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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
婀栧崡甯寖澶у纰╁＋鐮旂┒鐢熷叆瀛歌€冭│鑷懡椤岃€冭│澶х侗
鑰冭│绉戠洰浠ｇ⒓锛歔寰╄│绉戠洰] 鑰冭│绉戠洰鍚嶇ū锛氫笘鐣屽湴鐞�
涓€銆佽€冭│褰㈠紡鑸囪│鍗风祼(ji茅)妲�
1)瑭﹀嵎鎴愮妇鍙婅€冭│鏅傞枔锛�
鏈│鍗锋豢鍒嗙偤 100 鍒嗭紝鑰冭│鏅傞枔鐐� 180 鍒嗛悩銆�
2)绛旈鏂瑰紡锛氶枆鍗枫€佺瓎瑭�
3)瑭﹀嵎鍏�(n猫i)瀹圭祼(ji茅)妲�
锛堜竴锛夊瑙€椤岄儴鍒� 40%
锛堜簩锛変富瑙€椤岄儴鍒� 60%
4)椤屽瀷绲�(ji茅)妲�
a: 鍠爡閬告搰椤�锛�20 灏忛锛屾瘡灏忛 1 鍒嗭紝鍏� 20 鍒�
b: 璁€鍦栫躬鍦栭锛�2 灏忛锛屾瘡灏忛 10 鍒�锛屽叡 20 鍒�
c: 鍟忕瓟椤�锛�5 灏忛锛屾瘡灏忛 6 鍒�锛屽叡 30 鍒�
d锛氱稖鍚堥锛�2 灏忛锛屾瘡灏忛 15 鍒�锛屽叡 30 鍒�
浜屻€佽€冭│鍏�(n猫i)瀹硅垏鑰冭│瑕佹眰
绗竴绔� 鍏ㄧ悆鍦拌〃褰㈡厠(t脿i)鑸囧叏鐞冩埃鍊�
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 鍏ㄧ悆鍦拌〃褰㈡厠(t脿i)
锛�2锛� 鍏ㄧ悆姘ｅ€欏付鍜屾埃鍊欏瀷
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻″叏鐞冩捣闄稿垎甯冨ぇ鍕�锛岀悊瑙ｅ湴琛ㄥ舰鎱�(t脿i)婕斿寲
锛�2锛夋帉鎻″叏鐞冩埃鍊欏付鍜屾埃鍊欏瀷浠ュ強涓栫晫姘ｅ€欑殑鍒嗗竷瑕�(gu墨)寰�
绗簩绔� 鍏ㄧ悆闄稿湴鑷劧甯剁殑鍩烘湰鏍煎眬鍙婂叾鐞嗚珫鐮旂┒
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 闄稿湴鑷劧甯剁殑褰㈡垚鑸囧垎甯�
锛�2锛夎嚜鐒跺湴鐞嗙挵(hu谩n)澧冪殑鏁村樊鐞嗚珫鍜屽湴鍩熷垎鐣�
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻￠櫢鍦拌嚜鐒跺付鍒嗗竷鍙婄壒寰�锛岀悊瑙ｈ嚜鐒跺付鐨勬紨鍖栭亷绋�
锛�2锛夌悊瑙ｈ嚜鐒跺湴鐞嗙挵(hu谩n)澧冪殑鏁撮珨鎬у拰宸暟鎬�锛屾帉鎻¤嚜鐒跺湴鐞嗙挵(hu谩n)澧冪殑鍦板煙鍒嗙暟
绗笁绔� 缍�(j墨ng)婵熷叏鐞冨寲鑸囧崁(q奴)鍩熺稉(j墨ng)婵熶竴楂斿寲
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛夌稉(j墨ng)婵熷叏鐞冨寲锛岀暥浠ｄ笘鐣岀稉(j墨ng)婵熺殑鍦扮悊鏍煎眬
锛�2锛夊崁(q奴)鍩熺稉(j墨ng)婵熶竴楂斿寲鐨勭悊璜栬垏瀵﹁笎
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻＄稉(j墨ng)婵熷叏鐞冨寲鐨勫収(n猫i)娑�锛岀悊瑙ｅ垎鏋愮稉(j墨ng)婵熷叏鐞冨寲鐨勭櫦(f膩)灞曡定鍕�
锛�2锛夌悊瑙ｄ笘鐣岀稉(j墨ng)婵熺櫦(f膩)灞曠殑涓嶅钩琛℃€т互鍙婄暥鍓嶄笘鐣岀稉(j墨ng)婵熸牸灞€
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绗洓绔� 浜炴床
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 浜炴床鑷劧鍦扮悊姒傝堪锛屼簽娲茬殑灞呮皯鑸囧湅瀹�
锛�2锛� 鏃ユ湰
锛�3锛� 瑗夸簽鍖楅潪
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻′簽娲蹭綅缃�銆侀潰绌嶅拰澶ч櫢杓粨
锛�2锛夌啛绶存帉鎻′簽娲插湴褰㈠拰浜炴床姘ｅ€欑殑鐗瑰緛銆佸垎鍗€(q奴)绛�
锛�3锛夌悊瑙ｄ簽娲茬殑浜哄彛銆佹皯鏃�銆佽獮瑷€鍙婂畻鏁�锛屽苟鑳界悊瑙ｅ垎鏋愪簽娲插湴绶ｉ棞绯诲晱椤�
锛�4锛夌啛绶存帉鎻℃棩鏈湴鐞嗕綅缃�銆佽嚜鐒剁挵(hu谩n)澧冪壒榛炲強鍏舵剰缇�锛屾帉鎻℃埌(zh脿n)鍚庢棩鏈稉(j墨ng)婵熺櫦(f膩)灞�
鐨勫熀鏈壒寰佷互鍙婃棩鏈埌(zh脿n)鍚庣稉(j墨ng)婵熼珮閫熺櫦(f膩)灞曠殑鍘熷洜
锛�5锛夌啛绶存帉鎻¤タ浜炲寳闈炲湴鐞嗕綅缃拰鑷劧鐠�(hu谩n)澧冪壒寰�锛岀悊瑙ｈタ浜炲寳闈炰汉鏂囩櫦(f膩)灞曞拰绀�
鏈冪祼(ji茅)妲嬬壒寰�锛屾帉鎻¤タ浜炲寳闈炵殑鐭虫补缍�(j墨ng)婵�銆�
绗簲绔� 姝愭床
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 姝愭床鑷劧鍦扮悊
锛�2锛� 姝愭床浜烘枃鍦扮悊
锛�3锛� 姝愮洘
鑰冭│瑕佹眰锛�
锛�1锛夌啛绶存帉鎻℃瓙娲插湴鐞嗕綅缃�銆佸湴褰€€佹埃鍊�銆佹按鏂�銆佺う鐢�(ch菐n)绛夎嚜鐒剁壒寰�
锛�2锛夌悊瑙ｆ瓙娲茬殑鍦嬪銆佷汉鍙�銆佹皯鏃�銆佺ó鏃忓拰瑾炶█锛屼互鍙婃瓙娲茬櫦(f膩)灞曠殑绀炬渻娣垫簮
锛�3锛変簡瑙ｆ瓙娲蹭竴楂斿寲鐨勬绋嬶紝鎺屾彙姝愮洘涓昏鐢�(ch菐n)妤�(y猫)閮ㄩ杸鐨勭櫦(f膩)灞曞拰甯冨眬锛屾帉鎻℃瓙鐩�
杈�(n贸ng)妤�(y猫)鐧�(f膩)灞曞強鍏跺皥闁€鍖�銆�
绗叚绔� 闈炴床
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 闈炴床鑷劧鍦扮悊
锛�2锛� 闈炴床浜烘枃鍦扮悊
锛�3锛� 闈炴床鍦扮悊鍒嗗崁(q奴)
鑰冭│瑕佹眰锛�
锛�1锛夌啛绶存帉鎻￠潪娲插湴鐞嗕綅缃€佸ぇ闄歌吉寤�銆佽嚜鐒跺湴鐞嗙壒寰佹サ鍏跺湴鐞嗘剰缇╋紝鐞嗚В闈�
娲茶睈瀵岀殑绀︾敘(ch菐n)璩囨簮锛�
锛�2锛変簡瑙ｉ潪娲叉鍙茬櫦(f膩)灞曞拰鏀挎不鍦板湒婕旇畩锛屼互鍙婇潪娲蹭汉鍙�銆佺ó鏃�銆佹皯鏃忓拰瀹楁暀锛�
鎺屾彙闈炴床杈�(n贸ng)妤�(y猫)鍜屽伐绀︽キ(y猫)鐨勭壒寰�
锛�3锛夋帉鎻℃澅闈�銆佷腑闈炪€佽タ闈�銆佸崡闈炵殑鍩烘湰鐗瑰緛
绗竷绔� 鍖楃編娲�
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 鍖楃編娲茶嚜鐒跺湴鐞�
锛�2锛� 缇庡湅
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻″寳缇庢床鍦扮悊浣嶇疆銆佸湴褰€€佹埃鍊�銆佹渤娴�銆佹箹娉婄瓑鑷劧鍦扮悊鐗瑰緛锛�
锛�2锛夌悊瑙ｇ編鍦嬩綅缃垏闋樺湡绲勬垚锛屾帉鎻＄編鍦嬬殑鑷劧鍦扮悊鐗瑰緛鍜岃嚜鐒惰硣婧愭鎴�锛屾帉
鎻＄編鍦嬬稉(j墨ng)婵熺壒寰�锛�
绗叓绔� 鍗楃編娲�
鑰冭│鍏�(n猫i)瀹癸細
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锛�2锛� 鍗楃編娲蹭汉鏂囧湴鐞�
鑰冭│瑕佹眰锛�
锛�1锛夋帉鎻″崡缇庢床鍦扮悊浣嶇疆銆佸湴褰㈠湴璨�銆佹埃鍊欓鍨嬭垏鍒嗗竷銆佹按绯诲強涓昏绀︾敘(ch菐n)锛�
锛�2锛夌悊瑙ｅ崡缇庢床姝峰彶娣垫簮鍜屼汉鏂囪儗鏅�锛�
锛�3锛夋帉鎻″崡缇庢床缍�(j墨ng)婵熺櫦(f膩)灞曞拰鐢�(ch菐n)妤�(y猫)甯冨眬锛�
绗節绔� 澶ф磱娲�
鑰冭│鍏�(n猫i)瀹癸細
锛�1锛� 澶ф磱娲叉杩�
锛�2锛� 婢冲ぇ鍒╀簽
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锛�1锛夋帉鎻″ぇ娲嬫床鐨勫湴鐞嗚寖鍦嶄互鍙婂ぇ娲嬫床鑷劧鍦扮悊鐠�(hu谩n)澧冪殑鍩烘湰鐗归粸
锛�2锛変簡瑙ｅぇ娲嬫床鐨勫眳姘戝拰鍦嬪
锛�3锛夌啛绶存帉鎻℃境澶у埄浜炰綅缃�銆侀潰绌�銆佸ぇ闄歌吉寤撲互鍙婄崹鐗圭殑鑷劧鐠�(hu谩n)澧冪壒寰�锛屾帉鎻�
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涓€銆佽€冭│褰㈠紡鑸囪│鍗风祼(ji茅)妲�
1)瑭﹀嵎鎴愮妇鍙婅€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�
2)绛旈鏂瑰紡
绛旈鏂瑰紡鐐洪枆鍗�銆佺瓎瑭�銆�
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鏁欒偛蹇冪悊瀛� 绱� 30 鍒�
4)椤屽瀷绲�(ji茅)妲�
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鑰冭│鍏�(n猫i)瀹癸細
涓€銆佹暀鑲插姒傝堪
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鑰冭│绉戠洰浠ｇ⒓锛歔302] 鑰冭│绉戠洰鍚嶇ū锛氭暩(sh霉)瀛镐簩
涓€銆佽│鍗风祼(ji茅)妲�
1) 瑭﹀嵎鎴愮妇鍙婅€冭│鏅傞枔
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锛堜竴锛夐珮绛夋暩(sh霉)瀛搁儴鍒�
1銆佸嚱鏁�(sh霉)銆佹サ闄�銆侀€ｇ簩(x霉)
鑰冭│鍏�(n猫i)瀹�
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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�
绯荤殑寤虹珛
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鍑芥暩(sh霉)鐨勬€ц唱(zh矛)
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｅ嚱鏁�(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�锛屼簡瑙ｅ弽鍑芥暩(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�
宸�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�
鐒＄灏忛噺姹傛サ闄愶紟
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�
鍨嬶紟
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€�
璩�(zh矛)锛堟湁鐣屾€�銆佹渶澶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 灏庢暩(sh霉)鐨勫咕浣曟剰缇╁拰鐗╃悊鎰忕京 鍑芥暩(sh霉)鐨勫彲灏庢€ц垏閫ｇ簩(x霉)鎬�
涔嬮枔鐨勯棞绯� 骞抽潰鏇茬窔鐨勫垏绶氬拰娉曠窔 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�
灏庢暩(sh霉) 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 楂橀殠灏�
鏁�(sh霉) 涓€闅庡井鍒嗗舰寮忕殑涓嶈畩鎬� 寰垎涓€煎畾鐞� 娲涘繀閬旓紙L鈥橦ospital锛夋硶鍓� 鍑芥暩(sh霉)鍠�
瑾�(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)鍦栧舰鐨勬弿绻�
鍑芥暩(sh霉)鐨勬渶澶у€艰垏鏈€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
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�锛屼簡瑙ｅ皫鏁�(sh霉)鐨勭墿鐞嗘剰缇╋紝鏈冪敤灏庢暩(sh霉)鎻忚堪
涓€浜涚墿鐞嗛噺锛岀悊瑙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�锛屾帉鎻″熀鏈垵绛夊嚱鏁�(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�
鍑芥暩(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�锛屾帉鎻＄敤灏庢暩(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紙娉細鍦ㄥ崁(q奴)闁�( , )a b 鍏�(n猫i)锛岃ō鍑芥暩(sh霉) ( )f x 鍏�
鏈変簩闅庡皫鏁�(sh霉)銆傜暥 ( ) 0f x?? ? 鏅�锛� ( )f x 鐨勫湒褰㈡槸鍑圭殑锛涚暥 ( ) 0f x?? ? 鏅傦紝 ( )f x 鐨勫湒褰�
鏄嚫鐨勶級锛屾渻姹傚嚱鏁�(sh霉)鍦栧舰鐨勬嫄榛炰互鍙婃按骞炽€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
锛�9锛変簡瑙ｆ洸鐜�銆佹洸鐜囧湏鑸囨洸鐜囧崐寰戠殑姒傚康锛屾渻瑷堢畻鏇茬巼鍜屾洸鐜囧崐寰戯紟
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 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)鍙婂叾灏庢暩(sh霉) 鐗涢爴-钀婂竷灏�
鑼紙Newton-Leibniz锛夊叕寮� 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鍠劇鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒� 鍙嶅父锛堝唬缇╋級绌嶅垎 瀹氱⿳鍒�
鐨勬噳鐢�
鑰冭│瑕佹眰
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�
鍊煎畾鐞�锛屾帉鎻℃彌鍏冪⿳鍒嗘硶鑸囧垎閮ㄧ⿳鍒嗘硶锛�
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〃閬斿拰瑷堢畻涓€浜涘咕浣曢噺鑸囩墿鐞嗛噺锛堝钩闈㈠湒褰㈢殑闈㈢⿳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嶃€佸姛銆�
寮曞姏銆佸鍔�銆佽唱(zh矛)蹇�銆佸舰蹇冪瓑锛夊強鍑芥暩(sh霉)鐨勫钩鍧囧€硷紟
4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�銆佸钩琛岀殑姊濅欢 鍏╁悜閲忕殑澶捐 鍚戦噺鐨勫潗妯欒〃閬斿紡鍙婂叾閬嬬畻 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▼ 鐩寸窔鏂�
绋� 骞抽潰鑸囧钩闈€€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 榛炲埌
骞抽潰鍜岄粸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潗妯欓潰涓婄殑鎶曞奖鏇茬窔鏂圭▼
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｇ┖闁撶洿瑙掑潗妯欑郴锛岀悊瑙ｅ悜閲忕殑姒傚康鍙婂叾琛ㄧず.
锛�2锛夋帉鎻″悜閲忕殑閬嬬畻锛堢窔鎬ч亱绠�銆佹暩(sh霉)閲忕⿳銆佸悜閲忕⿳銆佹贩鍚堢⿳锛夛紝浜嗚В鍏╁€�
鍚戦噺鍨傜洿銆佸钩琛岀殑姊濅欢.
锛�3锛夌悊瑙ｅ柈浣嶅悜閲�銆佹柟鍚戞暩(sh霉)鑸囨柟鍚戜綑寮︺€佸悜閲忕殑鍧愭琛ㄩ仈寮�锛屾帉鎻＄敤鍧愭
琛ㄩ仈寮忛€茶鍚戦噺閬嬬畻鐨勬柟娉�.
锛�4锛夋帉鎻″钩闈㈡柟绋嬪拰鐩寸窔鏂圭▼鍙婂叾姹傛硶.
锛�5锛夋渻姹傚钩闈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�锛屽苟鏈冨埄鐢ㄥ钩
闈�銆佺洿绶氱殑鐩镐簰闂滅郴锛堝钩琛屻€佸瀭鐩�銆佺浉浜ょ瓑锛夎В姹烘湁闂滃晱椤�.
锛�6锛夋渻姹傞粸鍒扮洿绶氫互鍙婇粸鍒板钩闈㈢殑璺濋洟.
锛�7锛変簡瑙ｆ洸闈㈡柟绋嬪拰绌洪枔鏇茬窔鏂圭▼鐨勬蹇�.
锛�8锛変簡瑙ｅ父鐢ㄤ簩娆℃洸闈㈢殑鏂圭▼鍙婂叾鍦栧舰锛屾渻姹傜啊鍠殑鏌遍潰鍜屾棆杞�(zhu菐n)鏇查潰鐨勬柟
绋�.
锛�9锛変簡瑙ｇ┖闁撴洸绶氱殑鍙冩暩(sh霉)鏂圭▼鍜屼竴鑸柟绋�.浜嗚В绌洪枔鏇茬窔鍦ㄥ潗妯欏钩闈笂鐨勬姇
褰�锛屽苟鏈冩眰瑭叉姇褰辨洸绶氱殑鏂圭▼.
