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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骞达紝2013骞�锛涘潎鎻愪緵鏀惰不(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
銆婃暩(sh霉)瀛�(xu茅)鍒嗘瀽銆嬭€冭│澶х侗
1.鍑芥暩(sh霉)
1.1 鎺屾彙瀵�(sh铆)鏁�(sh霉)姒傚康鍙婂叾鍩烘湰鎬ц唱(zh矛)銆傛帉鎻″(sh铆)鏁�(sh霉)绲曞皪鍊肩殑姒傚康鍜屾湁闂�(gu膩n)鐨勪笉绛夊紡銆�
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�(f霉)鍚堝嚱鏁�(sh霉)鍜屽弽鍑芥暩(sh霉)鐨勬蹇�銆�
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�(di脿o)鍑芥暩(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�銆�
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(zh矛)銆�
1.6 鎺屾彙甯哥敤鐨勫咕鍊�(g猫)闈炲垵绛夊嚱鏁�(sh霉)锛屽绗﹁櫉鍑芥暩(sh霉)锛岀媱鍒╁厠闆峰嚱鏁�(sh霉)绛�銆�
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�(hu矛)浣跨敤鈥� 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(zh矛)銆�
2.3 鎺屾彙鍠(di脿o)鏈夌晫鍘熺悊,鑷村瘑鎬у畾鐞嗗強 Cauchy 鏀舵杺婧�(zh菙n)鍓囥€�
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(zh矛)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(ji茅)鍘熷墖鍙婃煰瑗挎簴(zh菙n)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�(y墨ng)鐢�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�銆�
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�(di菐n)鍙婂叾鍒嗛銆�
4.2 鎺屾彙閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勫眬閮ㄦ€ц唱(zh矛),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(zh矛)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�(d菐o)鏁�(sh霉)鑸囧井鍒�
5.1 鎺屾彙灏�(d菐o)鏁�(sh霉)鐨勬蹇靛強鍏跺咕浣曟剰缇┿€�
5.2 鎺屾彙姹傚皫(d菐o)娉曞墖,鎺屾彙鍙冭畩閲忓嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)娉曞墖, 鎺屾彙楂橀殠灏�(d菐o)鏁�(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┿€�
5.4 鎺屾彙寰垎鐨勯亱(y霉n)绠楁硶鍓�,浜嗚В楂橀殠寰垎,浜嗚В寰垎鍦ㄨ繎浼艰▓(j矛)绠椾腑鐨勬噳(y墨ng)鐢�銆�
6. 寰垎涓€煎畾鐞嗗強鍏舵噳(y墨ng)鐢�
6.1 鐔熺反鎺屾彙涓€煎畾鐞嗙殑姊濅欢銆佺祼(ji茅)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�(d谩)娉曞墖鍙婂叾鎳�(y墨ng)鐢�銆�
6.3 鎺屾彙娉板嫆鍏紡锛屾帉鎻＄敤澶氶爡(xi脿ng)寮忛€艰繎鍑芥暩(sh霉)鐨勬€濇兂銆�
