸绌嶅垎銆佷笁閲嶇⿳鍒嗙殑姒傚康锛屼簡瑙ｉ噸绌嶅垎鐨勬€ц唱(zh矛)锛屼簡瑙ｄ簩閲嶇⿳鍒嗙殑涓�
鍊煎畾鐞�.
2.鎺屾彙浜岄噸绌嶅垎鐨勮▓(j矛)绠楁柟娉�(鐩磋鍧愭(bi膩o)銆佹サ鍧愭(bi膩o))锛屾渻(hu矛)瑷�(j矛)绠椾笁閲嶇⿳鍒�(鐩磋鍧愭(bi膩o)銆�
鏌遍潰鍧愭(bi膩o)銆佺悆闈㈠潗妯�(bi膩o)).
3.鐞嗚В鍏╅鏇茬窔绌嶅垎鐨勬蹇�锛屼簡瑙ｅ叐椤炴洸绶氱⿳鍒嗙殑鎬ц唱(zh矛)鍙婂叐椤炴洸绶氱⿳鍒嗙殑闂�(gu膩n)
绯�.
4.鎺屾彙瑷�(j矛)绠楀叐椤炴洸绶氱⿳鍒嗙殑鏂规硶.
5.鎺屾彙鏍兼灄鍏紡骞舵渻(hu矛)閬�(y霉n)鐢ㄥ钩闈㈡洸绶氱⿳鍒嗚垏璺緫鐒�(w煤)闂�(gu膩n)鐨勬浠�锛屾渻(hu矛)姹備簩鍏冨嚱鏁�(sh霉)鍏�
寰垎鐨勫師鍑芥暩(sh霉).
6.浜嗚В鍏╅鏇查潰绌嶅垎鐨勬蹇�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¤▓(j矛)绠楀叐椤炴洸
闈㈢⿳鍒嗙殑鏂规硶锛屾帉鎻＄敤楂樻柉鍏紡瑷�(j矛)绠楁洸闈㈢⿳鍒嗙殑鏂规硶锛屽苟鏈�(hu矛)鐢ㄦ柉鎵樺厠鏂叕寮忚▓(j矛)绠�
鏇茬窔绌嶅垎.
7.鐞嗚В鏁ｅ害鑸囨棆搴︾殑姒傚康锛屽苟鏈�(hu矛)瑷�(j矛)绠�.
8.鏈�(hu矛)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(骞抽潰鍦栧舰鐨勯潰
绌�銆侀珨绌�銆佹洸闈㈤潰绌嶃€佸姬闀�(zh菐ng)銆佽唱(zh矛)閲忋€佽唱(zh矛)蹇�銆併€佸舰蹇�銆佽綁(zhu菐n)鍕�(d貌ng)鎱ｉ噺銆佸紩鍔�銆佸姛鍙婃祦閲�
绛�).
涓�銆佺劇(w煤)绐礆(j铆)鏁�(sh霉)
鑰冭│鍏�(n猫i)瀹�
甯告暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁ｇ殑姒傚康 鏀舵杺绱�(j铆)鏁�(sh霉)鐨勫拰鐨勬蹇� 绱�(j铆)鏁�(sh霉)鐨勫熀鏈€ц唱(zh矛)
鑸囨敹鏂傜殑蹇呰姊濅欢 骞句綍绱�(j铆)鏁�(sh霉)鑸� 绱�(j铆)鏁�(sh霉)鍙婂叾鏀舵杺鎬� 姝ｉ爡(xi脿ng)绱�(j铆)鏁�(sh霉)鏀舵杺鎬х殑鍒ゅ垾娉�
浜ら尟(cu貌)绱�(j铆)鏁�(sh霉)鑸囪悐甯冨凹鑼ㄥ畾鐞� 浠绘剰闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勭禃灏�(du矛)鏀舵杺鑸囨浠舵敹鏂� 鍑芥暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨�
鏀舵杺鍩熻垏鍜屽嚱鏁�(sh霉)鐨勬蹇� 鍐礆(j铆)鏁�(sh霉)鍙婂叾鏀舵杺鍗婂緫銆佹敹鏂傚崁(q奴)闁�(鎸囬枊鍗€(q奴)闁�)鍜屾敹鏂傚煙
鍐礆(j铆)鏁�(sh霉)鐨勫拰鍑芥暩(sh霉) 鍐礆(j铆)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�(ji菐n)鍠啰绱�(j铆)鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勬眰
娉� 鍒濈瓑鍑芥暩(sh霉)鐨勫啰绱�(j铆)鏁�(sh霉)灞曢枊寮� 鍑芥暩(sh霉)鐨勫倕閲岃憠(Fourier)绯绘暩(sh霉)鑸囧倕閲岃憠绱�(j铆)鏁�(sh霉) 鐙勫埄
鍏嬮浄(Dirichlet)瀹氱悊 鍑芥暩(sh霉)鍦� 涓婄殑鍌呴噷钁夌礆(j铆)鏁�(sh霉) 鍑芥暩(sh霉)鍦� 涓婄殑姝ｅ鸡绱�(j铆)鏁�(sh霉)鍜屼綑寮︾礆(j铆)
鏁�(sh霉)
鑰冭│瑕佹眰
1.鐞嗚В甯告暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鏀舵杺銆佺櫦(f膩)鏁ｄ互鍙婃敹鏂傜礆(j铆)鏁�(sh霉)鐨勫拰鐨勬蹇碉紝鎺屾彙绱�(j铆)鏁�(sh霉)鐨勫熀鏈€�
璩�(zh矛)鍙婃敹鏂傜殑蹇呰姊濅欢.