5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� 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)鐨勫亸灏庢暩(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╁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) 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� 浜屽厓鍑芥暩(sh霉)鐨勪簩闅庢嘲
鍕掑叕寮� 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€�銆佹渶灏忓€煎強鍏剁啊鍠噳鐢�
鑰冭│瑕佹眰
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�锛屾渻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€�.
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)鐨勬サ鍊硷紝鏈冪敤鎷夋牸鏈楁棩
涔樻暩(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.
6銆佸鍏冨嚱鏁�(sh霉)绌嶅垎瀛�
鑰冭│鍏�(n猫i)瀹�
浜岄噸绌嶅垎鑸囦笁閲嶇⿳鍒嗙殑姒傚康銆佹€ц唱(zh矛)銆佽▓绠楀拰鎳夌敤 鍏╅鏇茬窔绌嶅垎鐨勬蹇�銆佹€�
璩�(zh矛)鍙婅▓绠� 鍏╅鏇茬窔绌嶅垎鐨勯棞绯� 鏍兼灄锛圙reen锛夊叕寮� 骞抽潰鏇茬窔绌嶅垎鑸囪矾寰戠劇
闂滅殑姊濅欢 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▓绠� 鍏╅
鏇查潰绌嶅垎鐨勯棞绯� 楂樻柉锛圙auss锛夊叕寮� 鏂墭鍏嬫柉锛圫tokes)鍏紡 鏁ｅ害銆佹棆搴︾殑
姒傚康鍙婅▓绠� 鏇茬窔绌嶅垎鍜屾洸闈㈢⿳鍒嗙殑鎳夌敤
鑰冭│瑕佹眰
锛�1锛夌悊瑙ｄ簩閲嶇⿳鍒�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�
鐨勪腑鍊煎畾鐞�.
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欍€佹サ鍧愭锛�锛屾渻瑷堢畻涓夐噸绌嶅垎锛堢洿
瑙掑潗妯欍€佹煴闈㈠潗妯�銆佺悆闈㈠潗妯欙級.
锛�3锛夌悊瑙ｅ叐椤炴洸绶氱⿳鍒嗙殑姒傚康锛屼簡瑙ｅ叐椤炴洸绶氱⿳鍒嗙殑鎬ц唱(zh矛)鍙婂叐椤炴洸绶氱⿳鍒�
鐨勯棞绯�.
锛�4锛夋帉鎻¤▓绠楀叐椤炴洸绶氱⿳鍒嗙殑鏂规硶.
锛�5锛夋帉鎻℃牸鏋楀叕寮忓苟鏈冮亱鐢ㄥ钩闈㈡洸绶氱⿳鍒嗚垏璺緫鐒￠棞鐨勬浠�锛屾渻姹備簩鍏冨嚱
鏁�(sh霉)鍏ㄥ井鍒嗙殑鍘熷嚱鏁�(sh霉).
锛�6锛変簡瑙ｅ叐椤炴洸闈㈢⿳鍒嗙殑姒傚康銆佹€ц唱(zh矛)鍙婂叐椤炴洸闈㈢⿳鍒嗙殑闂滅郴锛屾帉鎻¤▓绠楀叐
椤炴洸闈㈢⿳鍒嗙殑鏂规硶锛屾帉鎻＄敤楂樻柉鍏紡瑷堢畻鏇查潰绌嶅垎鐨勬柟娉�锛屽苟鏈冪敤鏂墭鍏嬫柉鍏紡
瑷堢畻鏇茬窔绌嶅垎.
锛�7锛変簡瑙ｆ暎搴﹁垏鏃嬪害鐨勬蹇碉紝骞舵渻瑷堢畻.
锛�8锛夋渻鐢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锛堝钩闈㈠湒褰�
鐨勯潰绌�銆侀珨绌嶃€佹洸闈㈤潰绌�銆佸姬闀�銆佽唱(zh矛)閲�銆佽唱(zh矛)蹇�銆�銆佸舰蹇冦€佽綁(zhu菐n)鍕曟叄閲�銆佸紩鍔涖€佸姛鍙�
娴侀噺绛夛級.
