|
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骞达紱鍧囨彁渚涙敹璨讳笅杓夈€� 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
1
2019 骞村叏鍦嬬ⅸ澹爺绌剁敓鍏ュ(xu茅)鑰冭│
婀栧寳甯寖澶у(xu茅)鑷懡椤岃€冭│绉戠洰鑰冭│澶х侗
锛堢鐩悕绋憋細鏁�(sh霉)瀛�(xu茅)鍒嗘瀽 涓€ 绉戠洰浠ｇ⒓:601锛�
涓€銆佽€冩煡鐩
鏁�(sh霉)瀛�(xu茅)鍒嗘瀽绉戠洰鑰冭│鍏�(n猫i)瀹瑰寘鎷サ闄愯垏閫ｇ簩(x霉)銆佸井鍒嗗(xu茅)銆佺⿳鍒嗗(xu茅)鍜岀礆鏁�(sh霉)瑕佹眰鑰冪敓绯�
绲�(t菕ng)鎺屾彙鐩搁棞(gu膩n)鍏�(n猫i)瀹圭殑鍩烘湰鐭ヨ瓨銆佸熀绀�(ch菙)鐞嗚珫銆佸熀鏈柟娉曘€佸熀鏈▓绠�锛屽苟鑳介亱鐢ㄧ浉闂�(gu膩n)鐞�
璜栧拰鏂规硶鍒嗘瀽銆佽В姹哄闅涘晱椤�銆�
浜屻€佽€冭│褰㈠紡鑸囪│鍗风祼(ji茅)妲�(g貌u)
锛堜竴锛夎│鍗锋垚绺惧強鑰冭│鏅傞枔
鏈│鍗锋豢鍒嗙偤 150 鍒�锛岃€冭│鏅傞枔鐐� 180 鍒嗛悩銆�
锛堜簩锛夌瓟椤屾柟寮�
绛旈鏂瑰紡鐐洪枆鍗枫€佺瓎瑭�銆�
锛堜笁锛夎│鍗峰収(n猫i)瀹圭祼(ji茅)妲�(g貌u)
鍚勯儴鍒嗗収(n猫i)瀹规墍鍗犲垎鍊肩偤锛�
妤甸檺鑸囬€ｇ簩(x霉) 绱� 40 鍒�
涓€鍏冨井绌嶅垎 绱� 40 鍒�
澶氬厓寰⿳鍒� 绱� 40 鍒�
鐒＄绱氭暩(sh霉) 绱� 30 鍒�
锛堝洓锛夎│鍗烽鍨嬬祼(ji茅)妲�(g貌u)
瑷堢畻椤岋細4 灏忛锛屾瘡灏忛 15 鍒嗭紝鍏� 60 鍒�
璀夋槑椤岋細6 灏忛锛屾瘡灏忛 15 鍒�锛屽叡 90 鍒�
(浜�)涓昏鍙冭€冩浉鐩�
鑿澅甯寖澶у(xu茅)鏁�(sh霉)瀛�(xu茅)绯讳富绶細銆婃暩(sh霉)瀛�(xu茅)鍒嗘瀽銆嬶紙绗笁鐗堬級锛岄珮绛夋暀鑲插嚭鐗堢ぞ 2001
骞淬€�
2
涓夈€佽€冩煡鑼冨湇
锛堜竴锛夎€冩煡鐩
1銆佺郴绲�(t菕ng)鎺屾彙鏁�(sh霉)瀛�(xu茅)鍒嗘瀽鍘熺悊鐨勫熀鏈蹇�銆佸熀绀�(ch菙)鐭ヨ瓨銆佸熀鏈悊璜栧拰鍩烘湰瑷堢畻銆�
2銆佹帉鎻″拰鐞嗚В妤甸檺鐞嗚珫鍜屾柟娉曪紝鐢辨鑰岀敘(ch菐n)鐢熺殑閫ｇ簩(x霉)鎬�銆佸井鍒嗗(xu茅)銆佺⿳鍒嗗(xu茅)鍜�
鐒＄绱氭暩(sh霉)銆�
3銆佽兘闈堟椿閬嬬敤鍩烘湰瀹氱悊鍜屽熀鏈柟娉曡瓑鏄庡晱椤岋紝鑳介潏娲婚亱鐢ㄥ熀鏈叕寮忚▓绠楀晱
椤�锛屼互鍙婄稖鍚堥亱鐢�銆�
锛堜簩锛夎€冭│鍏�(n猫i)瀹�
涓€锛夐泦鍚堣垏鍑芥暩(sh霉)
1. 瀵︽暩(sh霉)闆� ? 銆佹湁鐞嗘暩(sh霉)鑸囩劇鐞嗘暩(sh霉)鐨勭瀵嗘€�锛屽鏁�(sh霉)闆嗙殑鐣岃垏纰虹晫銆佺⒑鐣屽瓨鍦ㄦ€�
瀹氱悊銆侀枆鍗€(q奴)闁撳瀹氱悊銆佽仛榛炲畾鐞嗐€佹湁闄愯钃嬪畾鐞�銆�
2.