2.鎺屾彙骞句綍绱�(j铆)鏁�(sh霉)鑸� 绱�(j铆)鏁�(sh霉)鐨勬敹鏂傝垏鐧�(f膩)鏁ｇ殑姊濅欢.
3.鎺屾彙姝ｉ爡(xi脿ng)绱�(j铆)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(hu矛)鐢ㄦ牴鍊煎垽鍒ユ硶.
4.鎺屾彙浜ら尟(cu貌)绱�(j铆)鏁�(sh霉)鐨勮悐甯冨凹鑼ㄥ垽鍒ユ硶.
5. 浜嗚В浠绘剰闋�(xi脿ng)绱�(j铆)鏁�(sh霉)绲曞皪(du矛)鏀舵杺鑸囨浠舵敹鏂傜殑姒傚康浠ュ強绲曞皪(du矛)鏀舵杺鑸囨敹鏂傜殑闂�(gu膩n)绯�.
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�.
7.鐞嗚В鍐礆(j铆)鏁�(sh霉)鏀舵杺鍗婂緫鐨勬蹇�銆佸苟鎺屾彙鍐礆(j铆)鏁�(sh霉)鐨勬敹鏂傚崐寰戙€佹敹鏂傚崁(q奴)闁撳強鏀舵杺
鍩熺殑姹傛硶.
8.浜嗚В鍐礆(j铆)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)(鍜屽嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�銆侀€愰爡(xi脿ng)姹傚皫(d菐o)鍜岄€愰爡(xi脿ng)
绌嶅垎)锛屾渻(hu矛)姹備竴浜涘啰绱�(j铆)鏁�(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�(hu矛)鐢辨姹傚嚭鏌愪簺鏁�(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨�
鍜�.
9.浜嗚В鍑芥暩(sh霉)灞曢枊鐐烘嘲鍕掔礆(j铆)鏁�(sh霉)鐨勫厖鍒嗗繀瑕佹浠�.
10.鎺屾彙 锛� 锛� 锛� 鍙� 鐨勯亥鍏嬪嫗鏋�(Maclaurin)灞曢枊寮�锛屾渻(hu矛)鐢ㄥ畠鍊戝皣涓€浜涚啊(ji菐n)鍠�
5
鍑芥暩(sh霉)闁撴帴灞曢枊鎴愬啰绱�(j铆)鏁�(sh霉).
11.浜嗚В鍌呴噷钁夌礆(j铆)鏁�(sh霉)鐨勬蹇靛拰鐙勫埄鍏嬮浄鏀舵杺瀹氱悊锛屾渻(hu矛)灏囧畾缇╁湪( , )l l? 涓婄殑鍑芥暩(sh霉)
灞曢枊鐐哄倕閲岃憠绱�(j铆)鏁�(sh霉)锛屾渻(hu矛)灏囧畾缇╁湪 (0, )l 涓婄殑鍑芥暩(sh霉)灞曢枊鐐烘寮︾礆(j铆)鏁�(sh霉)鑸囦綑寮︾礆(j铆)鏁�(sh霉)锛屾渻(hu矛)
瀵嚭鍌呴噷钁夌礆(j铆)鏁�(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勮〃閬�(d谩)寮�.
鍏€佸父寰垎鏂圭▼
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▼ 榻婃寰垎鏂圭▼ 涓€闅庣窔
鎬у井鍒嗘柟绋� 浼姫鍒�(Bernoulli)鏂圭▼ 鍏ㄥ井鍒嗘柟绋� 鍙敤绨�(ji菐n)鍠殑璁婇噺浠ｆ彌姹傝В鐨�
鏌愪簺寰垎鏂圭▼ 鍙檷闅庣殑楂橀殠寰垎鏂圭▼ 绶氭€у井鍒嗘柟绋嬭В鐨勬€ц唱(zh矛)鍙婅В鐨勭祼(ji茅)妲�(g貌u)瀹�
鐞� 浜岄殠甯哥郴鏁�(sh霉)榻婃绶氭€у井鍒嗘柟绋� 楂樹簬浜岄殠鐨勬煇浜涘父绯绘暩(sh霉)榻婃绶氭€у井鍒嗘柟绋�
绨�(ji菐n)鍠殑浜岄殠甯哥郴鏁�(sh霉)闈為綂娆＄窔鎬у井鍒嗘柟绋� 姝愭媺(Euler)鏂圭▼ 寰垎鏂圭▼鐨勭啊(ji菐n)鍠噳(y墨ng)鐢�
鑰冭│瑕佹眰
1.浜嗚В寰垎鏂圭▼鍙婂叾闅�銆佽В銆侀€氳В銆佸垵濮嬫浠跺拰鐗硅В绛夋蹇�.