7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 鏀舵杺绱氭暩(sh霉)鐨勫拰鐨勬蹇� 绱氭暩(sh霉)鐨勫熀鏈€ц唱(zh矛)
鑸囨敹鏂傜殑蹇呰姊濅欢 骞句綍绱氭暩(sh霉)鑸� p
绱氭暩(sh霉)鍙婂叾鏀舵杺鎬� 姝ｉ爡绱氭暩(sh霉)鏀舵杺鎬х殑鍒ゅ垾娉�
浜ら尟绱氭暩(sh霉)鑸囪悐甯冨凹鑼ㄥ畾鐞� 浠绘剰闋呯礆鏁�(sh霉)鐨勭禃灏嶆敹鏂傝垏姊濅欢鏀舵杺 鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨�
鏀舵杺鍩熻垏鍜屽嚱鏁�(sh霉)鐨勬蹇� 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
鍐礆鏁�(sh霉)鐨勫拰鍑芥暩(sh霉) 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� 鍒濈瓑鍑芥暩(sh霉)鐨勫啰绱氭暩(sh霉)灞曢枊寮� 鍑芥暩(sh霉)鐨勫倕閲岃憠锛團ourier锛夌郴鏁�(sh霉)鑸囧倕閲岃憠绱氭暩(sh霉) 鐙�
鍒╁厠闆凤紙Dirichlet锛夊畾鐞� 鍑芥暩(sh霉)鍦╗ , ]l l?
涓婄殑鍌呴噷钁夌礆鏁�(sh霉) 鍑芥暩(sh霉)鍦╗0, ]l
涓婄殑姝ｅ鸡绱�
鏁�(sh霉)鍜屼綑寮︾礆鏁�(sh霉)
鑰冭│瑕佹眰
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� p 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.
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�
绯�.
锛�6锛変簡瑙ｅ嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鐨勬敹鏂傚煙鍙婂拰鍑芥暩(sh霉)鐨勬蹇�.
锛�7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)鐨勬敹鏂傚崐寰戙€佹敹鏂傚崁(q奴)闁撳強
鏀舵杺鍩熺殑姹傛硶.
锛�8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�
绱氭暩(sh霉)鐨勫拰.
锛�9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�10锛夋帉鎻�
x
e 锛宻in x 锛宑os x 锛宭n(1 )x? 鍙�(1 )x
?
?
鐨勯亥鍏嬪嫗鏋楋紙Maclaurin锛夊睍闁�
寮�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�11锛変簡瑙ｅ倕閲岃憠绱氭暩(sh霉)鐨勬蹇靛拰鐙勫埄鍏嬮浄鏀舵杺瀹氱悊锛屾渻灏囧畾缇╁湪[ , ]l l? 涓婄殑
鍑芥暩(sh霉)灞曢枊鐐哄倕閲岃憠绱氭暩(sh霉)锛屾渻灏囧畾缇╁湪[0, ]l 涓婄殑鍑芥暩(sh霉)灞曢枊鐐烘寮︾礆鏁�(sh霉)鑸囦綑寮︾礆鏁�(sh霉)锛�
鏈冨鍑哄倕閲岃憠绱氭暩(sh霉)鐨勫拰鍑芥暩(sh霉)鐨勮〃閬斿紡.
8銆佸父寰垎鏂圭▼
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� 锛圔ernoulli锛夋柟绋� 鍏ㄥ井鍒嗘柟绋� 鍙敤绨″柈鐨勮畩閲忎唬鎻涙眰
瑙ｇ殑鏌愪簺寰垎鏂圭▼ 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)
妲嬪畾鐞� 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�
鏂圭▼ 绨″柈鐨勪簩闅庡父绯绘暩(sh霉)闈為綂娆＄窔鎬у井鍒嗘柟绋� 姝愭媺锛圗uler锛夋柟绋� 寰垎鏂圭▼鐨�
绨″柈鎳夌敤
鑰冭│瑕佹眰
锛�1锛変簡瑙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�.
锛�2锛夋帉鎻¤畩閲忓彲鍒嗛洟鐨勫井鍒嗘柟绋嬪強涓€闅庣窔鎬у井鍒嗘柟绋嬬殑瑙ｆ硶锛�
锛�3锛夋渻瑙ｉ綂娆″井鍒嗘柟绋�銆佷集鍔埄鏂圭▼鍜屽叏寰垎鏂圭▼锛屾渻鐢ㄧ啊鍠殑璁婇噺浠ｆ彌
瑙ｆ煇浜涘井鍒嗘柟绋嬶紟
锛�4锛夋渻鐢ㄩ檷闅庢硶瑙ｄ笅鍒楀舰寮忕殑寰垎鏂圭▼锛�
( )
( ), ( , )
n
y f x y f x y?? ?? ? 鍜� ( , )y f y y?? ?? 锛�
锛�5锛夌悊瑙ｇ窔鎬у井鍒嗘柟绋嬭В鐨勬€ц唱(zh矛)鍙婅В鐨勭祼(ji茅)妲嬶紟
锛�6锛夋帉鎻′簩闅庡父绯绘暩(sh霉)榻婃绶氭€у井鍒嗘柟绋嬬殑瑙ｆ硶锛屽苟鏈冭В鏌愪簺楂樹簬浜岄殠鐨勫父
绯绘暩(sh霉)榻婃绶氭€у井鍒嗘柟绋�.