2
? 涓婄殑璺濋洟銆侀劙鍩�銆佽仛榛�銆佺晫榛�銆侀倞鐣�銆侀枊闆�銆侀枆闆�銆佹湁鐣岋紙鐒＄晫锛夐泦銆�
2
? 涓婄殑闁夌煩褰㈠瀹氱悊銆佽仛榛炲畾鐞�銆佹湁闄愬京(f霉)钃嬪畾鐞嗐€佸熀鏈粸鍒�锛屼互鍙婁笂杩版蹇靛拰
瀹氱悊鍦�
n
? 涓婄殑鎺ㄥ唬銆�
3. 鍑芥暩(sh霉)銆佹槧灏勩€佽畩鎻涙蹇靛強鍏跺咕浣曟剰缇�锛岄毐鍑芥暩(sh霉)姒傚康锛屽弽鍑芥暩(sh霉)鑸囬€嗚畩鎻涳紝
鍙嶅嚱鏁�(sh霉)瀛樺湪鎬у畾鐞�锛屽垵绛夊嚱鏁�(sh霉)浠ュ強鑸囦箣鐩搁棞(gu膩n)鐨勬€ц唱(zh矛)銆�
浜岋級妤甸檺鑸囬€ｇ簩(x霉)
1. 鏁�(sh霉)鍒楁サ闄�銆佹敹鏂傛暩(sh霉)鍒楃殑鍩烘湰鎬ц唱(zh矛)锛堟サ闄愬敮涓€鎬с€佹湁鐣屾€�銆佷繚铏熸€с€佷笉绛�
寮忔€ц唱(zh矛)锛�銆�
2. 鏁�(sh霉)鍒楁敹鏂傜殑姊濅欢锛圕auchy 婧栧墖銆佽揩鏂傛€�銆佸柈瑾�(di脿o)鏈夌晫鍘熺悊銆佹暩(sh霉)鍒楁敹鏂傝垏鍏�
瀛愬垪鏀舵杺鐨勯棞(gu膩n)绯伙級锛屾サ闄�
1
lim (1 )
n
n
e
n? ?
? ?
鍙婂叾鎳�(y墨ng)鐢ㄣ€�
3.涓€鍏冨嚱鏁�(sh霉)妤甸檺鐨勫畾缇�銆佸嚱鏁�(sh霉)妤甸檺鐨勫熀鏈€ц唱(zh矛)锛堝敮涓€鎬�銆佸眬閮ㄦ湁鐣屾€с€佷繚铏�
鎬�銆佷笉绛夊紡鎬ц唱(zh矛)銆佽揩鏂傛€э級锛屾绲�(ji茅)鍘熷墖鍜� Cauchy 鏀舵杺婧栧墖锛屽叐鍊嬮噸瑕佹サ闄�
s i n 1
0
lim 1, lim (1 )
xx
x x
x x
e
? ? ?