2.鎺屾彙璁婇噺鍙垎闆㈢殑寰垎鏂圭▼鍙婁竴闅庣窔鎬у井鍒嗘柟绋嬬殑瑙ｆ硶.
3.鏈�(hu矛)瑙ｉ綂娆″井鍒嗘柟绋嬨€佷集鍔埄鏂圭▼鍜屽叏寰垎鏂圭▼锛屾渻(hu矛)鐢ㄧ啊(ji菐n)鍠殑璁婇噺浠ｆ彌瑙ｆ煇
浜涘井鍒嗘柟绋�.
4.鏈�(hu矛)鐢ㄩ檷闅庢硶瑙ｄ笅鍒楀舰寮忕殑寰垎鏂圭▼锛� .
5.鐞嗚В绶氭€у井鍒嗘柟绋嬭В鐨勬€ц唱(zh矛)鍙婅В鐨勭祼(ji茅)妲�(g貌u).
6.鎺屾彙浜岄殠甯哥郴鏁�(sh霉)榻婃绶氭€у井鍒嗘柟绋嬬殑瑙ｆ硶锛屽苟鏈�(hu矛)瑙ｆ煇浜涢珮浜庝簩闅庣殑甯哥郴鏁�(sh霉)
榻婃绶氭€у井鍒嗘柟绋�.
7.鏈�(hu矛)瑙ｈ嚜鐢遍爡(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€戠殑鍜岃垏绌�
鐨勪簩闅庡父绯绘暩(sh霉)闈為綂娆＄窔鎬у井鍒嗘柟绋�.
8.鏈�(hu矛)瑙ｆ瓙鎷夋柟绋�.
9.鏈�(hu矛)鐢ㄥ井鍒嗘柟绋嬭В姹轰竴浜涚啊(ji菐n)鍠殑鎳�(y墨ng)鐢ㄥ晱椤�.
绶氭€т唬鏁�(sh霉)
涓€銆佽鍒楀紡
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�(鍒�)灞曢枊瀹氱悊
鑰冭│瑕佹眰锛�
1.浜嗚В琛屽垪寮忕殑姒傚康锛屾帉鎻¤鍒楀紡鐨勬€ц唱(zh矛).
2.鏈�(hu矛)鎳�(y墨ng)鐢ㄨ鍒楀紡鐨勬€ц唱(zh矛)鍜岃鍒楀紡鎸夎(鍒�)灞曢枊瀹氱悊瑷�(j矛)绠楄鍒楀紡.
浜屻€佺煩闄�
鑰冭│鍏�(n猫i)瀹�
鐭╅櫍鐨勬蹇� 鐭╅櫍鐨勭窔鎬ч亱(y霉n)绠� 鐭╅櫍鐨勪箻娉� 鏂归櫍鐨勫啰 鏂归櫍涔樼⿳鐨勮鍒�
寮� 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╅櫍 鐭╅櫍鐨勭З 鐭╅櫍鐨勭瓑鍍�(ji脿) 鍒嗗鐭╅櫍鍙婂叾閬�(y霉n)绠�
鑰冭│瑕佹眰
1.鐞嗚В鐭╅櫍鐨勬蹇�锛屼簡瑙ｅ柈浣嶇煩闄�銆佹暩(sh霉)閲忕煩闄�銆佸皪(du矛)瑙掔煩闄�銆佷笁瑙掔煩闄�銆佸皪(du矛)绋�
鐭╅櫍鍜屽弽灏�(du矛)绋辩煩闄�锛屼互鍙婂畠鍊戠殑鎬ц唱(zh矛).
2.鎺屾彙鐭╅櫍鐨勭窔鎬ч亱(y霉n)绠�銆佷箻娉曘€佽綁(zhu菐n)缃互鍙婂畠鍊戠殑閬�(y霉n)绠楄(gu墨)寰�锛屼簡瑙ｆ柟闄ｇ殑鍐垏
鏂归櫍涔樼⿳鐨勮鍒楀紡鐨勬€ц唱(zh矛).
6
3.鐞嗚В閫嗙煩闄ｇ殑姒傚康锛屾帉鎻￠€嗙煩闄ｇ殑鎬ц唱(zh矛)锛屼互鍙婄煩闄ｅ彲閫嗙殑鍏呭垎蹇呰姊濅欢锛�
鐞嗚В浼撮毃鐭╅櫍鐨勬蹇�锛屾渻(hu矛)鐢ㄤ即闅ㄧ煩闄ｆ眰閫嗙煩闄�.
4.鐞嗚В鐭╅櫍鍒濈瓑璁婃彌鐨勬蹇�锛屼簡瑙ｅ垵绛夌煩闄ｇ殑鎬ц唱(zh矛)鍜岀煩闄ｇ瓑鍍�(ji脿)鐨勬蹇碉紝鐞嗚В
鐭╅櫍鐨勭З鐨勬蹇�锛屾帉鎻＄敤鍒濈瓑璁婃彌姹傜煩闄ｇ殑绉╁拰閫嗙煩闄ｇ殑鏂规硶.
