|
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�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
鍗椾含杈�(n贸ng)妤�(y猫)澶у(xu茅) 2018 骞寸ⅸ澹爺绌剁敓鍏ュ(xu茅)鑰冭│澶х侗
鈥滄暩(sh霉)瀛�(xu茅)鍒嗘瀽 鈥濊绋嬪弮鑰冩浉濡備笅锛�
鍙冭€冩浉鐩�
1. 鑿澅甯寖澶у(xu茅)鏁�(sh霉)瀛�(xu茅)绯伙紟銆婃暩(sh霉)瀛�(xu茅)鍒嗘瀽銆嬶紙涓婂唺銆佷笅鍐婏級锛堢涓�
鐗堬級锛岄珮绛夋暀鑲插嚭鐗堢ぞ锛� 2. W. Rudin. Principles of
Mathematical Analysis, McGraw Hill Inc., 1976.
鑰冭│澶х侗
鏁�(sh霉)瀛�(xu茅)鍒嗘瀽鑰冭│澶х侗锛�2009 鐗堬級
涓€銆佽€冭│鍏�(n猫i)瀹硅垏瑕佹眰
(涓€) 妤甸檺璜�
锛�1锛夌悊瑙ｅ拰鎺屾彙鏁�(sh霉)鍒楁サ闄愶紝鍑芥暩(sh霉)妤甸檺鐨勬蹇�銆傜啛绶存帉鎻″苟鑳介亱
鐢ㄦサ闄� 蔚 -N锛屛� -X锛屛� -未 瑾炶█銆�
锛�2锛夋帉鎻℃敹鏂傛暩(sh霉)鍒楃殑鎬ц唱(zh矛)鍙婇亱绠�銆傛帉鎻℃暩(sh霉)鍒楁サ闄愮殑瀛樺湪姊濅欢(鍠�
瑾�(di脿o)鏈夌晫婧栧墖锛岃揩鏂傛€ф硶鍓�锛屾煰瑗挎簴鍓�)锛涙帉鎻″嚱鏁�(sh霉)妤甸檺鐨勬€ц唱(zh矛)鍜�
姝哥祼(ji茅)鍘熷墖锛涚啛绶存帉鎻″叐鍊嬮噸瑕佹サ闄愪締铏曠悊妤甸檺鍟忛銆�
锛�3锛夌悊瑙ｇ劇绐皬閲忓拰鐒＄澶ч噺鐨勫畾缇┿€佹€ц唱(zh矛)鍜岄棞(gu膩n)绯�锛屾帉鎻＄劇绐�
灏忛噺闅庣殑姣旇純鍜屾柟娉�銆�
锛�4锛夌悊瑙ｈ垏鎺屾彙涓€鍏冨嚱鏁�(sh霉)閫ｇ簩(x霉)鎬х殑瀹氱京(榛烇紝鍗€(q奴)闁�)锛岄枔鏂烽粸鍙�
鍏跺垎椤�锛岄€ｇ簩(x霉)鍑芥暩(sh霉)鐨勫眬閮ㄦ€ц唱(zh矛)锛涚悊瑙ｅ柈鍋�(c猫)閫ｇ簩(x霉)鐨勬蹇�銆�
锛�5锛夋帉鎻″拰鎳�(y墨ng)鐢ㄩ枆鍗€(q奴)闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛堟渶澶ф渶灏忓€兼€�銆佹湁
鐣屾€�銆佷粙鍊兼€�銆佷竴鑷撮€ｇ簩(x霉)鎬э級锛涙帉鎻″垵绛夊嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�锛岀悊瑙�
寰�(f霉)鍚堝嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�锛屽弽鍑芥暩(sh霉)鐨勯€ｇ簩(x霉)鎬�銆�
锛�6锛夋帉鎻″鏁�(sh霉)閫ｇ簩(x霉)鎬у畾鐞嗭細闁夊崁(q奴)闁撳瀹氱悊銆佸柈瑾�(di脿o)鏈夌晫瀹氱悊銆佹煰
瑗挎敹鏂傛簴鍓囥€佺⒑鐣屽瓨鍦ㄥ畾鐞�銆佽仛榛炲畾鐞�銆佹湁闄愯钃嬪畾鐞�銆�
锛�7锛夌悊瑙ｅ钩闈㈤粸闆嗙殑鍩烘湰姒傚康锛屼簩鍏冨嚱鏁�(sh霉)鐨勬サ闄�锛岀疮娆℃サ闄�锛�
閫ｇ簩(x霉)鎬ф蹇碉紱浜嗚В闁夊崁(q奴)闁撶殑濂楀畾鐞�锛屾湁闄愯钃嬪畾鐞嗭紝澶氬厓閫ｇ簩(x霉)
鍑芥暩(sh霉)鐨勬€ц唱(zh矛)銆�
(浜�) 寰垎瀛�(xu茅)
锛�1锛夌悊瑙ｅ拰鎺屾彙灏�(d菐o)鏁�(sh霉)鑸囧井鍒嗘蹇靛拰骞句綍鎰忕京锛涜兘鐔熺反鍦伴亱鐢ㄥ皫(d菐o)
鏁�(sh霉)鐨勯亱绠楁€ц唱(zh矛)鍜屾眰灏�(d菐o)娉曞墖姹傚嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)(鐗瑰垾鏄京(f霉)鍚堝嚱鏁�(sh霉))銆�
锛�2锛夌悊瑙ｅ柈鍋�(c猫)灏�(d菐o)鏁�(sh霉)銆佸彲灏�(d菐o)鎬ц垏閫ｇ簩(x霉)鎬х殑闂�(gu膩n)绯�锛岄珮闅庡皫(d菐o)鏁�(sh霉)鐨勬眰娉曪紱
鎺屾彙灏�(d菐o)鏁�(sh霉)鐨勫咕浣曟噳(y墨ng)鐢�锛屽井鍒嗗湪杩戜技瑷堢畻涓殑鎳�(y墨ng)鐢ㄣ€�
锛�3锛夋帉鎻′腑鍊煎畾鐞嗙殑鍏�(n猫i)瀹�銆佽瓑鏄庡強鍏舵噳(y墨ng)鐢紱鎺屾彙娉板嫆鍏紡鍙婂湪
杩戜技瑷堢畻涓殑鎳�(y墨ng)鐢�锛岃兘澶犳妸鏌愪簺鍑芥暩(sh霉)鎸夋嘲鍕掑叕寮忓睍闁�銆�
锛�4锛夎兘鐔熺反鍦伴亱鐢ㄧ緟蹇呴仈娉曞墖姹備笉瀹氬紡鐨勬サ闄�锛涙帉鎻″嚱鏁�(sh霉)鐨勬煇
浜涘熀鏈壒鎬�(鍠(di脿o)鎬�銆佹サ鍊艰垏鏈€鍊笺€佸嚬鍑告€�銆佹嫄榛炲強婕歌繎绶�)锛�
鑳借純姝ｇ⒑鍦颁綔鍑烘煇浜涘嚱鏁�(sh霉)鐨勫湒璞�銆�
锛�5锛夋帉鎻″亸灏�(d菐o)鏁�(sh霉)銆佸叏寰垎銆佹柟鍚�?q奴)顫�?sh霉)銆侀珮闅庡亸灏�(d菐o)鏁�(sh霉)妤靛€肩瓑姒傚康锛�
鐞嗚В鍏ㄥ井鍒嗐€佸亸灏�(d菐o)鏁�(sh霉)銆侀€ｇ簩(x霉)涔嬮枔鐨勯棞(gu膩n)绯伙紱鎺屾彙澶氬厓鍑芥暩(sh霉)娉板嫆鍏�
寮�锛涙渻姹傚鍏冨嚱鏁�(sh霉)鐨勬サ鍊�銆�
锛�6锛夋帉鎻￠毐鍑芥暩(sh霉)鐨勬蹇靛強闅卞嚱鏁�(sh霉)鐨勫瓨鍦ㄥ畾鐞�锛涙渻姹傞毐鍑芥暩(sh霉)鐨勫皫(d菐o)
鏁�(sh霉)锛涙渻姹傛洸绶氱殑鍒囩窔鏂圭▼锛屾硶骞抽潰鏂圭▼锛屾洸闈㈢殑鍒囧钩闈㈡柟绋嬪拰
娉曠窔鏂圭▼锛涙帉鎻℃浠舵サ鍊兼蹇靛強姹傛硶銆�
(涓�) 绌嶅垎瀛�(xu茅)
锛�1锛夋帉鎻″師鍑芥暩(sh霉)鍜屼笉瀹氱⿳鍒嗘蹇碉紱鐔熺反鎺屾彙鎻涘厓绌嶅垎娉�銆佸垎閮�
绌嶅垎娉曘€佹湁鐞嗗紡绌嶅垎娉曞拰涓夎鏈夌悊寮忕⿳鍒嗘硶锛屽苟鑳藉埄鐢ㄥ畠鍊戜締
姹傚嚱鏁�(sh霉)鐨勭⿳鍒�锛涙渻瑷堢畻绨″柈鐨勭劇鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒�銆�
锛�2锛夌悊瑙ｅ畾绌嶅垎姒傚康鍙婂嚱鏁�(sh霉)鍙⿳鐨勬浠�锛涚啛鎮変竴浜涘彲绌嶅垎鍑芥暩(sh霉)
椤烇紱 鎺屾彙瀹氱⿳鍒嗚垏鍙畩涓婇檺绌嶅垎鐨勬€ц唱(zh矛)锛涜兘杓冨ソ鍦伴亱鐢ㄧ墰闋�-
钀婂竷灏艰尣鍏紡锛屾彌鍏冪⿳鍒嗘硶锛屽垎閮ㄧ⿳鍒嗘硶瑷堢畻涓€浜涘畾绌嶅垎銆�
锛�3锛夋帉鎻″畾绌嶅垎鐨勫咕浣曟噳(y墨ng)鐢�锛涙帉鎻″畾绌嶅垎鍦ㄧ墿鐞嗕笂鐨勬噳(y墨ng)鐢紱鎺�
鎻�"寰厓娉�"銆�
锛�4锛夋帉鎻″唬缇╃⿳鍒嗙殑鏀舵杺銆佺櫦(f膩)鏁ｃ€佺禃灏嶆敹鏂傝垏姊濅欢鏀舵杺绛夋蹇碉紱.
鑳界敤鏀舵杺鎬у垽鍒ユ硶鍒ゆ柗鏌愪簺鍙嶅父绌嶅垎鐨勬敹鏂傛€�銆�
锛�5锛夋帉鎻″惈鍙冭畩閲忓畾绌嶅垎鐨勬蹇佃垏鎬ц唱(zh矛)锛� 鎺屾彙鍚弮璁婇噺寤ｇ京
绌嶅垎鐨勬敹鏂傝垏涓€鑷存敹鏂傜殑姒傚康锛涙帉鎻″惈鍙冭畩閲忓唬缇╃⿳鍒嗕竴鑷存敹
鏂傜殑鍒ゅ垾娉�锛涚啛绶存噳(y墨ng)鐢ㄦ瓙鎷夊叕寮�銆�
锛�6锛夋帉鎻″叐椤炴洸绶氱⿳鍒嗙殑姒傚康鍙婅▓绠�锛涙帉鎻″叐椤炴洸绶氱⿳鍒嗙殑鎬�
璩�(zh矛)锛涙帉鎻″叐椤炴洸绶氱⿳鍒嗙殑闂�(gu膩n)绯�锛涙帉鎻℃牸鏋楀叕寮忕殑璀夋槑鏌愪簺鎳�(y墨ng)鐢�锛�
鏈冭▓绠楁洸绶氱⿳鍒�銆�
锛�7锛夋帉鎻′簩閲�銆佷笁閲嶇⿳鍒嗙殑姒傚康銆佹€ц唱(zh矛)锛涙渻瑷堢畻閲嶇⿳鍒嗭紱鏈冩眰
鍦栧舰鐨勯潰绌�锛岄珨绌嶅強鐗╅珨鐨勮唱(zh矛)閲忚垏閲嶅績銆�
锛�8锛夋帉鎻″叐椤炴洸闈㈢⿳鍒嗙殑姒傚康鍙婅▓绠�锛涙帉鎻″叐椤炴洸闈㈢⿳鍒嗙殑鎬�
璩�(zh矛)锛� 鎺屾彙鍏╅鍏╅鏇查潰绌嶅垎鐨勯棞(gu膩n)绯�锛涙渻瑷堢畻鏇查潰绌嶅垎銆�
锛�9锛夌悊瑙ｅ牬璜栦腑鐨勫熀鏈蹇碉紙姊害銆佹暎搴�銆佺挵(hu谩n)閲�銆佹棆搴�銆佷繚瀹�
鍫村拰鍕㈠嚱鏁�(sh霉)锛夛紝鎺屾彙淇濆畧鍫寸殑鍒ゅ垾姊濅欢銆�
锛堝洓锛夌礆鏁�(sh霉)璜�
锛�1锛夌悊瑙ｇ劇绐礆鏁�(sh霉)鐨勬敹鏂�锛岀櫦(f膩)鏁ｏ紝绲曞皪鏀舵杺鑸囨浠舵敹鏂傜瓑姒傚康锛�
姝ｇ⒑鏁樿堪鏀舵杺绱氭暩(sh霉)鐨勬€ц唱(zh矛)锛涙噳(y墨ng)鐢ㄦ闋呯礆鏁�(sh霉)鑸囦换鎰忛爡绱氭暩(sh霉)鐨勬杺鏁�
鎬у垽鍒ユ硶鍒ゆ柗绱氭暩(sh霉)鐨勬杺鏁ｆ€�锛涚啛鎮夊咕浣曠礆鏁�(sh霉)瑾�(di脿o)鍜岀礆鏁�(sh霉)鑸� p 绱氭暩(sh霉)銆�
锛�2锛夋帉鎻℃敹鏂傚煙銆佹サ闄愬嚱鏁�(sh霉)鑸囧拰鍑芥暩(sh霉)涓€鑷存杺绛夋蹇�锛涙帉鎻℃サ闄�
鍑芥暩(sh霉)鑸囧拰鍑芥暩(sh霉)鐨勫垎鏋愭€ц唱(zh矛)(鏈冭瓑鏄�)锛涜兘澶犳瘮杓冪啛绶村湴鍒ゆ柗涓€浜�
鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鑸囧嚱鏁�(sh霉)鍒楃殑涓€鑷存敹鏂�銆�
锛�3锛夋帉鎻″啰绱氭暩(sh霉)锛屽嚱鏁�(sh霉)鐨勫啰绱氭暩(sh霉)鍙婂嚱鏁�(sh霉)鐨勫彲灞曟垚鍐礆鏁�(sh霉)绛夋蹇�锛�
鎺屾彙鍐礆鏁�(sh霉)鐨勬€ц唱(zh矛)锛涙渻姹傚啰绱氭暩(sh霉)鐨勬敹鏂傚崐寰戣垏涓€浜涘啰绱氭暩(sh霉)鐨勬敹
鏂傚煙锛涙渻鎶婁竴浜涘嚱鏁�(sh霉)灞曢枊鎴愬啰绱氭暩(sh霉)锛屽寘鎷渻鐢ㄩ枔鎺ュ睍闁嬫硶姹傚嚱
鏁�(sh霉)鐨勬嘲鍕掑睍闁嬪紡銆�
锛�4锛夋帉鎻′笁瑙掑嚱鏁�(sh霉)绯荤殑姝ｄ氦鎬ц垏鍑芥暩(sh霉)鐨� Fourier 绱氭暩(sh霉)鐨勬蹇�锛�
鑳芥纰哄湴鏁樿堪 Fourier 绱氭暩(sh霉)鏀舵杺鎬у垽鍒ユ硶锛涜兘灏囦竴浜涘嚱鏁�(sh霉)灞曢枊
鎴� Fourier 绱氭暩(sh霉)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わ紝鍙︼細鏈枃鍍呬唬琛ㄤ綔鑰呭€嬩汉瑙€榛�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�銆佹枃瀛楃殑鐪熷鎬с€佸畬鏁存€�銆佸強鏅傛€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︾浉闂�(gu膩n)鍏�(n猫i)瀹广€�
|
鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