锛�7锛夋渻瑙ｈ嚜鐢遍爡鐐哄闋呭紡銆佹寚鏁�(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�
鑸囩⿳鐨勪簩闅庡父绯绘暩(sh霉)闈為綂娆＄窔鎬у井鍒嗘柟绋嬶紟
锛�8锛夋渻瑙ｆ瓙鎷夋柟绋嬶紟
锛�9锛夋渻鐢ㄥ井鍒嗘柟绋嬭В姹轰竴浜涚啊鍠殑鎳夌敤鍟忛锛�
锛堜簩锛夌窔鎬т唬鏁�(sh霉)
1銆佽鍒楀紡
鑰冭│鍏�(n猫i)瀹�
顥ヮ棩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
鑰冭│瑕佹眰
锛�1锛変簡瑙ｈ鍒楀紡鐨勬蹇�锛屾帉鎻¤鍒楀紡鐨勬€ц唱(zh矛)锛�
锛�2锛夋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銆佺煩闄�
鑰冭│鍏�(n猫i)瀹�
顥ヮ棩顥ョ煩闄ｇ殑姒傚康 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�
闄� 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� 鍒嗗鐭╅櫍鍙婂叾閬�
绠�
鑰冭│瑕佹眰
顥ワ紙1锛夌悊瑙ｇ煩闄ｇ殑姒傚康锛屼簡瑙ｅ柈浣嶇煩闄�銆佹暩(sh霉)閲忕煩闄ｃ€佸皪瑙掔煩闄�銆佷笁瑙掔煩闄ｃ€佸皪
绋辩煩闄ｅ拰鍙嶅皪绋辩煩闄ｄ互鍙婂畠鍊戠殑鎬ц唱(zh矛)锛�
锛�2锛夋帉鎻＄煩闄ｇ殑绶氭€ч亱绠�銆佷箻娉�銆佽綁(zhu菐n)缃互鍙婂畠鍊戠殑閬嬬畻瑕�(gu墨)寰嬶紝浜嗚В鏂归櫍鐨勫啰
鑸囨柟闄ｄ箻绌嶇殑琛屽垪寮忕殑鎬ц唱(zh矛).
锛�3锛夌悊瑙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�
鐞嗚В浼撮毃鐭╅櫍鐨勬蹇�锛屾渻鐢ㄤ即闅ㄧ煩闄ｆ眰閫嗙煩闄ｏ紟
锛�4锛夌悊瑙ｇ煩闄ｅ垵绛夎畩鎻涚殑姒傚康锛屼簡瑙ｅ垵绛夌煩闄ｇ殑鎬ц唱(zh矛)鍜岀煩闄ｇ瓑鍍圭殑姒傚康锛岀悊
瑙ｇ煩闄ｇ殑绉╃殑姒傚康锛屾帉鎻＄敤鍒濈瓑璁婃彌姹傜煩闄ｇ殑绉╁拰閫嗙煩闄ｇ殑鏂规硶锛�
锛�5锛変簡瑙ｅ垎濉婄煩闄ｅ強鍏堕亱绠楋紟
3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浉闂滆垏绶氭€х劇闂�
鍚戦噺绲勭殑妤靛ぇ绶氭€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� 鍚戦噺绌洪枔鍙婂叾鐩搁棞姒傚康 n 缍悜閲忕┖闁撶殑鍩鸿畩鎻涘拰鍧愭璁婃彌 閬�
娓＄煩闄� 鍚戦噺鐨勫収(n猫i)绌� 绶氭€х劇闂滃悜閲忕祫鐨勬浜よ(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
锛�1锛夌悊瑙� n 缍悜閲忋€佸悜閲忕殑绶氭€х祫鍚堣垏绶氭€ц〃绀虹殑姒傚康锛�
锛�2锛夌悊瑙ｅ悜閲忕祫绶氭€х浉闂�銆佺窔鎬х劇闂滅殑姒傚康锛屾帉鎻″悜閲忕祫绶氭€х浉闂�銆佺窔鎬�
鐒￠棞鐨勬湁闂滄€ц唱(zh矛)鍙婂垽鍒ユ硶锛�
锛�3锛夌悊瑙ｅ悜閲忕祫鐨勬サ澶х窔鎬х劇闂滅祫鍜屽悜閲忕祫鐨勭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�
锛�4锛夌悊瑙ｅ悜閲忕祫绛夊児鐨勬蹇�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
闂滅郴.