5.浜嗚В鍒嗗鐭╅櫍鍙婂叾閬�(y霉n)绠�.
涓�銆佸悜閲�
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�(gu膩n)鑸囩窔鎬х劇(w煤)闂�(gu膩n) 鍚�
閲忕祫鐨勬サ澶х窔鎬х劇(w煤)闂�(gu膩n)绲� 绛夊児(ji脿)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�
闂�(gu膩n)绯� 鍚戦噺绌洪枔鍙婂叾鐩搁棞(gu膩n)姒傚康 缍悜閲忕┖闁撶殑鍩鸿畩鎻涘拰鍧愭(bi膩o)璁婃彌 閬庢浮鐭╅櫍 鍚戦噺
鐨勫収(n猫i)绌� 绶氭€х劇(w煤)闂�(gu膩n)鍚戦噺绲勭殑姝ｄ氦瑕�(gu墨)鑼冨寲鏂规硶 瑕�(gu墨)鑼冩浜ゅ熀 姝ｄ氦鐭╅櫍鍙婂叾鎬ц唱(zh矛)
鑰冭│瑕佹眰
1.鐞嗚В 缍悜閲忋€佸悜閲忕殑绶氭€х祫鍚堣垏绶氭€ц〃绀虹殑姒傚康.
2.鐞嗚В鍚戦噺绲勭窔鎬х浉闂�(gu膩n)銆佺窔鎬х劇(w煤)闂�(gu膩n)鐨勬蹇�锛屾帉鎻″悜閲忕祫绶氭€х浉闂�(gu膩n)銆佺窔鎬х劇(w煤)闂�(gu膩n)
鐨勬湁闂�(gu膩n)鎬ц唱(zh矛)鍙婂垽鍒ユ硶.
3.鐞嗚В鍚戦噺绲勭殑妤靛ぇ绶氭€х劇(w煤)闂�(gu膩n)绲勫拰鍚戦噺绲勭殑绉╃殑姒傚康锛屾渻(hu矛)姹傚悜閲忕祫鐨勬サ澶х窔
鎬х劇(w煤)闂�(gu膩n)绲勫強绉�.
4.鐞嗚В鍚戦噺绲勭瓑鍍�(ji脿)鐨勬蹇�锛岀悊瑙ｇ煩闄ｇ殑绉╄垏鍏惰(鍒�)鍚戦噺绲勭殑绉╀箣闁撶殑闂�(gu膩n)绯�.
5.浜嗚В 缍悜閲忕┖闁�銆佸瓙绌洪枔銆佸熀搴�銆佺董鏁�(sh霉)銆佸潗妯�(bi膩o)绛夋蹇�.
6.浜嗚В鍩鸿畩鎻涘拰鍧愭(bi膩o)璁婃彌鍏紡锛屾渻(hu矛)姹傞亷娓＄煩闄�.
7.浜嗚В鍏�(n猫i)绌嶇殑姒傚康锛屾帉鎻＄窔鎬х劇(w煤)闂�(gu膩n)鍚戦噺绲勬浜よ(gu墨)鑼冨寲鐨勬柦瀵嗙壒(Schmidt)鏂规硶.
8.浜嗚В瑕�(gu墨)鑼冩浜ゅ熀銆佹浜ょ煩闄ｇ殑姒傚康浠ュ強瀹冨€戠殑鎬ц唱(zh矛).
鍥�銆佺窔鎬ф柟绋嬬祫
鑰冭│鍏�(n猫i)瀹�
绶氭€ф柟绋嬬祫鐨勫厠钀婂(Cramer)娉曞墖 榻婃绶氭€ф柟绋嬬祫鏈夐潪闆惰В鐨勫厖鍒嗗繀瑕佹
浠� 闈為綂娆＄窔鎬ф柟绋嬬祫鏈夎В鐨勫厖鍒嗗繀瑕佹浠� 绶氭€ф柟绋嬬祫瑙ｇ殑鎬ц唱(zh矛)鍜岃В鐨勭祼(ji茅)妲�(g貌u) 榻�
娆＄窔鎬ф柟绋嬬祫鐨勫熀绀�(ch菙)瑙ｇ郴鍜岄€氳В 瑙ｇ┖闁� 闈為綂娆＄窔鎬ф柟绋嬬祫鐨勯€氳В
鑰冭│瑕佹眰
l.鏈�(hu矛)鐢ㄥ厠钀婂娉曞墖.
2.鐞嗚В榻婃绶氭€ф柟绋嬬祫鏈夐潪闆惰В鐨勫厖鍒嗗繀瑕佹浠跺強闈為綂娆＄窔鎬ф柟绋嬬祫鏈夎В
鐨勫厖鍒嗗繀瑕佹浠�.
3.鐞嗚В榻婃绶氭€ф柟绋嬬祫鐨勫熀绀�(ch菙)瑙ｇ郴銆侀€氳В鍙婅В绌洪枔鐨勬蹇�锛屾帉鎻￠綂娆＄窔鎬ф柟
绋嬬祫鐨勫熀绀�(ch菙)瑙ｇ郴鍜岄€氳В鐨勬眰娉�.