6.4 鏈�(hu矛)鍒嗘瀽鍑芥暩(sh霉)鐨勬€ф厠(t脿i),鏈�(hu矛)姹傚嚱鏁�(sh霉)鐨勫柈瑾�(di脿o)鍗€(q奴)闁撳拰妤靛€�锛屾渻(hu矛)鍒ゆ柗鍑芥暩(sh霉)鐨勫嚫鎬у拰鎷愰粸(di菐n),
鏈�(hu矛)杓冨畬鍠勫湴浣滃嚭鍑芥暩(sh霉)鐨勫湒褰�銆�
7. 瀵�(sh铆)鏁�(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(di菐n)姒傚康鍙婂悇绋瓑鍍�(ji脿)瀹氱京锛岃兘鐔熺反浣跨敤鑱氶粸(di菐n)瀹氱悊銆�
7.3 鐞嗚В锛堥枊锛夎钃嬬殑瀹氱京骞朵笖鏈�(hu矛)鐢ㄩ泦鍚堣(sh霉)瑾炶〃閬�(d谩)锛岄珨鏈�(hu矛)濡備綍妲�(g貌u)閫犻枊瑕嗚搵骞朵笖鏈�(hu矛)
鐢ㄩ枊瑕嗚搵瀹氱悊銆�
7.4 鐭ユ泬瀵�(sh铆)鏁�(sh霉)瀹屽倷鎬х殑鍏ó绛夊児(ji脿)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▓(j矛)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(zh矛)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▓(j矛)绠楁柟娉�銆�
8.5 浜嗚В鏌愪簺鍏跺畠椤炲瀷涓嶅畾绌嶅垎鐨勮▓(j矛)绠楁柟娉曘€�
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�(zh菙n)鍓囧強鍙⿳鍑芥暩(sh霉)椤�銆�
9.3 鐔熺反鎺屾彙瀹氱⿳鍒嗙殑鎬ц唱(zh矛)鍙婄⿳鍒嗕腑鍊煎畾鐞�銆�
9.4 閲嶉粸(di菐n)鎺屾彙寰⿳鍒嗗(xu茅)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�(xu茅)绉戠殑鍟忛銆�
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�(xi脿ng)绱氭暩(sh霉)
11.1 娣卞叆鐞嗚В鏁�(sh霉)闋�(xi脿ng)绱氭暩(sh霉)鐨勬蹇靛強鍏剁敘(ch菐n)鐢熻儗鏅�銆�
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(xi脿ng)绱氭暩(sh霉)鍜屼竴鑸爡(xi脿ng)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�(xi脿ng)绱氭暩(sh霉)鍜屽啰绱氭暩(sh霉)
12.1 娣卞叆鐞嗚В閫愰粸(di菐n)鏀舵杺鍜屼竴鑷存敹鏂傛蹇�锛岄噸榛�(di菐n)鍦ㄤ竴鑷存敹鏂�銆�
12.2 鐔熺反浣跨敤涓€鑷存敹鏂傜殑 Cauchy 婧�(zh菙n)鍓囧強鏀舵杺鍒ゅ垾娉�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�(xi脿ng)绱氭暩(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(zh矛)锛�
鍗抽€ｇ簩(x霉)鎬�銆佸彲绌嶆€с€佸彲寰€�銆�
12.4 鑳界啛绶存眰鍑轰竴鍊�(g猫)鍐礆鏁�(sh霉)鐨勬敹鏂傚崐寰戙€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(zh矛)(鍏�(n猫i)闁変竴鑷存敹鏂傛€с€侀€ｇ簩(x霉)鎬�銆侀€愰爡(xi脿ng)鍙⿳鍜�
閫愰爡(xi脿ng)鍙皫(d菐o)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�(hu矛)鍋氫竴鍊�(g猫)鍙⿳鍑芥暩(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�銆丅essel 涓嶇瓑寮忓拰 Riemann-Lebesgue 寮曠悊銆�
13.4 浜嗚В鏈夐棞(gu膩n)鍌呴噷钁夌礆鏁�(sh霉)鏀舵杺鎬х殑涓€浜涚祼(ji茅)鏋溿€�
14. 澶氬厓鍑芥暩(sh霉)寰垎瀛�(xu茅)
14.1鎺屾彙骞抽潰榛�(di菐n)闆嗙殑涓€浜涙蹇�: 閯板煙銆佸収(n猫i)榛�(di菐n)銆佺晫榛�(di菐n)銆佽仛榛�(di菐n)銆佸崁(q奴)鍩�銆侀枆鍗€(q奴)鍩熴€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(zh矛)銆�
14.4 鐞嗚В鍙井鎬х殑姊濅欢銆佸咕浣曟剰缇╁強鎳�(y墨ng)鐢ㄣ€�
14.5 鐔熺反瑷�(j矛)绠楀亸灏�(d菐o)鏁�(sh霉)鍜岄珮闅庡亸灏�(d菐o)鏁�(sh霉)銆�
14.6 浜嗚В鏂瑰悜?q奴)顫�?sh霉)鑸囨搴︾殑瀹氱京銆�
14.7 鏈�(hu矛)閬�(y霉n)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�(y霉n)鐢�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�銆�
16.3 鐞嗚В姝愭媺绌嶅垎骞舵渻(hu矛)鎳�(y墨ng)鐢�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(zh矛)銆�
17.2 鎺屾彙浜岄噸绌嶅垎鐨勮▓(j矛)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�(y墨ng)鐢ㄣ€�
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▓(j矛)绠楋紝鎺屾彙涓夐噸绌嶅垎鐨勮畩閲忚畩鎻涘拰鎳�(y墨ng)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�(j矛)绠椼€�
18.3 鏈�(hu矛)閬�(y霉n)鐢ㄦ牸鏋楀叕寮忓拰绌嶅垎鑸囪矾寰戠劇闂�(gu膩n)鐨勬浠惰В姹哄晱椤�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�(j矛)绠�銆�
18.6 鏈�(hu矛)閬�(y霉n)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(zh矛)銆�
1.2 鐔熺反鎺屾彙琛屽垪寮忕殑姒傚康銆佹€ц唱(zh矛)銆�
1.3 鎺屾彙琛屽垪寮忕殑瑷�(j矛)绠楁柟娉�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�銆�
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�(y霉n)绠�銆�
2.2 鐔熺反鎺屾彙鍚戦噺绲勭殑绶氭€х浉闂�(gu膩n)鎬�锛岀悊瑙ｅ悜閲忕祫鐨勬サ澶х劇闂�(gu膩n)绲�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▓(j矛)绠楁柟娉�銆�
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�(ch菙)瑙ｇ郴鐨勬蹇靛拰瑷�(j矛)绠楁柟娉�锛岀啛绶存帉鎻＄窔
鎬ф柟绋嬬祫鐨勮В鐨勭祼(ji茅)妲�(g貌u)瀹氱悊锛屾渻(hu矛)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€�
3.2 鐔熺反鎺屾彙鐭╅櫍鐨勯亱(y霉n)绠楀強閬�(y霉n)绠楀緥銆�
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(gu膩n)绯�銆�
3.4 娣卞叆鐞嗚В鐭╅櫍鍙€�銆侀€嗙煩闄ｃ€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(hu矛)
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�锛屾帉鎻″垎濉婄煩闄ｇ殑閬�(y霉n)绠楀強鎬ц唱(zh矛)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�(gu膩n)绯伙紝鐔熺反鎺屾彙鍒╃敤鍒�
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涳紝鏈�(hu矛)灏囩煩闄ｅ垎濉婅垏鍒濈瓑璁婃彌绲�(ji茅)鍚堥€�(j矛n)琛岀煩闄ｉ亱(y霉n)绠�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(zh矛)銆�
4.2 鎺屾彙鍖栦簩娆″瀷鐐烘(bi膩o)婧�(zh菙n)褰㈢殑鏂规硶銆�
4.3 娣卞埢鐞嗚В灏嶇ū鐭╅櫍鑸囦簩娆″瀷鐨勯棞(gu膩n)绯�锛屾帉鎻″皪绋辩煩闄ｇ殑鎬ц唱(zh矛)銆�
4.4 鎺屾彙鎱ｆ€у畾鐞嗭紝鐔熺反鎺屾彙姝ｅ畾浜屾鍨嬬殑绛夊児(ji脿)姊濅欢銆�
4.5 鎺屾彙鍗婃瀹氫簩娆″瀷鐨勭瓑鍍�(ji脿)姊濅欢銆�
5. 绶氭€х┖闁�
5.1 鎺屾彙闆嗗悎鑸囨槧灏勭殑鐩搁棞(gu膩n)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�(gu膩n)姒傚康銆�
5.3 鏈�(hu矛)姹傜窔鎬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(bi膩o)璁婃彌鐨勫叕寮�锛�銆�
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曘€�
5.6 鎺屾彙瀛愮┖闁撶殑浜よ垏鍜岀殑瀹氱京鍙婃€ц唱(zh矛)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�(g貌u)鐨勫畾缇�銆佹€ц唱(zh矛)鍙婃湁闄愮董绌洪枔鍚屾(g貌u)鐨勫厖瑕佹浠�銆�
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(zh矛)銆�
6.2 鎺屾彙绶氭€ц畩鎻涚殑閬�(y霉n)绠楀強閬�(y霉n)绠楀緥锛岀悊瑙ｇ窔鎬ц畩鎻涚殑澶氶爡(xi脿ng)寮�銆�
6.3 鎺屾彙绶氭€ц畩鎻涜垏鐭╅櫍鐨勯棞(gu膩n)绯伙紝鎺屾彙鐭╅櫍鐩镐技鐨勬蹇靛強鎬ц唱(zh矛)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�(xi脿ng)寮忕殑姒傚康鍙婃€ц唱(zh矛)锛屾渻(hu矛)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(gu膩n)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�(gu膩n)绯�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(zh矛)銆�
7.3 姝ｇ⒑鐞嗚В姝ｄ氦鍚戦噺绲�銆佹(bi膩o)婧�(zh菙n)姝ｄ氦鍩虹殑姒傚康锛屾帉鎻℃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�(ji脿)姊濅欢锛屾帉鎻℃浜よ畩鎻涜垏鍚戦噺闀峰害銆佹(bi膩o)婧�(zh菙n)姝�
浜ゅ熀浠ュ強姝ｄ氦鐭╅櫍鐨勯棞(gu膩n)绯汇€�
7.5 鐞嗚В鍏╁€�(g猫)瀛愮┖闁撴浜ょ殑姒傚康锛屾帉鎻℃浜よ垏鐩村拰鐨勯棞(gu膩n)绯汇€�
7.6 鐔熺反鎺屾彙瀵�(sh铆)灏嶇ū鐭╅櫍鐨勯€�(j矛n)涓€姝ユ€ц唱(zh矛)銆�
8. 澶氶爡(xi脿ng)寮�
8.1 浜嗚В澶氶爡(xi脿ng)寮忕殑瀹氱京鑸囧熀鏈亱(y霉n)绠�銆�
8.2 鎺屾彙澶氶爡(xi脿ng)寮忔暣闄ょ殑姒傚康銆佹€ц唱(zh矛)鑸囧付浣欓櫎娉�銆�
8.3 鎺屾彙鏈€澶у叕鍥犲紡鐨勬蹇�銆佸瓨鍦ㄦ€ц垏姹傛硶,鎺屾彙澶氶爡(xi脿ng)寮忎簰绱犵殑姒傚康鑸囩浉闂�(gu膩n)鎬ц唱(zh矛)銆�
8.4 鎺屾彙涓嶅彲绱勫闋�(xi脿ng)寮忕殑姒傚康銆佹€ц唱(zh矛)銆�
8.5 浜嗚В鍥犲紡鍒嗚В瀹氱悊浠ュ強寰�(f霉)绯绘暩(sh霉)鑸囧(sh铆)绯绘暩(sh霉)澶氶爡(xi脿ng)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(xi脿ng)寮忔湁閲嶅洜寮忕殑鍏呰姊濅欢銆�
8.7 浜嗚В澶氶爡(xi脿ng)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(xi脿ng)寮忕殑鍏ㄩ儴鏈夌悊鏍圭殑鏂规硶浠ュ強 Eisenstein 鍒ゅ垾娉�銆�
9. ?? 鐭╅櫍
9.1 浜嗚В ?? 鐭╅櫍鐨勫畾缇�銆� ?? 鐭╅櫍鐨勫垵绛夎畩鎻�銆� ?? 鐭╅櫍鐨勬(bi膩o)婧�(zh菙n)褰互鍙� ?? 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(ji脿)鐨勫厖瑕佹浠�,鎺屾彙鐢ㄥ垵
绛夎畩鎻涘皣 ?? 鐭╅櫍鍖栫偤妯�(bi膩o)婧�(zh菙n)褰㈢殑鏂规硶銆�
9.2 鎺屾彙鐭╅櫍鍒濈瓑鍥犲瓙鐨勬蹇点€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�(bi膩o)婧�(zh菙n)褰互鍙婃湁鐞嗘(bi膩o)婧�(zh菙n)褰㈢殑姒傚康锛屾帉鎻＄煩闄ｇ殑 Jordan 妯�(bi膩o)婧�(zh菙n)
褰㈢殑姹傛硶锛屼簡瑙ｇ煩闄ｆ湁鐞嗘(bi膩o)婧�(zh菙n)褰㈢殑姹傛硶銆�
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(r猫n)璀樺父寰垎鏂圭▼瑾茬▼鐨勬暣楂旂祼(ji茅)妲�(g貌u)銆�
1.2 鎺屾彙鍒嗛洟璁婇噺娉�锛屾渻(hu矛)鐢ㄨ┎鏂规硶姹傝В璁婇噺鍙垎闆㈡柟绋�銆�
1.3 鎺屾彙鍏╅鍙綁(zhu菐n)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�(di菐n)鎺屾彙榻婃鏂圭▼瑙ｆ硶銆�
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)璁婃槗娉曪紝鏈�(hu矛)鐢ㄨ┎鏂规硶姹傝В闈為綂娆℃柟
绋�銆�
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碉紝鎺屾彙鍏ㄥ井鍒嗘柟绋嬫眰瑙ｆ硶锛屾渻(hu矛)鐢ㄧ⿳鍒�
鍥犲瓙娉曞皣闈炲叏寰垎鏂圭▼杞�(zhu菐n)鍖栫偤鍏ㄥ井鍒嗘柟绋�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(hu矛)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(y墨ng)鐢ㄨ垑渚� 1.绛夎杌岀窔锛�2.鍦ㄥ嫊(d貌ng)鍔涘(xu茅)涓殑鎳�(y墨ng)鐢ㄣ€�
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�锛屾帉鎻″井鍒嗘柟绋嬭В鐨勫咕浣曟剰缇�銆�
2.2 閲嶉粸(di菐n)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�?xi脿ng)l浠躲€�
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(zh矛)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�(lu貌)鐨勬蹇靛強姹傝В鍖呯怠(lu貌)鐨勬柟娉�銆傛帉鎻�
鍏嬭悐娲涙柟绋嬬殑椤炲瀷鍙婃眰瑙ｆ柟娉�銆�
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с€�
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�(ji茅)妲�(g貌u)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�(y霉n)鐢ㄧ壒寰佹牴姹傝В甯哥郴鏁�(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€鑸悊璜栵紝鍖呮嫭閫氳В绲�(ji茅)妲�(g貌u)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�(ji茅)妲�(g貌u)锛屽凡鐭ラ綂娆℃柟绋嬮€氳В鏈�(hu矛)閬�(y霉n)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(di菐n) n 闅庡父绯绘暩(sh霉)绶氭€ч綂娆℃柟绋嬭В娉�锛屽嵆閬�(y霉n)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(y霉n)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(d貌ng)鐝�(xi脿n)璞＄殑闂�(gu膩n)绯汇€�
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�銆�
銆婂京(f霉)璁婂嚱鏁�(sh霉)銆嬭€冭│澶х侗
1. 寰�(f霉)鏁�(sh霉)鍙婂叾骞句綍琛ㄧず
1.1 鎺屾彙寰�(f霉)鏁�(sh霉)鍙婂叾閬�(y霉n)绠楋紝鎺屾彙寰�(f霉)鏁�(sh霉)鍩熸蹇�銆�
1.2 鎺屾彙寰�(f霉)鏁�(sh霉)鐨勫咕绋〃绀烘柟娉�銆�
1.3 鎺屾彙寰�(f霉)鏁�(sh霉)鐨勭悆妤靛皠褰�銆佸京(f霉)鐞冮潰銆佺劇绐ぇ鍙婃摯(ku貌)鍏呯殑寰�(f霉)骞抽潰绛夋蹇�銆�
1.4 鎺屾彙鍏�(n猫i)榛�(di菐n)銆佽仛榛�(di菐n)銆侀倞鐣岄粸(di菐n)銆侀枊闆�銆侀枆闆嗗強绶婇泦绛夊京(f霉)骞抽潰鎷�?f霉)娑撴媿鐫�?br/>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�(d膩ng)瀹氱悊銆�
2. 寰�(f霉)璁婂嚱鏁�(sh霉)
2.1 鎺屾彙寰�(f霉)璁婂嚱鏁�(sh霉)浠ュ強寰�(f霉)璁婂嚱鏁�(sh霉)鐨勬サ闄�銆侀€ｇ簩(x霉)銆佸彲寰拰瑙ｆ瀽绛夋蹇�銆�
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(di菐n)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�(f霉)璁婂嚱鏁�(sh霉)鐨勭⿳鍒�
3.1 鎺屾彙寰�(f霉)璁婂嚱鏁�(sh霉)绌嶅垎鐨勫畾缇╁強鎬ц唱(zh矛)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(zh矛), 鎺屾彙绌嶅垎鑸囧師鍑芥暩(sh霉)鐨勯棞(gu膩n)绯�銆�
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(hu矛)閬�(y霉n)鐢ㄨ┎鍏紡閫�(j矛n)琛岀⿳鍒嗚▓(j矛)绠�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(zh矛),鎺屾彙寰�(f霉)鏁�(sh霉)闋�(xi脿ng)绱氭暩(sh霉)鍜屽京(f霉)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€э紝鎺屾彙鍐礆鏁�(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�(di菐n)銆侀浂榛�(di菐n)鐨勯殠鍙婇浂榛�(di菐n)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�(di菐n), 鎺屾彙瀛ょ珛濂囬粸(di菐n)鐨勫垽鍒ユ柟娉�銆�
4.7 鎺屾彙瑙ｆ瀽鍑芥暩(sh霉)鍦ㄧ劇绐仩(yu菐n)榛�(di菐n)鐨勬€ц唱(zh矛)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▓(j矛)绠楁柟娉�銆�
5.2 鎺屾彙鐣欐暩(sh霉)鍦ㄨ▓(j矛)绠楀畾绌嶅垎鍜屽唬缇╃⿳鍒嗚▓(j矛)绠椾腑鐨勬噳(y墨ng)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(zh矛)銆�
6.2 鎺屾彙灏�(d菐o)鏁�(sh霉)鐨勫咕浣曟剰缇�銆�
6.3 鎺屾彙鍒嗗紡绶氭€у嚱鏁�(sh霉)鐨勬蹇碉紝鎺屾彙鍒嗗紡绶氭€у嚱鏁�(sh霉)鐨勬(g貌u)鎴�銆�
6.4 鎺屾彙鍒嗗紡绶氭€у嚱鏁�(sh霉)鐨勬槧灏勬€ц唱(zh矛)銆�
6.5 鎺屾彙鍏╁€�(g猫)鐗规畩鐨勫垎寮忕窔鎬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(sh铆)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�(y霉n)绠�: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(di菐n)鎺屾彙鍙暩(sh霉)闆嗗悎鐨勬€ц唱(zh矛)銆�
1.4 浜嗚В涓嶅彲鏁�(sh霉)鐒＄闆�銆�
1.5 鎺屾彙閯板煙銆佸収(n猫i)閮ㄣ€佸皫(d菐o)闆�銆侀枊闆�銆侀枆闆�銆佸畬鍌欓泦鐨勬蹇点€�
1.6 鎺屾彙闁嬮泦銆侀枆闆�銆佸畬鍌欓泦銆丅orel 闆嗙殑鎬ц唱(zh矛)鍙婃(g貌u)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(zh矛)銆�
2.2 閲嶉粸(di菐n)鎺屾彙娓害鐨勫畾缇╁強鍏舵€ц唱(zh矛)銆�
2.3 閲嶉粸(di菐n)鎺屾彙涓€缍┖闁撻粸(di菐n)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�(di菐n)闆嗙殑娓害銆�
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(zh矛)銆�
3.2 鎺屾彙骞句箮铏曡檿鐨勬蹇�銆�
3.3 閲嶉粸(di菐n)鎺屾彙 Egoroff 瀹氱悊銆�
3.4 閲嶉粸(di菐n)鎺屾彙鍙脯鍑芥暩(sh霉)鐨勭祼(ji茅)妲�(g貌u)鍙� Lusin 瀹氱悊銆�
3.5 閲嶉粸(di菐n)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(f霉)鍙脯鍑芥暩(sh霉)绌嶅垎鐨勫畾缇╁強鎬ц唱(zh矛)銆�
4.2 鎺屾彙鍙脯鍑芥暩(sh霉)绌嶅垎鐨勫畾缇╁強鎬ц唱(zh矛)銆�
4.3 閲嶉粸(di菐n)鎺屾彙 Levi 瀹氱悊銆�
4.4 閲嶉粸(di菐n)鎺屾彙 Fatou 寮曠悊銆�
4.5 閲嶉粸(di菐n)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闆嗗悎鐨勬蹇碉紝浜嗚В鍏冪礌鑸囬泦鍚堜箣闁撶殑闂�(gu膩n)绯�锛屼互鍙婇泦鍚堜箣闁撶殑閬�(y霉n)绠�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(gu膩n)绯�锛屽苟鍒ゆ柗鍏╁€�(g猫)鏄犲皠鏄惁鐩稿悓銆�
1.3 鎺屾彙浠ｆ暩(sh霉)閬�(y霉n)绠楃殑姒傚康鍙婂叾婊胯冻鐨勯亱(y霉n)绠楀緥锛岃兘寤虹珛鏈夐檺闆嗗悎涔嬮枔鐨勯亱(y霉n)绠楄〃銆�
1.4 鎺屾彙鍚屾厠(t脿i)鏄犲皠鍜屽悓妲�(g貌u)鏄犲皠鐨勬蹇碉紝鐞嗚В鍚屾厠(t脿i)鑸囧悓鎱�(t脿i)婊垮皠鐨勯棞(gu膩n)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�(gu膩n)绯诲拰绛夊児(ji脿)闂�(gu膩n)绯荤殑姒傚康锛屾帉鎻＄瓑鍍�(ji脿)闂�(gu膩n)绯诲拰鍒嗛涔嬮枔鐨勮綁(zhu菐n)鎻涘畾鐞�锛屽拰鐔熺反
鍒ゅ畾绲﹀畾鐨勯棞(gu膩n)绯绘槸鍚︽槸绛夊児(ji脿)闂�(gu膩n)绯�锛屽苟鐔熸倝鍓╀綑椤炵殑鍩烘湰鐗规€э紝浠ヤ究鐐虹兢銆佺挵(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�锛屾帉鎻℃湁闄愮兢銆佺劇闄�
缇�銆佺兢鐨勯殠鍜屼氦鎻涚兢鐨勬蹇�銆�
2.2 鐞嗚В缇ゅ悓妲�(g貌u)銆佸悓鎱�(t脿i)鐨勫畾缇�锛屾帉鎻＄兢鍚屾厠(t脿i)鐨勬湁闂�(gu膩n)鎬ц唱(zh矛)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(zh矛)鑸囩壒榛�(di菐n)锛岀啛绶存帉鎻″墿浣欓鍔�
缇ょ殑鎬ц唱(zh矛)鍜岄亱(y霉n)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(g貌u)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(y霉n)绠楋紝鐞嗚В寰挵(hu谩n)缃彌銆佸皪鎻涘畾缇┿€�
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(gu膩n)绯�锛屾帉鎻℃瑕�(gu墨)瀛愮兢鐨勫畾缇╁拰鍒ゅ畾姊�
浠跺強鍏舵€ц唱(zh矛)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(ji脿)闂�(gu膩n)绯诲拰鍒嗛涔嬮枔鐨勯棞(gu膩n)绯伙紝浜嗚В瀛愮兢鑸囬櫔闆嗕箣闁�
鐨勬槧灏勯棞(gu膩n)绯�锛屾帉鎻￠棞(gu膩n)浜庣兢鐨勯殠鏁�(sh霉)鍜屾寚鏁�(sh霉)鐨勫咕鍊�(g猫)閲嶈瀹氱悊銆�
2.7 鐞嗚В缇ゅ悓鎱�(t脿i)鍜屽悓妲�(g貌u)鐨勫畾缇╋紝閲嶉粸(di菐n)鎺屾彙缇ゅ悓鎱�(t脿i)鍩烘湰瀹氱悊鍜岀兢鍚屾(g貌u)瀹氱悊锛屾帉鎻＄兢
鍚屾厠(t脿i)鍩烘湰瀹氱悊鍜屽悓妲�(g貌u)瀹氱悊璀夋槑鐨勬噳(y墨ng)鐢�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�锛岀啛鎮夊柈浣嶅厓銆侀€嗗厓鍜岄浂鍥犲瓙鐨勬€ц唱(zh矛)骞惰兘鐔熺反閬�(y霉n)鐢�,
鎺屾彙娑堝幓寰嬭垏闆跺洜瀛愮殑闂�(gu膩n)绯�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�锛岀悊瑙ｇ挵(hu谩n)鐗瑰緛鐨勫畾缇╋紝鎺屾彙鍒ゅ垾鐠�(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╋紝鏈�(hu矛)鍒ゅ垾涓€鍊�(g猫)鐞嗘兂瀛愮挵(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(y霉n)绠楋紝浜嗚В鍦ㄥ悓鎱�(t脿i)鏄犲皠涓嬬殑鍏╁€�(g猫)鐠�(hu谩n)鐩�
浜掍箣闁撶殑闂�(gu膩n)绯汇€佹€ц唱(zh矛)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(gu膩n)绯汇€�
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�銆�
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�(gu膩n)鐨勫畾鐞�銆�
5. 鍩熺殑鎿�(ku貌)寮�
5.1 浜嗚В鎿�(ku貌)鍩熺殑瀹氱京鍜岀浉闂�(gu膩n)瀹氱悊锛岀悊瑙ｅ柈鎿�(ku貌)鍩�銆佺礌鍩熺殑瀹氱京銆�
5.2 浜嗚В瓒呰秺鍏�锛屽柈瓒呰秺鎿�(ku貌)鍩�锛涗唬鏁�(sh霉)鍏�锛屽柈浠ｆ暩(sh霉)鎿�(ku貌)鍩熺殑瀹氱京銆�
鍏嶈铂(z茅)鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘�锛岃珛鑱�(li谩n)绯绘垜鍊戠珛鍗冲埅闄�锛屽彟锛氭湰鏂囧儏浠ｈ〃浣滆€呭€�(g猫)浜鸿榛�(di菐n)锛岃垏鏈恫(w菐ng)绔欑劇闂�(gu膩n)銆傚叾鍘熷壍(chu脿ng)鎬т互鍙婃枃涓櫝杩版枃瀛楀拰鍏�(n猫i)瀹规湭缍�(j墨ng)鏈珯璀夊(sh铆)锛屽皪鏈枃浠ュ強鍏朵腑鍏ㄩ儴鎴栬€呴儴鍒嗗収(n猫i)瀹广€佹枃瀛楃殑鐪熷(sh铆)鎬�銆佸畬鏁存€с€佸強鏅�(sh铆)鎬ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛璁€鑰呭儏浣滃弮鑰�锛屽苟璜嬭嚜琛屾牳瀵�(sh铆)鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