锛�5锛変簡瑙� n 缍悜閲忕┖闁�銆佸瓙绌洪枔銆佸熀搴曘€佺董鏁�(sh霉)銆佸潗妯欑瓑姒傚康锛�
锛�6锛変簡瑙ｅ熀璁婃彌鍜屽潗妯欒畩鎻涘叕寮�锛屾渻姹傞亷娓＄煩闄ｏ紟
锛�7锛変簡瑙ｅ収(n猫i)绌嶇殑姒傚康锛屾帉鎻＄窔鎬х劇闂滃悜閲忕祫姝ｄ氦瑕�(gu墨)鑼冨寲鐨勬柦瀵嗙壒锛圫chmidt锛�
鏂规硶锛�
锛�8锛変簡瑙ｈ(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)
4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锛圕ramer锛夋硶鍓� 榻婃绶氭€ф柟绋嬬祫鏈夐潪闆惰В鐨勫厖鍒嗗繀瑕�
姊濅欢 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� 榻婃绶氭€ф柟绋嬬祫鐨勫熀绀庤В绯诲拰閫氳В 瑙ｇ┖闁� 闈為綂娆＄窔鎬ф柟绋嬬祫鐨勯€氳В
鑰冭│瑕佹眰
锛�1锛夋渻鐢ㄥ厠钀婂娉曞墖锛�
锛�2锛夌悊瑙ｉ綂娆＄窔鎬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�
瑙ｇ殑鍏呭垎蹇呰姊濅欢锛�
锛�3锛夌悊瑙ｉ綂娆＄窔鎬ф柟绋嬬祫鐨勫熀绀庤В绯�銆侀€氳В鍙婅В绌洪枔鐨勬蹇�锛屾帉鎻￠綂娆＄窔
鎬ф柟绋嬬祫鐨勫熀绀庤В绯诲拰閫氳В鐨勬眰娉�.
锛�4锛夌悊瑙ｉ潪榻婃绶氭€ф柟绋嬬祫瑙ｇ殑绲�(ji茅)妲嬪強閫氳В鐨勬蹇碉紟
锛�5锛夋帉鎻＄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
5銆佺煩闄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╅櫍鍙浉浼煎皪瑙掑寲鐨勫厖鍒嗗繀瑕佹浠跺強鐩镐技灏嶈鐭╅櫍 瀵﹀皪绋辩煩闄ｇ殑鐗瑰緛鍊�銆佺壒寰�
鍚戦噺鍙婂叾鐩镐技灏嶈鐭╅櫍
鑰冭│瑕佹眰:
锛�1锛夌悊瑙ｇ煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚戦噺鐨勬蹇靛強鎬ц唱(zh矛)锛屾渻姹傜煩闄ｇ殑鐗瑰緛鍊煎拰鐗�
寰佸悜閲�.
锛�2锛夌悊瑙ｇ浉浼肩煩闄ｇ殑姒傚康銆佹€ц唱(zh矛)鍙婄煩闄ｅ彲鐩镐技灏嶈鍖栫殑鍏呭垎蹇呰姊濅欢锛屾帉
鎻″皣鐭╅櫍鍖栫偤鐩镐技灏嶈鐭╅櫍鐨勬柟娉�.
锛�3锛夋帉鎻″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�
6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� 浜屾鍨�
鐨勬婧栧舰鍜岃(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欐簴褰� 浜屾鍨嬪強鍏剁煩闄ｇ殑
姝ｅ畾鎬�
鑰冭│瑕佹眰
锛�1锛夋帉鎻′簩娆″瀷鍙婂叾鐭╅櫍琛ㄧず锛屼簡瑙ｄ簩娆″瀷绉╃殑姒傚康锛屼簡瑙ｅ悎鍚岃畩鎻涜垏鍚�
鍚岀煩闄ｇ殑姒傚康锛屼簡瑙ｄ簩娆″瀷鐨勬婧栧舰銆佽(gu墨)鑼冨舰鐨勬蹇典互鍙婃叄鎬у畾鐞嗭紟
锛�2锛夋帉鎻＄敤姝ｄ氦璁婃彌鍖栦簩娆″瀷鐐烘婧栧舰鐨勬柟娉曪紝鏈冪敤閰嶆柟娉曞寲浜屾鍨嬬偤妯�
婧栧舰锛�
锛�3锛夌悊瑙ｆ瀹氫簩娆″瀷銆佹瀹氱煩闄ｇ殑姒傚康锛屽苟鎺屾彙鍏跺垽鍒ユ硶锛�
涓�銆佸弮鑰冩浉鐩�
[1] 鍚屾繜澶у鏁�(sh霉)瀛哥郴绶�. 楂樼瓑鏁�(sh霉)瀛革紙绗叚鐗堬級. 楂樼瓑鏁欒偛鍑虹増绀�, 2007
[2] 鏌存儬鏂�, 瀹椾簯鍗�. 绶氭€т唬鏁�(sh霉). 楂樼瓑鏁欒偛鍑虹増绀�, 2011
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