4.鐞嗚В闈為綂娆＄窔鎬ф柟绋嬬祫瑙ｇ殑绲�(ji茅)妲�(g貌u)鍙婇€氳В鐨勬蹇�.
5.鎺屾彙鐢ㄥ垵绛夎璁婃彌姹傝В绶氭€ф柟绋嬬祫鐨勬柟娉�.
浜斻€佺煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚戦噺
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) 鐩镐技璁婃彌銆佺浉浼肩煩闄ｇ殑姒傚康鍙婃€ц唱(zh矛)
鐭╅櫍鍙浉浼煎皪(du矛)瑙掑寲鐨勫厖鍒嗗繀瑕佹浠跺強鐩镐技灏�(du矛)瑙掔煩闄� 瀵�(sh铆)灏�(du矛)绋辩煩闄ｇ殑鐗瑰緛鍊�銆佺壒寰�
鍚戦噺鍙婂叾鐩镐技灏�(du矛)瑙掔煩闄�
鑰冭│瑕佹眰
1.鐞嗚В鐭╅櫍鐨勭壒寰佸€煎拰鐗瑰緛鍚戦噺鐨勬蹇靛強鎬ц唱(zh矛)锛屾渻(hu矛)姹傜煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚�
閲�.
2.鐞嗚В鐩镐技鐭╅櫍鐨勬蹇�銆佹€ц唱(zh矛)鍙婄煩闄ｅ彲鐩镐技灏�(du矛)瑙掑寲鐨勫厖鍒嗗繀瑕佹浠讹紝鎺屾彙灏�
7
鐭╅櫍鍖栫偤鐩镐技灏�(du矛)瑙掔煩闄ｇ殑鏂规硶.
3.鎺屾彙瀵�(sh铆)灏�(du矛)绋辩煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚戦噺鐨勬€ц唱(zh矛).
鍏�銆佷簩娆″瀷
鑰冭│鍏�(n猫i)瀹�
浜屾鍨嬪強鍏剁煩闄ｈ〃绀� 鍚堝悓璁婃彌鑸囧悎鍚岀煩闄� 浜屾鍨嬬殑绉� 鎱ｆ€у畾鐞� 浜�
娆″瀷鐨勬(bi膩o)婧�(zh菙n)褰㈠拰瑕�(gu墨)鑼冨舰 鐢ㄦ浜よ畩鎻涘拰閰嶆柟娉曞寲浜屾鍨嬬偤妯�(bi膩o)婧�(zh菙n)褰� 浜屾鍨嬪強鍏剁煩
闄ｇ殑姝ｅ畾鎬�
鑰冭│瑕佹眰
1.鎺屾彙浜屾鍨嬪強鍏剁煩闄ｈ〃绀猴紝浜嗚В浜屾鍨嬬З鐨勬蹇�锛屼簡瑙ｅ悎鍚岃畩鎻涜垏鍚堝悓鐭�
闄ｇ殑姒傚康锛屼簡瑙ｄ簩娆″瀷鐨勬(bi膩o)婧�(zh菙n)褰€€佽(gu墨)鑼冨舰鐨勬蹇典互鍙婃叄鎬у畾鐞�.
2.鎺屾彙鐢ㄦ浜よ畩鎻涘寲浜屾鍨嬬偤妯�(bi膩o)婧�(zh菙n)褰㈢殑鏂规硶锛屾渻(hu矛)鐢ㄩ厤鏂规硶鍖栦簩娆″瀷鐐烘(bi膩o)婧�(zh菙n)褰�.
3.鐞嗚В姝ｅ畾浜屾鍨嬨€佹瀹氱煩闄ｇ殑姒傚康锛屽苟鎺屾彙鍏跺垽鍒ユ硶.
姒傜巼璜栬垏鏁�(sh霉)鐞嗙当(t菕ng)瑷�(j矛)
涓€銆侀毃姗�(j墨)浜嬩欢鍜屾鐜�
鑰冭│鍏�(n猫i)瀹�
闅ㄦ(j墨)浜嬩欢鑸囨ǎ鏈┖闁� 浜嬩欢鐨勯棞(gu膩n)绯昏垏閬�(y霉n)绠� 瀹屽倷浜嬩欢绲� 姒傜巼鐨勬蹇� 姒傜巼鐨�
鍩烘湰鎬ц唱(zh矛) 鍙ゅ吀鍨嬫鐜� 骞句綍鍨嬫鐜� 姊濅欢姒傜巼 姒傜巼鐨勫熀鏈叕寮� 浜嬩欢鐨勭崹(d煤)绔嬫€�
鐛�(d煤)绔嬮噸寰�(f霉)瑭﹂(y脿n)
鑰冭│瑕佹眰
1.浜嗚В妯ｆ湰绌洪枔(鍩烘湰浜嬩欢绌洪枔)鐨勬蹇�锛岀悊瑙ｉ毃姗�(j墨)浜嬩欢鐨勬蹇碉紝鎺屾彙浜嬩欢鐨�
闂�(gu膩n)绯诲強閬�(y霉n)绠�.