? ? ?
鍙婂叾鎳�(y墨ng)鐢�锛岃▓绠椾竴鍏冨嚱鏁�(sh霉)妤甸檺鐨勫悇绋柟娉�锛岀劇绐皬閲忚垏
鐒＄澶ч噺銆侀殠鐨勬瘮杓�锛岃铏� O 鑸� o 鐨勬剰缇�锛屽鍏冨嚱鏁�(sh霉)閲嶆サ闄愯垏绱妤甸檺姒傚康銆佸熀
鏈€ц唱(zh矛)锛屼簩鍏冨嚱鏁�(sh霉)鐨勪簩閲嶆サ闄愯垏绱妤甸檺鐨勯棞(gu膩n)绯�銆�
3
4. 鍑芥暩(sh霉)閫ｇ簩(x霉)鑸囬枔鏂�銆佷竴鑷撮€ｇ簩(x霉)鎬�銆侀€ｇ簩(x霉)鍑芥暩(sh霉)鐨勫眬閮ㄦ€ц唱(zh矛)锛堝眬閮ㄦ湁鐣屾€с€佷繚
铏熸€э級锛屾湁鐣岄枆闆嗕笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)锛堟湁鐣屾€�銆佹渶澶у€兼渶灏忓€煎畾鐞嗐€佷粙鍊煎畾鐞�銆�
涓€鑷撮€ｇ簩(x霉)鎬э級銆�
涓夛級涓€鍏冨嚱鏁�(sh霉)寰垎瀛�(xu茅)
1.灏�(d菐o)鏁�(sh霉)鍙婂叾骞句綍鎰忕京銆佸彲灏�(d菐o)鑸囬€ｇ簩(x霉)鐨勯棞(gu膩n)绯�銆佸皫(d菐o)鏁�(sh霉)鐨勫悇绋▓绠楁柟娉�锛屽井鍒嗗強鍏�
骞句綍鎰忕京銆佸彲寰垏鍙皫(d菐o)鐨勯棞(gu膩n)绯�銆佷竴闅庡井鍒嗗舰寮忎笉璁婃€�銆�
2.寰垎瀛�(xu茅)鍩烘湰瀹氱悊锛欶ermat 瀹氱悊锛孯olle 瀹氱悊锛孡agrange 瀹氱悊锛孋auchy 瀹�
鐞嗭紝Taylor 鍏紡(Peano 浣欓爡鑸� Lagrange 浣欓爡)銆�
3.涓€鍏冨井鍒嗗(xu茅)鐨勬噳(y墨ng)鐢細鍑芥暩(sh霉)鍠(di脿o)鎬х殑鍒ゅ垾銆佹サ鍊�銆佹渶澶у€煎拰鏈€灏忓€笺€佸嚫鍑芥暩(sh霉)
鍙婂叾鎳�(y墨ng)鐢�銆佹洸绶氱殑鍑瑰嚫鎬с€佹嫄榛�銆佹几杩戠窔銆佸嚱鏁�(sh霉)鍦栬薄鐨勮◣璜栥€佹礇蹇呴仈锛圠'Hospital锛�
娉曞墖銆佽繎浼艰▓绠�銆�
鍥涳級澶氬厓鍑芥暩(sh霉)寰垎瀛�(xu茅)
1. 鍋忓皫(d菐o)鏁�(sh霉)銆佸叏寰垎鍙婂叾骞句綍鎰忕京锛屽彲寰垏鍋忓皫(d菐o)瀛樺湪銆侀€ｇ簩(x霉)涔嬮枔鐨勯棞(gu膩n)绯�锛屽京(f霉)
