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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骞达紝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
銆婃暩(sh霉)瀛稿垎鏋愩€嬭€冭│澶х侗
1.鍑芥暩(sh霉)
1.1 鎺屾彙瀵︽暩(sh霉)姒傚康鍙婂叾鍩烘湰鎬ц唱銆傛帉鎻″鏁�(sh霉)绲曞皪鍊肩殑姒傚康鍜屾湁闂滅殑涓嶇瓑寮忋€�
1.2 鎺屾彙閯板煙姒傚康, 鎺屾彙纰虹晫瀹氱悊銆�
1.3 鎺屾彙鍑芥暩(sh霉)鐨勬蹇靛強鍚勭ó琛ㄧず鏂规硶,鎺屾彙寰╁悎鍑芥暩(sh霉)鍜屽弽鍑芥暩(sh霉)鐨勬蹇点€�
1.4 鎺屾彙鏈夌晫鍑芥暩(sh霉)鑸囩劇鐣屽嚱鏁�(sh霉)銆佸柈瑾垮嚱鏁�(sh霉)銆佸鍑芥暩(sh霉)鍜屽伓鍑芥暩(sh霉)銆佸懆鏈熷嚱鏁�(sh霉)绛夋蹇点€�
1.5 鎺屾彙鍏鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨勫畾缇╁拰鎬ц唱銆�
1.6 鎺屾彙甯哥敤鐨勫咕鍊嬮潪鍒濈瓑鍑芥暩(sh霉)锛屽绗﹁櫉鍑芥暩(sh霉)锛岀媱鍒╁厠闆峰嚱鏁�(sh霉)绛夈€�
2. 鏁�(sh霉)鍒楁サ闄�
2.1 鎺屾彙鏁�(sh霉)鍒楁サ闄愮殑 N?? 鐨勫畾缇�, 鏈冧娇鐢ㄢ€� N?? 瑾炶█鈥濊瓑鏄庢暩(sh霉)鍒楃殑妤甸檺銆�
2.2 姝ｇ⒑鐞嗚В鍜屾帉鎻℃敹鏂傛暩(sh霉)鍒楃殑鎬ц唱銆�
2.3 鎺屾彙鍠鏈夌晫鍘熺悊,鑷村瘑鎬у畾鐞嗗強 Cauchy 鏀舵杺婧栧墖銆�
3. 鍑芥暩(sh霉)妤甸檺
3.1 鎺屾彙鍑芥暩(sh霉)妤甸檺鐨� M?? 鍜� ?? ? 瀹氱京銆�
3.2 鎺屾彙鍑芥暩(sh霉)妤甸檺鐨勬€ц唱銆�
3.3 鎺屾彙鍑芥暩(sh霉)妤甸檺瀛樺湪鐨勬浠�, 鎺屾彙姝哥祼鍘熷墖鍙婃煰瑗挎簴鍓囥€�
3.4 鎺屾彙閲嶈妤甸檺 1
sin
lim
0
?
? x
x
x
鍜�
1
lim(1 )
x
x
e
x? ?
? ? 鍙婂叾鎳夌敤銆�
3.5 姝ｇ⒑鐞嗚В鍜屾帉鎻＄劇绐ぇ鍜岀劇绐皬鐨勬蹇靛強鐒＄灏忕殑闅庛€�
4. 鍑芥暩(sh霉)鐨勯€ｇ簩(x霉)鎬�
4.1 鎺屾彙閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬蹇�, 鎺屾彙闁撴柗榛炲強鍏跺垎椤�銆�
4.2 鎺屾彙閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勫眬閮ㄦ€ц唱,鎺屾彙闁夊崁(q奴)闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱銆�
4.3 鎺屾彙鍙嶅嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�,鎺屾彙鍑芥暩(sh霉)鐨勪竴鑷撮€ｇ簩(x霉)鎬�銆�
4.4 鎺屾彙鍒濈瓑鍑芥暩(sh霉)鍦ㄥ叾瀹氱京鍩熶笂鐨勯€ｇ簩(x霉)鎬�銆�
5. 灏庢暩(sh霉)鑸囧井鍒�
5.1 鎺屾彙灏庢暩(sh霉)鐨勬蹇靛強鍏跺咕浣曟剰缇�銆�
5.2 鎺屾彙姹傚皫娉曞墖,鎺屾彙鍙冭畩閲忓嚱鏁�(sh霉)鐨勫皫鏁�(sh霉)娉曞墖, 鎺屾彙楂橀殠灏庢暩(sh霉)鐨勬眰娉�銆�
5.3 鎺屾彙寰垎鐨勬蹇靛強鍏跺咕浣曟剰缇�銆�
5.4 鎺屾彙寰垎鐨勯亱绠楁硶鍓�,浜嗚В楂橀殠寰垎,浜嗚В寰垎鍦ㄨ繎浼艰▓绠椾腑鐨勬噳鐢�銆�
6. 寰垎涓€煎畾鐞嗗強鍏舵噳鐢�
6.1 鐔熺反鎺屾彙涓€煎畾鐞嗙殑姊濅欢銆佺祼璜栧拰璀夋槑鏂规硶銆�
6.2 鎺屾彙涓嶅畾寮忔サ闄愮殑姹傛硶,鐔熺反鎺屾彙娲涘繀閬旀硶鍓囧強鍏舵噳鐢�銆�
6.3 鎺屾彙娉板嫆鍏紡锛屾帉鎻＄敤澶氶爡寮忛€艰繎鍑芥暩(sh霉)鐨勬€濇兂銆�
6.4 鏈冨垎鏋愬嚱鏁�(sh霉)鐨勬€ф厠(t脿i),鏈冩眰鍑芥暩(sh霉)鐨勫柈瑾垮崁(q奴)闁撳拰妤靛€硷紝鏈冨垽鏂峰嚱鏁�(sh霉)鐨勫嚫鎬у拰鎷愰粸,
鏈冭純瀹屽杽鍦颁綔鍑哄嚱鏁�(sh霉)鐨勫湒褰�銆�
7. 瀵︽暩(sh霉)鐨勫畬鍌欐€�
7.1 鐞嗚В鍗€(q奴)闁撳姒傚康锛岃兘鐔熺反浣跨敤鍗€(q奴)闁撳瀹氱悊銆�
7.2 鎺屾彙鑱氶粸姒傚康鍙婂悇绋瓑鍍瑰畾缇�锛岃兘鐔熺反浣跨敤鑱氶粸瀹氱悊銆�
7.3 鐞嗚В锛堥枊锛夎钃嬬殑瀹氱京骞朵笖鏈冪敤闆嗗悎琛撹獮琛ㄩ仈锛岄珨鏈冨浣曟閫犻枊瑕嗚搵骞朵笖鏈�
鐢ㄩ枊瑕嗚搵瀹氱悊銆�
7.4 鐭ユ泬瀵︽暩(sh霉)瀹屽倷鎬х殑鍏ó绛夊児瑾硶鍙婂叾璀夋槑銆�
8. 鍘熷嚱鏁�(sh霉)鑸囦笉瀹氱⿳鍒�
8.1 鎺屾彙鍘熷嚱鏁�(sh霉)瀹氱京鍙婂敮涓€鎬э紙涓嶈▓甯告暩(sh霉)锛�銆�
8.2 鎺屾彙涓嶅畾绌嶅垎鐨勫畾缇�銆佹€ц唱銆�
8.3 鐔熺反浣跨敤鎻涘厓鍏紡鍜屽垎閮ㄧ⿳鍒嗗叕寮�銆�
8.4 浜嗚В鏈夌悊鍑芥暩(sh霉)涓嶅畾绌嶅垎鐨勮▓绠楁柟娉曘€�
8.5 浜嗚В鏌愪簺鍏跺畠椤炲瀷涓嶅畾绌嶅垎鐨勮▓绠楁柟娉�銆�
9. 瀹氱⿳鍒嗭紙Riemann 绌嶅垎锛�
9.1 娣卞叆鐞嗚В瀹氱⿳鍒嗘蹇靛強鍏剁敘(ch菐n)鐢熻儗鏅�銆�
9.2 鐔熺反鎺屾彙鍙⿳鎬х殑鍒ゅ垾婧栧墖鍙婂彲绌嶅嚱鏁�(sh霉)椤炪€�
9.3 鐔熺反鎺屾彙瀹氱⿳鍒嗙殑鎬ц唱鍙婄⿳鍒嗕腑鍊煎畾鐞�銆�
9.4 閲嶉粸鎺屾彙寰⿳鍒嗗鍩烘湰瀹氱悊鍜� Newton-Leibniz 鍏紡銆�
9.5 鐔熺反浣跨敤瀹氱⿳鍒嗗伐鍏疯В姹哄咕浣�銆佺墿鐞嗗拰瀛哥鐨勫晱椤�銆�
10. 鍙嶅父绌嶅垎
10.1 娣卞叆鐞嗚В鍙嶅父绌嶅垎姒傚康鍙婂叾鐢�(ch菐n)鐢熻儗鏅�銆�
10.2 鐔熺反浣跨敤鍙嶅父绌嶅垎鐨勬敹鏂傚垽鍒ユ硶銆�
11. 鏁�(sh霉)闋呯礆鏁�(sh霉)
11.1 娣卞叆鐞嗚В鏁�(sh霉)闋呯礆鏁�(sh霉)鐨勬蹇靛強鍏剁敘(ch菐n)鐢熻儗鏅€�
11.2 鐩磋鐞嗚В绲曞皪鏀舵杺鍜屾浠舵敹鏂傛蹇�銆�
11.3 鐔熺反浣跨敤姝ｉ爡绱氭暩(sh霉)鍜屼竴鑸爡绱氭暩(sh霉)鐨勬敹鏂傚垽鍒ユ硶銆�
12. 鍑芥暩(sh霉)鍒�銆佸嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鍜屽啰绱氭暩(sh霉)
12.1 娣卞叆鐞嗚В閫愰粸鏀舵杺鍜屼竴鑷存敹鏂傛蹇�锛岄噸榛炲湪涓€鑷存敹鏂�銆�
12.2 鐔熺反浣跨敤涓€鑷存敹鏂傜殑 Cauchy 婧栧墖鍙婃敹鏂傚垽鍒ユ硶銆�
12.3 鎺屾彙涓€鑷存敹鏂傚嚱鏁�(sh霉)鍒楋紙鍑芥暩(sh霉)闋呯礆鏁�(sh霉)锛変箣妤甸檺鍑芥暩(sh霉)锛堝拰鍑芥暩(sh霉)锛夌殑鍒嗘瀽鎬ц唱锛�
鍗抽€ｇ簩(x霉)鎬�銆佸彲绌嶆€�銆佸彲寰€�銆�
12.4 鑳界啛绶存眰鍑轰竴鍊嬪啰绱氭暩(sh霉)鐨勬敹鏂傚崐寰�銆佹敹鏂傚崁(q奴)闁撳拰鏀舵杺鍩�銆�
12.5 鐔熺煡鍐礆鏁�(sh霉)鍦ㄥ叾鏀舵杺鍗€(q奴)闁撲笂鐨勬€ц唱(鍏�(n猫i)闁変竴鑷存敹鏂傛€с€侀€ｇ簩(x霉)鎬�銆侀€愰爡鍙⿳鍜�
閫愰爡鍙皫鎬э級銆�
12.6 鎺屾彙灏囧厜婊戝嚱鏁�(sh霉)灞曠偤鍐礆鏁�(sh霉)鐨勫熀鏈柟娉�銆�
13. 鍌呴噷钁夛紙Fourier锛夌礆鏁�(sh霉)
13.1 娣卞叆鐞嗚В鍌呴噷钁夌礆鏁�(sh霉)鍙婂叾鐢�(ch菐n)鐢熺殑鐗╃悊鑳屾櫙銆�
13.2 鏈冨仛涓€鍊嬪彲绌嶅嚱鏁�(sh霉)鐨勫倕閲岃憠绱氭暩(sh霉)銆�
13.2 鎺屾彙涓夎鍑芥暩(sh霉)绯荤殑姝ｄ氦鎬с€丅essel 涓嶇瓑寮忓拰 Riemann-Lebesgue 寮曠悊銆�
13.4 浜嗚В鏈夐棞鍌呴噷钁夌礆鏁�(sh霉)鏀舵杺鎬х殑涓€浜涚祼鏋�銆�
14. 澶氬厓鍑芥暩(sh霉)寰垎瀛�
14.1鎺屾彙骞抽潰榛為泦鐨勪竴浜涙蹇�: 閯板煙銆佸収(n猫i)榛�銆佺晫榛�銆佽仛榛�銆佸崁(q奴)鍩�銆侀枆鍗€(q奴)鍩�銆佹湁鐣�
鍗€(q奴)鍩�銆佺劇鐣屽崁(q奴)鍩熺瓑銆�
14.2鎺屾彙浜屽厓鍑芥暩(sh霉)鍜屼簩鍏冨嚱鏁�(sh霉)妤甸檺鐨勫畾缇�,寮勬竻浜岄噸妤甸檺鑸囩疮娆℃サ闄愮殑鍗€(q奴)鍒ュ強鍏�
鑱�(li谩n)绯�銆�
14.3 鎺屾彙浜屽厓閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勫畾缇╀互鍙婃€ц唱銆�
14.4 鐞嗚В鍙井鎬х殑姊濅欢銆佸咕浣曟剰缇╁強鎳夌敤銆�
14.5 鐔熺反瑷堢畻鍋忓皫鏁�(sh霉)鍜岄珮闅庡亸灏庢暩(sh霉)銆�
14.6 浜嗚В鏂瑰悜灏庢暩(sh霉)鑸囨搴︾殑瀹氱京銆�
14.7 鏈冮亱鐢ㄦ嘲鍕掑叕寮忚В姹烘サ鍊煎晱椤�銆�
15. 闅卞嚱鏁�(sh霉)
15.1鐞嗚В闅卞嚱鏁�(sh霉)鐨勬蹇靛強瀛樺湪鎬х殑姊濅欢銆�
15.2浜嗚В闅卞嚱鏁�(sh霉)绲勭殑姒傚康鍙婂畾鐞嗗苟鎺屾彙骞句綍閬嬬敤銆�
15.3鎺屾彙姊濅欢妤靛€肩殑姹傛硶銆�
16.鍚弮璁婇噺鐨勭⿳鍒�
16.1 鎺屾彙鍚弮閲忔甯哥⿳鍒嗗強鍙嶆甯哥⿳鍒�銆�
16.2 鎺屾彙涓€鑷存敹鏂傜殑鍒ゅ垾娉曘€�
16.3 鐞嗚В姝愭媺绌嶅垎骞舵渻鎳夌敤銆�
17. 閲嶇⿳鍒�
17.1 鎺屾彙浜岄噸绌嶅垎鐨勬蹇碉紝鐞嗚В浜岄噸绌嶅垎鐨勫彲绌嶅嚱鏁�(sh霉)椤炶垏鎬ц唱銆�
17.2 鎺屾彙浜岄噸绌嶅垎鐨勮▓绠�锛屾帉鎻′簩閲嶇⿳鍒嗙殑璁婇噺璁婃彌鍜屼簩閲嶇⿳鍒嗙殑鎳夌敤銆�
17.3 鎺屾彙涓夐噸绌嶅垎鐨勬蹇�銆�
17.4 鎺屾彙涓夐噸绌嶅垎鐨勮▓绠�锛屾帉鎻′笁閲嶇⿳鍒嗙殑璁婇噺璁婃彌鍜屾噳鐢�銆�
18. 鏇茬窔绌嶅垎鑸囨洸闈㈢⿳鍒�
18.1 姝ｇ⒑鐞嗚В绗竴鍨嬫洸绶氱⿳鍒嗗拰绗簩鍨嬫洸绶氱⿳鍒嗙殑姒傚康銆�
18.2 鎺屾彙绗竴鍨嬫洸绶氱⿳鍒嗗拰绗簩鍨嬫洸绶氱⿳鍒嗙殑瑷堢畻銆�
18.3 鏈冮亱鐢ㄦ牸鏋楀叕寮忓拰绌嶅垎鑸囪矾寰戠劇闂滅殑姊濅欢瑙ｆ焙鍟忛銆�
18.4 姝ｇ⒑鐞嗚В绗竴鍨嬫洸闈㈢⿳鍒嗗拰绗簩鍨嬫洸闈㈢⿳鍒嗙殑姒傚康銆�
18.5 鎺屾彙绗竴鍨嬫洸闈㈢⿳鍒嗗拰绗簩鍨嬫洸闈㈢⿳鍒嗙殑瑷堢畻銆�
18.6 鏈冮亱鐢ㄩ珮鏂叕寮忓拰鏂墭鍏嬫柉鍏紡銆�
18.7 浜嗚В鍫寸殑姒傚康鍜屽悇绋牬銆�
銆婇珮绛変唬鏁�(sh霉)銆嬭€冭│澶х侗
1. 琛屽垪寮�
1.1 浜嗚В鎺掑垪鐨勬蹇靛強鎬ц唱銆�
1.2 鐔熺反鎺屾彙琛屽垪寮忕殑姒傚康銆佹€ц唱銆�
1.3 鎺屾彙琛屽垪寮忕殑瑷堢畻鏂规硶銆�
1.4 鐔熸倝鍏嬫媺濮嗘硶鍓�銆�
1.5 灏嶇煩闄ｅ強鐭╅櫍鐨勫垵绛夎畩鎻涙湁鍒濇鐨勪簡瑙ｃ€�
2. 绶氭€ф柟绋嬬祫
2.1 鎺屾彙 n 缍悜閲忓強 n 缍悜閲忕┖闁撶殑姒傚康锛岀啛绶存帉鎻″悜閲忕殑閬嬬畻銆�
2.2 鐔熺反鎺屾彙鍚戦噺绲勭殑绶氭€х浉闂滄€�锛岀悊瑙ｅ悜閲忕祫鐨勬サ澶х劇闂滅祫銆�
2.3 娣卞埢鐞嗚В鍚戦噺绲勭殑绉╁拰鐭╅櫍鐨勭З鐨勫畾缇�锛屾帉鎻＄煩闄ｇЗ鐨勮▓绠楁柟娉曘€�
2.4 鐔熺反鎺屾彙绶氭€ф柟绋嬬祫鐨勬湁瑙ｅ垽鍒ュ畾鐞�銆�
2.5 姝ｇ⒑鐞嗚В鍜屾帉鎻￠綂娆＄窔鎬ф柟绋嬬祫鐨勫熀绀庤В绯荤殑姒傚康鍜岃▓绠楁柟娉曪紝鐔熺反鎺屾彙绶�
鎬ф柟绋嬬祫鐨勮В鐨勭祼妲嬪畾鐞�锛屾渻姹傝В绶氭€ф柟绋嬬祫銆�
3. 鐭╅櫍
3.1 浜嗚В鐭╅櫍姒傚康鐨勪竴浜涜儗鏅�銆�
3.2 鐔熺反鎺屾彙鐭╅櫍鐨勯亱绠楀強閬嬬畻寰�銆�
3.3 鎺屾彙鐭╅櫍涔樼⿳鐨勮鍒楀紡瀹氱悊锛岀煩闄ｄ箻绌嶇殑绉╄垏瀹冪殑鍥犲瓙鐨勭З鐨勯棞绯�銆�
3.4 娣卞叆鐞嗚В鐭╅櫍鍙€�銆侀€嗙煩闄�銆佷即闅ㄧ煩闄ｇ瓑姒傚康锛屾帉鎻℃柟闄ｅ彲閫嗙殑鍏呰姊�锛屾渻
鐢ㄤ欢鍏紡娉曟眰鐭╅櫍鐨勯€嗙煩闄�銆�
3.5 鐞嗚В鍒嗗鐭╅櫍鐨勬剰缇╋紝鎺屾彙鍒嗗鐭╅櫍鐨勯亱绠楀強鎬ц唱銆�
3.6 姝ｇ⒑鐞嗚В鍜屾帉鎻″垵绛夌煩闄�銆佸垵绛夎畩鎻涚殑姒傚康鍙婂畠鍊戠殑闂滅郴锛岀啛绶存帉鎻″埄鐢ㄥ垵
绛夎畩鎻涙柟娉曟眰鐭╅櫍鐨勯€嗙煩闄�銆�
3.7 浜嗚В鍒嗗涔樻硶鐨勫垵绛夎畩鎻�锛屾渻灏囩煩闄ｅ垎濉婅垏鍒濈瓑璁婃彌绲愬悎閫茶鐭╅櫍閬嬬畻銆�
4. 浜屾鍨�
4.1 姝ｇ⒑鐞嗚В浜屾鍨嬮潪閫€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�锛屾帉鎻＄煩闄�
鍚堝悓鐨勬蹇佃垏鎬ц唱銆�
4.2 鎺屾彙鍖栦簩娆″瀷鐐烘婧栧舰鐨勬柟娉�銆�
4.3 娣卞埢鐞嗚В灏嶇ū鐭╅櫍鑸囦簩娆″瀷鐨勯棞绯伙紝鎺屾彙灏嶇ū鐭╅櫍鐨勬€ц唱銆�
4.4 鎺屾彙鎱ｆ€у畾鐞�锛岀啛绶存帉鎻℃瀹氫簩娆″瀷鐨勭瓑鍍规浠�銆�
4.5 鎺屾彙鍗婃瀹氫簩娆″瀷鐨勭瓑鍍规浠�銆�
5. 绶氭€х┖闁�
5.1 鎺屾彙闆嗗悎鑸囨槧灏勭殑鐩搁棞姒傚康銆�
5.2 鐔熺反鎺屾彙绶氭€х┖闁撳強鍏跺熀浜庣董鏁�(sh霉)绛夌浉闂滄蹇点€�
5.3 鏈冩眰绶氭€х┖闁撶殑鍩鸿垏缍暩(sh霉)銆�
5.4 鎺屾彙鍩鸿畩鎻涜垏鍧愭璁婃彌鐨勫叕寮�锛屻€�
5.5 鐔熺反鎺屾彙绶氭€у瓙绌洪枔鐨勬蹇靛強鍏跺垽瀹氭柟娉�銆�
5.6 鎺屾彙瀛愮┖闁撶殑浜よ垏鍜岀殑瀹氱京鍙婃€ц唱锛岀啛绶存帉鎻＄董鏁�(sh霉)鍏紡銆�
5.7 娣卞埢鐞嗚В瀛愮┖闁撶殑鐩村拰鐨勬蹇�锛屾帉鎻″垽瀹氱洿鍜岀殑鍏呰姊濅欢銆�
5.8 鐞嗚В骞舵帉鎻＄窔鎬х┖闁撳悓妲嬬殑瀹氱京銆佹€ц唱鍙婃湁闄愮董绌洪枔鍚屾鐨勫厖瑕佹浠躲€�
6. 绶氭€ц畩鎻�
6.1 鐞嗚В骞舵帉鎻＄窔鎬ц畩鎻涚殑瀹氱京鍙婃€ц唱銆�
6.2 鎺屾彙绶氭€ц畩鎻涚殑閬嬬畻鍙婇亱绠楀緥锛岀悊瑙ｇ窔鎬ц畩鎻涚殑澶氶爡寮�銆�
6.3 鎺屾彙绶氭€ц畩鎻涜垏鐭╅櫍鐨勯棞绯伙紝鎺屾彙鐭╅櫍鐩镐技鐨勬蹇靛強鎬ц唱銆�
6.4 鐞嗚В骞舵帉鎻＄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強鎬ц唱锛屾渻姹傜煩闄�
鐨勭壒寰佸€煎拰鐗瑰緛鍚戦噺锛屾帉鎻″搱瀵嗙埦闋�-鍑辫悐瀹氱悊銆�
6.5 鎺屾彙绶氭€ц畩鎻涚殑鍊煎煙鑸囨牳鐨勬蹇靛強鐩搁棞鐞嗚珫銆�
6.6 浜嗚В涓嶈畩瀛愮┖闁撹垏绶氭€ц畩鎻涚煩闄ｅ寲绨′箣闁撶殑闂滅郴銆�
7. 姝愬咕閲屽緱绌洪枔
7.1 娣卞埢鐞嗚В骞舵帉鎻℃瓙骞鹃噷寰楃┖闁撶殑鍩烘湰姒傚康鍜岀悊璜�銆�
7.2 鎺屾彙鍚戦噺鐨勫収(n猫i)绌嶅拰鍚戦噺鐨勫害閲忔€ц唱銆�
7.3 姝ｇ⒑鐞嗚В姝ｄ氦鍚戦噺绲�銆佹婧栨浜ゅ熀鐨勬蹇�锛屾帉鎻℃柦瀵嗙壒姝ｄ氦鍖栨柟娉曘€�
7.4 鐞嗚В骞舵帉鎻℃浜よ畩鎻涚殑姒傚康鑸囩瓑鍍规浠�锛屾帉鎻℃浜よ畩鎻涜垏鍚戦噺闀峰害銆佹婧栨
浜ゅ熀浠ュ強姝ｄ氦鐭╅櫍鐨勯棞绯汇€�
7.5 鐞嗚В鍏╁€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�銆�
7.6 鐔熺反鎺屾彙瀵﹀皪绋辩煩闄ｇ殑閫蹭竴姝ユ€ц唱銆�
8. 澶氶爡寮�
8.1 浜嗚В澶氶爡寮忕殑瀹氱京鑸囧熀鏈亱绠�銆�
8.2 鎺屾彙澶氶爡寮忔暣闄ょ殑姒傚康銆佹€ц唱鑸囧付浣欓櫎娉�銆�
8.3 鎺屾彙鏈€澶у叕鍥犲紡鐨勬蹇点€佸瓨鍦ㄦ€ц垏姹傛硶,鎺屾彙澶氶爡寮忎簰绱犵殑姒傚康鑸囩浉闂滄€ц唱銆�
8.4 鎺屾彙涓嶅彲绱勫闋呭紡鐨勬蹇点€佹€ц唱銆�
8.5 浜嗚В鍥犲紡鍒嗚В瀹氱悊浠ュ強寰╃郴鏁�(sh霉)鑸囧绯绘暩(sh霉)澶氶爡寮忕殑鍥犲紡鍒嗚В瀹氱悊銆�
8.6 浜嗚В閲嶅洜寮忕殑姒傚康浠ュ強澶氶爡寮忔湁閲嶅洜寮忕殑鍏呰姊濅欢銆�
8.7 浜嗚В澶氶爡寮忓嚱鏁�(sh霉)鐨勬蹇�銆佷綑鏁�(sh霉)瀹氱悊銆佷唬鏁�(sh霉)鍩烘湰瀹氱悊銆�
8.8 鎺屾彙姹傛湁鐞嗙郴鏁�(sh霉)澶氶爡寮忕殑鍏ㄩ儴鏈夌悊鏍圭殑鏂规硶浠ュ強 Eisenstein 鍒ゅ垾娉曘€�
9. ?? 鐭╅櫍
9.1 浜嗚В ?? 鐭╅櫍鐨勫畾缇�銆� ?? 鐭╅櫍鐨勫垵绛夎畩鎻涖€� ?? 鐭╅櫍鐨勬婧栧舰浠ュ強 ?? 鐭╅櫍
鐨勮鍒楀紡鍥犲瓙銆佷笉璁婂洜瀛愮瓑姒傚康锛屼簡瑙� ?? 鐭╅櫍绛夊児鐨勫厖瑕佹浠�,鎺屾彙鐢ㄥ垵
绛夎畩鎻涘皣 ?? 鐭╅櫍鍖栫偤妯欐簴褰㈢殑鏂规硶銆�
9.2 鎺屾彙鐭╅櫍鍒濈瓑鍥犲瓙鐨勬蹇�銆佹眰娉曚互鍙婃暩(sh霉)瀛楃煩闄ｇ浉浼肩殑鍏呰姊濅欢銆�
9.3 浜嗚В鐭╅櫍鐨� Jordan 妯欐簴褰互鍙婃湁鐞嗘婧栧舰鐨勬蹇碉紝鎺屾彙鐭╅櫍鐨� Jordan 妯欐簴
褰㈢殑姹傛硶锛屼簡瑙ｇ煩闄ｆ湁鐞嗘婧栧舰鐨勬眰娉�銆�
銆婂父寰垎鏂圭▼銆嬭€冭│澶х侗
1. 鍒濈瓑绌嶅垎娉�
1.1 鎺屾彙寰垎鏂圭▼鑸囪В鐨勫熀鏈畾缇�锛岃獚璀樺父寰垎鏂圭▼瑾茬▼鐨勬暣楂旂祼妲�銆�
1.2 鎺屾彙鍒嗛洟璁婇噺娉�锛屾渻鐢ㄨ┎鏂规硶姹傝В璁婇噺鍙垎闆㈡柟绋嬨€�
1.3 鎺屾彙鍏╅鍙綁鍖栫偤鍙垎闆㈣畩閲忓舰寮忓井鍒嗘柟绋嬬殑瑙ｆ硶锛岄噸榛炴帉鎻￠綂娆℃柟绋嬭В娉�銆�
1.4 鎺屾彙涓€闅庣窔鎬у父寰垎鏂圭▼鐨勮В娉曗€斺€斿父鏁�(sh霉)璁婃槗娉�锛屾渻鐢ㄨ┎鏂规硶姹傝В闈為綂娆℃柟
绋嬨€�
1.5 鎺屾彙鍏ㄥ井鍒嗘柟绋嬪強绌嶅垎鍥犲瓙鐨勫熀鏈蹇�锛屾帉鎻″叏寰垎鏂圭▼姹傝В娉�锛屾渻鐢ㄧ⿳鍒�
鍥犲瓙娉曞皣闈炲叏寰垎鏂圭▼杞夊寲鐐哄叏寰垎鏂圭▼銆�
1.6 鎺屾彙鍙冩暩(sh霉)娉曟眰瑙ｄ竴闅庨毐寮忓井鍒嗘柟绋�锛屽叿楂旀渻瑙� 4 绋舰寮忕殑涓€闅庨毐寮忓井鍒嗘柟
绋�銆�
1.7 鎺屾彙骞剧ó鍙檷闅庣殑楂橀殠鏂圭▼鐨勮В娉�銆�
1.8 浠嬬垂涓€闅庡井鍒嗘柟绋嬫噳鐢ㄨ垑渚� 1.绛夎杌岀窔锛�2.鍦ㄥ嫊鍔涘涓殑鎳夌敤銆�
2. 鍩烘湰瀹氱悊
2.1 浜嗚В寰垎鏂圭▼瀹氭€х悊璜栫殑鐧�(f膩)灞曡儗鏅紝鎺屾彙寰垎鏂圭▼瑙ｇ殑骞句綍鎰忕京銆�
2.2 閲嶉粸鎺屾彙瑙ｇ殑瀛樺湪鎬ц垏鍞竴鎬у畾鐞�锛岀悊瑙ｅ畾鐞嗘浠�銆�
2.3 鎺屾彙鍙欢灞曡В鑸囦笉鍙欢灞曡В鐨勫畾缇�锛屾帉鎻′笉鍙欢灞曡В鐨勫瓨鍦ㄥ畾鐞嗗拰鎬ц唱銆�
2.4 鎺屾彙濂囪В姒傚康鍙婃眰瑙ｅ瑙ｇ殑鏂规硶銆傛帉鎻″寘绲＄殑姒傚康鍙婃眰瑙ｅ寘绲＄殑鏂规硶銆傛帉鎻�
鍏嬭悐娲涙柟绋嬬殑椤炲瀷鍙婃眰瑙ｆ柟娉曘€�
2.5 鎺屾彙瑙ｅ皪鍒濆€肩殑閫ｇ簩(x霉)渚濊炒鎬у拰瑙ｅ皪鍒濆€肩殑鍙井鎬�銆�
3. 涓€闅庣窔鎬у井鍒嗘柟绋嬬祫
3.1 鎺屾彙绶氭€у井鍒嗘柟绋嬬祫鐨勪竴鑸悊璜栧強寰垎鏂圭▼绲勬墍鏈夎В鐨勪唬鏁�(sh霉)绲愭銆�
3.2 鎺屾彙榻婄窔鎬у井鍒嗘柟绋嬬祫鐨勫熀瑙ｇ煩闄�銆�
3.3 鎺屾彙闈為綂鏂圭▼绲勭殑甯告暩(sh霉)璁婃槗娉�銆�
3.4 鎺屾彙閬嬬敤鐗瑰緛鏍规眰瑙ｅ父绯绘暩(sh霉)榻婄窔鎬у井鍒嗘柟绋嬬祫鐨勫熀瑙ｇ煩闄�銆傚父绯绘暩(sh霉)闈為綂娆＄窔