2.鐞嗚В姒傜巼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(hu矛)瑷�(j矛)绠楀彜鍏稿瀷姒傜巼鍜�
骞句綍鍨嬫鐜�锛屾帉鎻℃鐜囩殑鍔犳硶鍏紡銆佹笡娉曞叕寮�銆佷箻娉曞叕寮�銆佸叏姒傜巼鍏紡锛屼互鍙婅矟
钁夋柉(Bayes)鍏紡.
3.鐞嗚В浜嬩欢鐛�(d煤)绔嬫€х殑姒傚康锛屾帉鎻＄敤浜嬩欢鐛�(d煤)绔嬫€ч€�(j矛n)琛屾鐜囪▓(j矛)绠�;鐞嗚В鐛�(d煤)绔嬮噸寰�(f霉)瑭�
椹�(y脿n)鐨勬蹇�锛屾帉鎻¤▓(j矛)绠楁湁闂�(gu膩n)浜嬩欢姒傜巼鐨勬柟娉�.
浜�銆侀毃姗�(j墨)璁婇噺鍙婂叾鍒嗗竷
鑰冭│鍏�(n猫i)瀹�
闅ㄦ(j墨)璁婇噺 闅ㄦ(j墨)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�(j墨)璁婇噺鐨勬鐜囧垎甯�
閫ｇ簩(x霉)鍨嬮毃姗�(j墨)璁婇噺鐨勬鐜囧瘑搴� 甯歌闅ㄦ(j墨)璁婇噺鐨勫垎甯� 闅ㄦ(j墨)璁婇噺鍑芥暩(sh霉)鐨勫垎甯�
鑰冭│瑕佹眰
1.鐞嗚В闅ㄦ(j墨)璁婇噺鐨勬蹇�锛岀悊瑙ｅ垎甯冨嚱鏁�(sh霉)
鐨勬蹇靛強鎬ц唱(zh矛)锛屾渻(hu矛)瑷�(j矛)绠楄垏闅ㄦ(j墨)璁婇噺鐩歌伅(li谩n)绯荤殑浜嬩欢鐨勬鐜�.
2.鐞嗚В闆㈡暎鍨嬮毃姗�(j墨)璁婇噺鍙婂叾姒傜巼鍒嗗竷鐨勬蹇碉紝鎺屾彙 0-1 鍒嗗竷銆佷簩闋�(xi脿ng)鍒嗗竷 銆佸咕
浣曞垎甯�銆佽秴骞句綍鍒嗗竷銆佹硦鏉�(Poisson)鍒嗗竷 鍙婂叾鎳�(y墨ng)鐢�.
3.浜嗚В娉婃澗瀹氱悊鐨勭祼(ji茅)璜栧拰鎳�(y墨ng)鐢ㄦ浠�锛屾渻(hu矛)鐢ㄦ硦鏉惧垎甯冭繎浼艰〃绀轰簩闋�(xi脿ng)鍒嗗竷.
4.鐞嗚В閫ｇ簩(x霉)鍨嬮毃姗�(j墨)璁婇噺鍙婂叾姒傜巼瀵嗗害鐨勬蹇�锛屾帉鎻″潎鍕诲垎甯� 銆佹鎱�(t脿i)鍒嗗竷 銆�
鎸囨暩(sh霉)鍒嗗竷鍙婂叾鎳�(y墨ng)鐢紝鍏朵腑鍙冩暩(sh霉)鐐� 鐨勬寚鏁�(sh霉)鍒嗗竷 鐨勬鐜囧瘑搴︾偤
5.鏈�(hu矛)姹傞毃姗�(j墨)璁婇噺鍑芥暩(sh霉)鐨勫垎甯�.
涓�銆佸缍毃姗�(j墨)璁婇噺鍙婂叾鍒嗗竷
鑰冭│鍏�(n猫i)瀹�
澶氱董闅ㄦ(j墨)璁婇噺鍙婂叾鍒嗗竷 浜岀董闆㈡暎鍨嬮毃姗�(j墨)璁婇噺鐨勬鐜囧垎甯冦€侀倞绶ｅ垎甯冨拰姊濅欢
鍒嗗竷 浜岀董閫ｇ簩(x霉)鍨嬮毃姗�(j墨)璁婇噺鐨勬鐜囧瘑搴�銆侀倞绶ｆ鐜囧瘑搴﹀拰姊濅欢瀵嗗害 闅ㄦ(j墨)璁婇噺鐨�
8
鐛�(d煤)绔嬫€у拰涓嶇浉闂�(gu膩n)鎬� 甯哥敤浜岀董闅ㄦ(j墨)璁婇噺鐨勫垎甯� 鍏╁€�(g猫)鍙婂叐鍊�(g猫)浠ヤ笂闅ㄦ(j墨)璁婇噺绨�(ji菐n)鍠�
鍑芥暩(sh霉)鐨勫垎甯�
鑰冭│瑕佹眰
1.鐞嗚В澶氱董闅ㄦ(j墨)璁婇噺鐨勬蹇�锛岀悊瑙ｅ缍毃姗�(j墨)璁婇噺鐨勫垎甯冪殑姒傚康鍜屾€ц唱(zh矛). 鐞嗚В
浜岀董闆㈡暎鍨嬮毃姗�(j墨)璁婇噺鐨勬鐜囧垎甯�銆侀倞绶ｅ垎甯冨拰姊濅欢鍒嗗竷锛岀悊瑙ｄ簩缍€ｇ簩(x霉)鍨嬮毃姗�(j墨)璁�
閲忕殑姒傜巼瀵嗗害銆侀倞绶ｅ瘑搴﹀拰姊濅欢瀵嗗害锛屾渻(hu矛)姹傝垏浜岀董闅ㄦ(j墨)璁婇噺鐩搁棞(gu膩n)浜嬩欢鐨勬鐜�.