鍚堝嚱鏁�(sh霉)鐨勫亸灏�(d菐o)鏁�(sh霉)鑸囧叏寰垎锛屼竴闅庡井鍒嗗舰寮忎笉璁婃€�锛屾柟鍚�?q奴)顫�?sh霉)鑸囨搴︼紝楂橀殠鍋忓皫(d菐o)鏁�(sh霉)锛�
娣峰悎鍋忓皫(d菐o)鏁�(sh霉)鑸囬爢搴忕劇闂�(gu膩n)鎬э紝浜屽厓鍑芥暩(sh霉)涓€煎畾鐞嗚垏 Taylor 鍏紡銆�
2.闅卞嚱鏁�(sh霉)瀛樺湪瀹氱悊銆侀毐鍑芥暩(sh霉)绲勫瓨鍦ㄥ畾鐞�銆侀毐鍑芥暩(sh霉)锛堢祫锛夋眰灏�(d菐o)鏂规硶銆佸弽鍑芥暩(sh霉)绲�
鑸囧潗妯欒畩鎻涖€�
3.骞句綍鎳�(y墨ng)鐢紙骞抽潰鏇茬窔鐨勫垏绶氳垏娉曠窔銆佺┖闁撴洸绶氱殑鍒囩窔鑸囨硶骞抽潰銆佹洸闈㈢殑鍒�
骞抽潰鑸囨硶绶氾級銆�
4.妤靛€煎晱椤岋紙蹇呰姊濅欢鑸囧厖鍒嗘浠讹級锛屾浠舵サ鍊艰垏 Lagrange 涔樻暩(sh霉)娉�銆�
浜旓級涓€鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)
1. 鍘熷嚱鏁�(sh霉)鑸囦笉瀹氱⿳鍒嗐€佷笉瀹氱⿳鍒嗙殑鍩烘湰瑷堢畻鏂规硶锛堢洿鎺ョ⿳鍒嗘硶銆佹彌鍏冩硶銆�
鍒嗛儴绌嶅垎娉曪級銆佹湁鐞嗗嚱鏁�(sh霉)绌嶅垎锛� (cos , sin )R x x dx?
鍨�锛�
2
( , )R x ax bx c dx? ? ? 鍨�銆�
2. 瀹氱⿳鍒嗗強鍏跺咕浣曟剰缇�銆佸彲绌嶆浠讹紙蹇呰姊濅欢銆佸厖瑕佹浠讹細 i i
x? ?? ?? 锛�銆�
鍙⿳鍑芥暩(sh霉)椤�銆�
3. 瀹氱⿳鍒嗙殑鎬ц唱(zh矛)锛堥棞(gu膩n)浜庡崁(q奴)闁撳彲鍔犳€�銆佷笉绛夊紡鎬ц唱(zh矛)銆佺禃灏嶅彲绌嶆€�銆佸畾绌嶅垎绗�
涓€涓€煎畾鐞嗭級銆佽畩涓婇檺绌嶅垎鍑芥暩(sh霉)銆佸井绌嶅垎鍩烘湰瀹氱悊銆丯-L 鍏紡鍙婂畾绌嶅垎瑷堢畻銆佸畾
绌嶅垎绗簩涓€煎畾鐞�銆�
4.鐒￠檺鍗€(q奴)闁撲笂鐨勫唬缇╃⿳鍒�銆丆anchy 鏀舵杺婧栧墖銆佺禃灏嶆敹鏂傝垏姊濅欢鏀舵杺銆� ( )f x
闈�
4
璨犳檪
( )
a
f x dx
??