鎬у井鍒嗘柟绋嬬祫鐨勯€氳В鍏紡銆�
3.5 鎺屾彙甯哥郴鏁�(sh霉)榻婃绶氭€у井鍒嗘柟绋嬬祫鐨勫熀瑙ｇ煩闄ｇ偤 xA
ex ?)(? 銆�
4锛巒 闅庣窔鎬у井鍒嗘柟绋�
4.1 鎺屾彙 n 闅庣窔鎬ч綂娆℃柟绋嬬殑涓€鑸悊璜�锛屽寘鎷€氳В绲愭銆佸熀鏈В绲勭殑姒傚康锛涙帉鎻�
闈為綂娆＄窔鎬у井鍒嗘柟绋嬬殑閫氳В绲愭锛屽凡鐭ラ綂娆℃柟绋嬮€氳В鏈冮亱鐢ㄥ父鏁�(sh霉)璁婃槗娉曟眰闈�
榻婃柟绋嬮€氳В銆�
4.2 閲嶉粸 n 闅庡父绯绘暩(sh霉)绶氭€ч綂娆℃柟绋嬭В娉曪紝鍗抽亱鐢ㄧ壒寰佹柟绋嬬殑鐗瑰緛鏍规眰瑙� n 闅庡父绯�
鏁�(sh霉)榻婄窔鎬ф柟绋嬬殑閫氳В銆�
4.3 鎺屾彙绯绘暩(sh霉)姣旇純娉曟眰瑙� n 闅庡父绯绘暩(sh霉)绶氭€ч潪榻婃鏂圭▼鐨勯亱绠楁妧宸�銆�
4.4 鐞嗚В浜岄殠甯哥郴鏁�(sh霉)绶氭€ф柟绋嬭垏鎸嫊鐝�(xi脿n)璞＄殑闂滅郴銆�
4.5 浜嗚В鎷夋櫘鎷夋柉璁婃彌銆�
5.甯稿井鍒嗘柟绋嬭В鐨勭┅(w臎n)瀹氭€т粙绱�
5.1 鎺屾彙甯稿井鍒嗘柟绋嬭В绌�(w臎n)瀹氭€ф蹇�,鍙婄┅(w臎n)瀹氭€х殑鍒ゅ畾鏂规硶銆�
5.2 鎺屾彙鏉庨泤鏅澶浜屾柟娉�銆�
5.3 浜嗚В骞抽潰鑷不绯荤当(t菕ng)鍩烘湰姒傚康锛屼簡瑙ｆ煇浜涘钩闈㈠畾鎬х悊璜栥€�
銆婂京璁婂嚱鏁�(sh霉)銆嬭€冭│澶х侗
1. 寰╂暩(sh霉)鍙婂叾骞句綍琛ㄧず
1.1 鎺屾彙寰╂暩(sh霉)鍙婂叾閬嬬畻锛屾帉鎻″京鏁�(sh霉)鍩熸蹇�銆�
1.2 鎺屾彙寰╂暩(sh霉)鐨勫咕绋〃绀烘柟娉�銆�
1.3 鎺屾彙寰╂暩(sh霉)鐨勭悆妤靛皠褰�銆佸京鐞冮潰銆佺劇绐ぇ鍙婃摯鍏呯殑寰╁钩闈㈢瓑姒傚康銆�
1.4 鎺屾彙鍏�(n猫i)榛�銆佽仛榛�銆侀倞鐣岄粸銆侀枊闆嗐€侀枆闆嗗強绶婇泦绛夊京骞抽潰鎷撴挷姒傚康銆�
1.5 鎺屾彙绨″柈鏇茬窔鍙婂厜婊戞洸绶氭蹇�,鎺屾彙鑻ョ埦鐣跺畾鐞嗐€�
2. 寰╄畩鍑芥暩(sh霉)
2.1 鎺屾彙寰╄畩鍑芥暩(sh霉)浠ュ強寰╄畩鍑芥暩(sh霉)鐨勬サ闄�銆侀€ｇ簩(x霉)銆佸彲寰拰瑙ｆ瀽绛夋蹇点€�
2.2 鐔熺反鎺屾彙鏌タ锛嶉粠鏇兼浠躲€�
2.3 鎺屾彙杓昏鍑芥暩(sh霉),浜嗚В澶氬€煎嚱鏁�(sh霉)銆�
2.4 鎺屾彙鏀粸姒傚康锛屾帉鎻℃寚鏁�(sh霉)鍑芥暩(sh霉)銆佸皪鏁�(sh霉)鍑芥暩(sh霉)銆佸啰鍑芥暩(sh霉)鍙婁笁瑙掑嚱鏁�(sh霉)绛夊垵绛夊嚱鏁�(sh霉)銆�
3. 寰╄畩鍑芥暩(sh霉)鐨勭⿳鍒�
3.1 鎺屾彙寰╄畩鍑芥暩(sh霉)绌嶅垎鐨勫畾缇╁強鎬ц唱銆�
3.2 鎺屾彙澶氶倞褰㈠崁(q奴)鍩熷懆鐣岀殑绌嶅垎鎬ц唱, 鎺屾彙绌嶅垎鑸囧師鍑芥暩(sh霉)鐨勯棞绯汇€�
3.3 鐔熺反鎺屾彙鏌タ瀹氱悊銆�
3.4 鐔熺反鎺屾彙鏌タ鍏紡骞舵渻閬嬬敤瑭插叕寮忛€茶绌嶅垎瑷堢畻銆�
3.5 鎺屾彙鑾浄鎷夊畾鐞�銆�
4. 绱氭暩(sh霉)
4.1 鎺屾彙绱氭暩(sh霉)鍜屾暩(sh霉)鍒楃殑鍩烘湰鎬ц唱,鎺屾彙寰╂暩(sh霉)闋呯礆鏁�(sh霉)鍜屽京鏁�(sh霉)搴忓垪鐨勬敹鏂傛€у強鏀舵杺鐨�
姊濅欢銆�
4.2 鎺屾彙鍐礆鏁�(sh霉)鐨勬敹鏂傛€�锛屾帉鎻″啰绱氭暩(sh霉)鐨勬敹鏂傚崐寰戠殑姹傛硶銆�
4.3 鎺屾彙瑙ｆ瀽鍑芥暩(sh霉)鐨勬嘲鍕掑睍寮�,鎺屾彙瑙ｆ瀽鍑芥暩(sh霉)娉板嫆灞曞紡鐨勫敮涓€鎬�銆�
4.4 鎺屾彙瑙ｆ瀽鍑芥暩(sh霉)鐨勯浂榛�銆侀浂榛炵殑闅庡強闆堕粸鐨勫绔嬫€�銆�
4.5 鎺屾彙瑙ｆ瀽鍑芥暩(sh霉)鐨勬礇鏈楀睍寮忓拰娲涙湕绱氭暩(sh霉), 鎺屾彙娲涙湕灞曞紡鐨勫敮涓€鎬с€�
4.6 鎺屾彙瑙ｆ瀽鍑芥暩(sh霉)鐨勫绔嬪榛�, 鎺屾彙瀛ょ珛濂囬粸鐨勫垽鍒ユ柟娉曘€�
4.7 鎺屾彙瑙ｆ瀽鍑芥暩(sh霉)鍦ㄧ劇绐仩榛炵殑鎬ц唱銆�
5. 鐣欐暩(sh霉)
5.1 鎺屾彙鐣欐暩(sh霉)姒傚康鍙婄暀鏁�(sh霉)瀹氱悊,鎺屾彙鐣欐暩(sh霉)鐨勮▓绠楁柟娉�銆�
5.2 鎺屾彙鐣欐暩(sh霉)鍦ㄨ▓绠楀畾绌嶅垎鍜屽唬缇╃⿳鍒嗚▓绠椾腑鐨勬噳鐢�銆�
6. 淇濆舰鏄犲皠
6.1 鎺屾彙鍠憠瑙ｆ瀽鍑芥暩(sh霉)姒傚康鍙婃€ц唱銆�
6.2 鎺屾彙灏庢暩(sh霉)鐨勫咕浣曟剰缇┿€�
6.3 鎺屾彙鍒嗗紡绶氭€у嚱鏁�(sh霉)鐨勬蹇�锛屾帉鎻″垎寮忕窔鎬у嚱鏁�(sh霉)鐨勬鎴�銆�
6.4 鎺屾彙鍒嗗紡绶氭€у嚱鏁�(sh霉)鐨勬槧灏勬€ц唱銆�
6.5 鎺屾彙鍏╁€嬬壒娈婄殑鍒嗗紡绶氭€у嚱鏁�(sh霉):鎶婁笂鍗婂钩闈繚褰㈡槧灏勬垚鍠綅鍦撶洡鐨勫垎寮忕窔
鎬у嚱鏁�(sh霉)锛涙妸鍠綅鍦撶洡淇濆舰鏄犲皠鎴愬柈浣嶅湏鐩ょ殑鍒嗗紡绶氭€у嚱鏁�(sh霉)銆�
6.6 浜嗚В鏈€澶фā鍘熺悊銆�
銆婂璁婂嚱鏁�(sh霉)銆嬭€冭│澶х侗
1. 闆嗗悎鑸囧熀鏁�(sh霉)
1.1 鎺屾彙闆嗗悎姒傚康鍙婂叾閬嬬畻:De Morgan 鍏紡銆�
1.2 鐔熺反鎺屾彙闆嗗悎鍩烘暩(sh霉)姒傚康銆�
1.3 閲嶉粸鎺屾彙鍙暩(sh霉)闆嗗悎鐨勬€ц唱銆�
1.4 浜嗚В涓嶅彲鏁�(sh霉)鐒＄闆嗐€�
1.5 鎺屾彙閯板煙銆佸収(n猫i)閮�銆佸皫闆�銆侀枊闆�銆侀枆闆�銆佸畬鍌欓泦鐨勬蹇�銆�
1.6 鎺屾彙闁嬮泦銆侀枆闆嗐€佸畬鍌欓泦銆丅orel 闆嗙殑鎬ц唱鍙婃閫�銆�
2. 娓害鐞嗚珫
2.1 鎺屾彙澶栨脯搴︾殑瀹氱京鍙婂叾鎬ц唱銆�
2.2 閲嶉粸鎺屾彙娓害鐨勫畾缇╁強鍏舵€ц唱銆�
2.3 閲嶉粸鎺屾彙涓€缍┖闁撻粸闆嗙殑娓害锛氶枊闆嗙殑娓害锛岄枆闆嗙殑娓害銆�
2.4 浜嗚В涔樼⿳绌洪枔榛為泦鐨勬脯搴�銆�
3. 鍙脯鍑芥暩(sh霉)
3.1 鎺屾彙鍙脯鍑芥暩(sh霉)鐨勫畾缇╁強鍏舵€ц唱銆�
3.2 鎺屾彙骞句箮铏曡檿鐨勬蹇�銆�
3.3 閲嶉粸鎺屾彙 Egoroff 瀹氱悊銆�
3.4 閲嶉粸鎺屾彙鍙脯鍑芥暩(sh霉)鐨勭祼妲嬪強 Lusin 瀹氱悊銆�
3.5 閲嶉粸鎺屾彙渚濇脯搴︽敹鏂�銆�
4. 绌嶅垎鐞嗚珫
4.1 鎺屾彙闈炶矤鍙脯鍑芥暩(sh霉)绌嶅垎鐨勫畾缇╁強鎬ц唱銆�
4.2 鎺屾彙鍙脯鍑芥暩(sh霉)绌嶅垎鐨勫畾缇╁強鎬ц唱銆�
4.3 閲嶉粸鎺屾彙 Levi 瀹氱悊銆�
4.4 閲嶉粸鎺屾彙 Fatou 寮曠悊銆�
4.5 閲嶉粸鎺屾彙 Lebesgue 鎺у埗鏀舵杺瀹氱悊銆�
4.6 浜嗚В Lebesgue 鏈夌晫鏀舵杺瀹氱悊銆�
4.7 浜嗚В Fubini 瀹氱悊銆�
4.8 浜嗚В涓嶅畾绌嶅垎銆�
銆婅繎涓栦唬鏁�(sh霉)銆嬭€冭│澶х侗
1. 鍩烘湰姒傚康
1.1 鐞嗚В闆嗗悎鐨勬蹇�锛屼簡瑙ｅ厓绱犺垏闆嗗悎涔嬮枔鐨勯棞绯�锛屼互鍙婇泦鍚堜箣闁撶殑閬嬬畻銆�
1.2 鐞嗚В鏄犲皠鐨勬蹇�锛岃兘鍦ㄩ泦鍚堜箣闁撳缓绔嬫槧灏勯棞绯伙紝骞跺垽鏂峰叐鍊嬫槧灏勬槸鍚︾浉鍚�銆�
1.3 鎺屾彙浠ｆ暩(sh霉)閬嬬畻鐨勬蹇靛強鍏舵豢瓒崇殑閬嬬畻寰�锛岃兘寤虹珛鏈夐檺闆嗗悎涔嬮枔鐨勯亱绠楄〃銆�
1.4 鎺屾彙鍚屾厠(t脿i)鏄犲皠鍜屽悓妲嬫槧灏勭殑姒傚康锛岀悊瑙ｅ悓鎱�(t脿i)鑸囧悓鎱�(t脿i)婊垮皠鐨勯棞绯�锛屽苟鑳藉垽瀹氭槧
灏勬槸鍚︽槸鍚屾厠(t脿i)婊垮皠鎴栨槸鍠皠锛屾帉鎻″叿鏈夊悓鎱�(t脿i)婊垮皠鐨勯泦鍚堜箣闁撶殑鑱�(li谩n)绯�銆�
1.5 鐞嗚В闂滅郴鍜岀瓑鍍归棞绯荤殑姒傚康锛屾帉鎻＄瓑鍍归棞绯诲拰鍒嗛涔嬮枔鐨勮綁鎻涘畾鐞�锛屽拰鐔熺反