2.鐞嗚В闅ㄦ(j墨)璁婇噺鐨勭崹(d煤)绔嬫€у強涓嶇浉闂�(gu膩n)鎬х殑姒傚康锛屾帉鎻￠毃姗�(j墨)璁婇噺鐩镐簰鐛�(d煤)绔嬬殑姊濅欢.
3.鎺屾彙浜岀董鍧囧嫽鍒嗗竷锛屼簡瑙ｄ簩缍鎱�(t脿i)鍒嗗竷 鐨勬鐜囧瘑搴�锛岀悊瑙ｅ叾涓弮鏁�(sh霉)鐨勬
鐜囨剰缇�.
4.鏈�(hu矛)姹傚叐鍊�(g猫)闅ㄦ(j墨)璁婇噺绨�(ji菐n)鍠嚱鏁�(sh霉)鐨勫垎甯冿紝鏈�(hu矛)姹傚鍊�(g猫)鐩镐簰鐛�(d煤)绔嬮毃姗�(j墨)璁婇噺绨�(ji菐n)鍠嚱鏁�(sh霉)
鐨勫垎甯�.
鍥�銆侀毃姗�(j墨)璁婇噺鐨勬暩(sh霉)瀛楃壒寰�
鑰冭│鍏�(n猫i)瀹�
闅ㄦ(j墨)璁婇噺鐨勬暩(sh霉)瀛�(xu茅)鏈熸湜(鍧囧€�)銆佹柟宸€佹(bi膩o)婧�(zh菙n)宸強鍏舵€ц唱(zh矛) 闅ㄦ(j墨)璁婇噺鍑芥暩(sh霉)鐨勬暩(sh霉)瀛�(xu茅)
鏈熸湜 鐭�銆佸崝(xi茅)鏂瑰樊銆佺浉闂�(gu膩n)绯绘暩(sh霉)鍙婂叾鎬ц唱(zh矛)
鑰冭│瑕佹眰
1.鐞嗚В闅ㄦ(j墨)璁婇噺鏁�(sh霉)瀛楃壒寰�(鏁�(sh霉)瀛�(xu茅)鏈熸湜銆佹柟宸€佹(bi膩o)婧�(zh菙n)宸�銆佺煩銆佸崝(xi茅)鏂瑰樊銆佺浉闂�(gu膩n)绯绘暩(sh霉))
鐨勬蹇�锛屾渻(hu矛)閬�(y霉n)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�.
2.鏈�(hu矛)姹傞毃姗�(j墨)璁婇噺鍑芥暩(sh霉)鐨勬暩(sh霉)瀛�(xu茅)鏈熸湜.
浜�銆佸ぇ鏁�(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�
寰� 杈涙(Khinchine)澶ф暩(sh霉)瀹氬緥 妫ｈ帿寮�-鎷夋櫘鎷夋柉(De Moivre-laplace)瀹氱悊 鍒楃董-
鏋楀痉浼牸(Levy-Lindberg)瀹氱悊
鑰冭│瑕佹眰
1.浜嗚В鍒囨瘮闆か涓嶇瓑寮�.
2.浜嗚В鍒囨瘮闆か澶ф暩(sh霉)瀹氬緥銆佷集鍔埄澶ф暩(sh霉)瀹氬緥鍜岃緵娆藉ぇ鏁�(sh霉)瀹氬緥(鐛�(d煤)绔嬪悓鍒嗗竷闅ㄦ(j墨)
璁婇噺搴忓垪鐨勫ぇ鏁�(sh霉)瀹氬緥).
3.浜嗚В妫ｈ帿寮�-鎷夋櫘鎷夋柉瀹氱悊(浜岄爡(xi脿ng)鍒嗗竷浠ユ鎱�(t脿i)鍒嗗竷鐐烘サ闄愬垎甯�)鍜屽垪缍�-鏋楀痉
浼牸瀹氱悊(鐛�(d煤)绔嬪悓鍒嗗竷闅ㄦ(j墨)璁婇噺搴忓垪鐨勪腑蹇冩サ闄愬畾鐞�).