鍒ゅ畾绲﹀畾鐨勯棞绯绘槸鍚︽槸绛夊児闂滅郴锛屽苟鐔熸倝鍓╀綑椤炵殑鍩烘湰鐗规€�锛屼互渚跨偤缇ゃ€佺挵(hu谩n)
鎻愪緵鍏稿瀷鐨勮寖渚�锛岃兘寤虹珛鏁存暩(sh霉)闁撶郸瀹氱殑妯＄殑鍓╀綑椤�
2. 缇�
2.1 鐔熸倝缇ょ殑瀹氱京锛岀悊瑙ｅ乏銆佸彸鍠綅鍏�锛屽乏銆佸彸閫嗗厓鐨勬剰缇╋紝鎺屾彙鏈夐檺缇�銆佺劇闄�
缇ゃ€佺兢鐨勯殠鍜屼氦鎻涚兢鐨勬蹇�銆�
2.2 鐞嗚В缇ゅ悓妲�銆佸悓鎱�(t脿i)鐨勫畾缇╋紝鎺屾彙缇ゅ悓鎱�(t脿i)鐨勬湁闂滄€ц唱銆�
2.3 鎺屾彙寰挵(hu谩n)缇ょ殑瀹氱京鍜岀敱鐢熸垚鍏冩焙瀹氬惊鐠�(hu谩n)缇ょ殑鎬ц唱鑸囩壒榛�锛岀啛绶存帉鎻″墿浣欓鍔�
缇ょ殑鎬ц唱鍜岄亱绠�锛岀煡閬撳惊鐠�(hu谩n)缇ゅ彲浠ヨ垏鏁存暩(sh霉)鍔犵兢鎴栨ā鐐� n 鐨勫墿浣欓鍔犵兢鍚屾銆�
2.4 浜嗚В璁婃彌缇ょ殑瀹氱京锛岀悊瑙ｇ疆鎻涚兢瀹氱京锛屾帉鎻″皪绋辩兢涓厓绱犵殑涔樻硶銆佸厓绱犳眰閫�
绛夐亱绠�锛岀悊瑙ｅ惊鐠�(hu谩n)缃彌銆佸皪鎻涘畾缇�銆�
2.5 浜嗚В瀛愮兢鐨勫畾缇╀互鍙婂瓙缇よ垏瀛愮兢涔嬮枔鐨勯棞绯伙紝鎺屾彙姝ｈ(gu墨)瀛愮兢鐨勫畾缇╁拰鍒ゅ畾姊�
浠跺強鍏舵€ц唱锛岀悊瑙ｅ晢缇ょ殑瀹氱京銆�
2.6 鎺屾彙闄泦鐨勫畾缇�锛屼互鍙婅垏绛夊児闂滅郴鍜屽垎椤炰箣闁撶殑闂滅郴锛屼簡瑙ｅ瓙缇よ垏闄泦涔嬮枔
鐨勬槧灏勯棞绯�锛屾帉鎻￠棞浜庣兢鐨勯殠鏁�(sh霉)鍜屾寚鏁�(sh霉)鐨勫咕鍊嬮噸瑕佸畾鐞�銆�
2.7 鐞嗚В缇ゅ悓鎱�(t脿i)鍜屽悓妲嬬殑瀹氱京锛岄噸榛炴帉鎻＄兢鍚屾厠(t脿i)鍩烘湰瀹氱悊鍜岀兢鍚屾瀹氱悊锛屾帉鎻＄兢
鍚屾厠(t脿i)鍩烘湰瀹氱悊鍜屽悓妲嬪畾鐞嗚瓑鏄庣殑鎳夌敤銆�
3. 鐠�(hu谩n)鑸囧煙
3.1 鐞嗚В鐠�(hu谩n)鍜屼氦鎻涚挵(hu谩n)鐨勫畾缇╋紝鐔熸倝鍠綅鍏�銆侀€嗗厓鍜岄浂鍥犲瓙鐨勬€ц唱骞惰兘鐔熺反閬嬬敤,
鎺屾彙娑堝幓寰嬭垏闆跺洜瀛愮殑闂滅郴銆�
3.2 鐞嗚В鏁寸挵(hu谩n)銆侀櫎鐠�(hu谩n)鍜屽煙鐨勫畾缇╋紝鐞嗚В鐠�(hu谩n)鐗瑰緛鐨勫畾缇�锛屾帉鎻″垽鍒ョ挵(hu谩n)鏄櫎鐠�(hu谩n)銆佸煙鐨�
鏂规硶銆�
3.3 浜嗚В瀛愮挵(hu谩n)銆佸瓙闄ょ挵(hu谩n)銆佸瓙鍩熷畾缇�锛屾帉鎻″垽鍒ュ瓙鐠�(hu谩n)銆佸瓙鍩熺殑鏂规硶銆�
3.4 鐞嗚В鐞嗘兂銆佷富鐞嗘兂鐨勫畾缇�锛屾渻鍒ゅ垾涓€鍊嬬悊鎯冲瓙鐠�(hu谩n)鏄惁鐐轰富鐞嗘兂瀛愮挵(hu谩n)銆�
3.5 鎺屾彙绱犵悊鎯炽€佹サ澶х悊鎯崇殑姒傚康锛屽苟浜嗚В閫欏叐椤炵悊鎯崇殑鍒ゅ垾鏂规硶銆�
3.6 浜嗚В鍟嗙挵(hu谩n)鐨勫畾缇�锛岀啛鎮夋ā n 鐨勫墿浣欓鐨勯亱绠�锛屼簡瑙ｅ湪鍚屾厠(t脿i)鏄犲皠涓嬬殑鍏╁€嬬挵(hu谩n)鐩�
浜掍箣闁撶殑闂滅郴銆佹€ц唱锛屾帉鎻＄挵(hu谩n)鐨勫悓鎱�(t脿i)鍩烘湰瀹氱悊銆�
4. 鍞竴鍒嗚В鏁寸挵(hu谩n)
4.1 浜嗚В鏁寸挵(hu谩n)鍏冪礌鏁撮櫎鐨勫畾缇�锛屼簡瑙ｅ柈浣嶃€佺浉浼村厓銆佺湡鍥犲瓙銆佹棦绱勫厓鐨勫畾缇╁強涔�
闁撻棞绯�銆�
4.2 鐞嗚В鍞竴鍒嗚В鐠�(hu谩n)鐨勫畾缇�锛屾帉鎻″垽鍒ュ敮涓€鍒嗚В鐠�(hu谩n)鐨勬柟娉曘€�
4.3 鐞嗚В涓荤悊鎯虫暣鐠�(hu谩n)銆佹瓙姘忕挵(hu谩n)鐨勫畾缇�锛屼簡瑙ｈ垏鍏剁浉闂滅殑瀹氱悊銆�
5. 鍩熺殑鎿村嫉
5.1 浜嗚В鎿村煙鐨勫畾缇╁拰鐩搁棞瀹氱悊锛岀悊瑙ｅ柈鎿村煙銆佺礌鍩熺殑瀹氱京銆�
5.2 浜嗚В瓒呰秺鍏冿紝鍠秴瓒婃摯鍩�锛涗唬鏁�(sh霉)鍏�锛屽柈浠ｆ暩(sh霉)鎿村煙鐨勫畾缇�銆�
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