鍏�銆佹暩(sh霉)鐞嗙当(t菕ng)瑷�(j矛)鐨勫熀鏈蹇�
鑰冭│鍏�(n猫i)瀹�
绺介珨 鍊�(g猫)楂� 绨�(ji菐n)鍠毃姗�(j墨)妯ｆ湰 绲�(t菕ng)瑷�(j矛)閲� 妯ｆ湰鍧囧€� 妯ｆ湰鏂瑰樊鍜屾ǎ鏈煩 鍒嗗竷 鍒嗗竷
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�
鑰冭│瑕佹眰
1.鐞嗚В绺介珨銆佺啊(ji菐n)鍠毃姗�(j墨)妯ｆ湰銆佺当(t菕ng)瑷�(j矛)閲忋€佹ǎ鏈潎鍊�銆佹ǎ鏈柟宸強妯ｆ湰鐭╃殑姒傚康锛�
鍏朵腑妯ｆ湰鏂瑰樊瀹氱京鐐猴細
2.浜嗚В 鍒嗗竷銆� 鍒嗗竷鍜� 鍒嗗竷鐨勬蹇靛強鎬ц唱(zh矛)锛屼簡瑙ｄ笂鍋�(c猫) 鍒嗕綅鏁�(sh霉)鐨勬蹇靛苟鏈�(hu矛)鏌�
琛ㄨ▓(j矛)绠�.
3.浜嗚В姝ｆ厠(t脿i)绺介珨鐨勫父鐢ㄦ娊妯ｅ垎甯�.
涓�銆佸弮鏁�(sh霉)浼拌▓(j矛)
鑰冭│鍏�(n猫i)瀹�
榛�(di菐n)浼拌▓(j矛)鐨勬蹇� 浼拌▓(j矛)閲忚垏浼拌▓(j矛)鍊� 鐭╀及瑷�(j矛)娉� 鏈€澶т技鐒朵及瑷�(j矛)娉� 浼拌▓(j矛)閲忕殑瑭�(p铆ng)閬�
妯�(bi膩o)婧�(zh菙n) 鍗€(q奴)闁撲及瑷�(j矛)鐨勬蹇� 鍠€�(g猫)姝ｆ厠(t脿i)绺介珨鐨勫潎鍊煎拰鏂瑰樊鐨勫崁(q奴)闁撲及瑷�(j矛) 鍏╁€�(g猫)姝ｆ厠(t脿i)绺介珨鐨�
9
鍧囧€煎樊鍜屾柟宸瘮鐨勫崁(q奴)闁撲及瑷�(j矛)
鑰冭│瑕佹眰
1.鐞嗚В鍙冩暩(sh霉)鐨勯粸(di菐n)浼拌▓(j矛)銆佷及瑷�(j矛)閲忚垏浼拌▓(j矛)鍊肩殑姒傚康.
2.鎺屾彙鐭╀及瑷�(j矛)娉�(涓€闅庣煩銆佷簩闅庣煩)鍜屾渶澶т技鐒朵及瑷�(j矛)娉�.
3.浜嗚В浼拌▓(j矛)閲忕殑鐒�(w煤)鍋忔€�銆佹湁鏁堟€�(鏈€灏忔柟宸€�)鍜屼竴鑷存€�(鐩稿悎鎬�)鐨勬蹇碉紝骞舵渻(hu矛)
椹�(y脿n)璀変及瑷�(j矛)閲忕殑鐒�(w煤)鍋忔€�.
4銆佺悊瑙ｅ崁(q奴)闁撲及瑷�(j矛)鐨勬蹇�锛屾渻(hu矛)姹傚柈鍊�(g猫)姝ｆ厠(t脿i)绺介珨鐨勫潎鍊煎拰鏂瑰樊鐨勭疆淇″崁(q奴)闁�锛屾渻(hu矛)
姹傚叐鍊�(g猫)姝ｆ厠(t脿i)绺介珨鐨勫潎鍊煎樊鍜屾柟宸瘮鐨勭疆淇″崁(q奴)闁�.
鍏�銆佸亣瑷�(sh猫)妾㈤(y脿n)
鑰冭│鍏�(n猫i)瀹�
椤憲鎬ф椹�(y脿n) 鍋囪ō(sh猫)妾㈤(y脿n)鐨勫叐椤為尟(cu貌)瑾� 鍠€�(g猫)鍙婂叐鍊�(g猫)姝ｆ厠(t脿i)绺介珨鐨勫潎鍊煎拰鏂瑰樊鐨勫亣
瑷�(sh猫)妾㈤(y脿n)
鑰冭│瑕佹眰
1.鐞嗚В椤憲鎬ф椹�(y脿n)鐨勫熀鏈€濇兂锛屾帉鎻″亣瑷�(sh猫)妾㈤(y脿n)鐨勫熀鏈椹�锛屼簡瑙ｅ亣瑷�(sh猫)妾㈤(y脿n)鍙�
鑳界敘(ch菐n)鐢熺殑鍏╅閷�(cu貌)瑾�.
2.鎺屾彙鍠€�(g猫)鍙婂叐鍊�(g猫)姝ｆ厠(t脿i)绺介珨鐨勫潎鍊煎拰鏂瑰樊鐨勫亣瑷�(sh猫)妾㈤(y脿n).
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