? 鐨勬敹鏂傛€у垽鍒ユ硶锛堟瘮杓冨師鍓�銆佹煰瑗垮垽鍒ユ硶锛夈€丄bel 鍒ゅ垾娉�銆�
Dirichlet 鍒ゅ垾娉�銆佺劇鐣屽嚱鏁�(sh霉)寤ｇ京绌嶅垎姒傚康鍙婂叾鏀舵杺鎬у垽鍒ユ硶銆�
5. 寰厓娉�銆佸咕浣曟噳(y墨ng)鐢紙骞抽潰鍦栧舰闈㈢⿳銆佸凡鐭ユ埅闈㈤潰绌嶅嚱鏁�(sh霉)鐨勯珨绌�銆佹洸绶氬姬
闀疯垏寮у井鍒�銆佹棆杞�(zhu菐n)楂旈珨绌嶏級锛屽強鍏跺畠鎳�(y墨ng)鐢�銆�
鍏級澶氬厓鍑芥暩(sh霉)绌嶅垎瀛�(xu茅)
1.浜岄噸绌嶅垎鍙婂叾骞句綍鎰忕京銆佷簩閲嶇⿳鍒嗙殑瑷堢畻锛堝寲鐐虹疮娆＄⿳鍒嗐€佹サ鍧愭璁婃彌銆�
涓€鑸潗妯欒畩鎻涳級銆�
2.涓夐噸绌嶅垎銆佷笁閲嶇⿳鍒嗚▓绠楋紙鍖栫偤绱绌嶅垎銆佹煴鍧愭銆佺悆鍧愭璁婃彌锛夈€�
3.閲嶇⿳鍒嗙殑鎳�(y墨ng)鐢紙楂旂⿳銆佹洸闈㈤潰绌�銆侀噸蹇�銆佽綁(zhu菐n)鍕曟叄閲忕瓑锛�銆�
4.鍚弮閲忔甯哥⿳鍒嗗強鍏堕€ｇ簩(x霉)鎬�銆佸彲寰€с€佸彲绌嶆€�锛岄亱绠楅爢搴忕殑鍙氦鎻涙€�.鍚�
鍙冮噺寤ｇ京绌嶅垎鐨勪竴鑷存敹鏂傛€у強鍏跺垽鍒ユ硶锛屽惈鍙冮噺寤ｇ京绌嶅垎鐨勯€ｇ簩(x霉)鎬с€佸彲寰€�銆佸彲
绌嶆€�锛岄亱绠楅爢搴忕殑鍙氦鎻涙€�銆�
5.绗竴鍨嬫洸绶氱⿳鍒�銆佹洸闈㈢⿳鍒嗙殑姒傚康銆佸熀鏈€ц唱(zh矛)銆佽▓绠�銆�
6.绗簩鍨嬫洸绶氱⿳鍒嗘蹇�銆佹€ц唱(zh矛)銆佽▓绠�锛汫reen 鍏紡锛屽钩闈㈡洸绶氱⿳鍒嗚垏璺緫鐒�
闂�(gu膩n)鐨勬浠�銆�
7.鏇查潰鐨勫伌(c猫)銆佺浜屽瀷鏇查潰绌嶅垎鐨勬蹇�銆佹€ц唱(zh矛)銆佽▓绠�锛屽ェ楂樺叕寮�銆丼toke 鍏紡锛�
鍏╅绶氱⿳鍒�銆佸叐椤為潰绌嶅垎涔嬮枔鐨勯棞(gu膩n)绯�銆�
涓冿級鐒＄绱氭暩(sh霉)
1. 鏁�(sh霉)闋呯礆鏁�(sh霉)
绱氭暩(sh霉)鍙婂叾鏂傛暎鎬�锛岀礆鏁�(sh霉)鐨勫拰锛孋auchy 婧栧墖锛屾敹鏂傜殑蹇呰姊濅欢锛屾敹鏂傜礆鏁�(sh霉)鍩�
鏈€ц唱(zh矛)锛涙闋呯礆鏁�(sh霉)鏀舵杺鐨勫厖鍒嗗繀瑕佹浠�锛屾瘮杓冨師鍓�銆佹瘮寮忓垽鍒ユ硶銆佹牴寮忓垽鍒ユ硶浠�
鍙婂畠鍊戠殑妤甸檺褰㈠紡锛涗氦閷礆鏁�(sh霉)鐨� Leibniz 鍒ゅ垾娉�锛涗竴鑸爡绱氭暩(sh霉)鐨勭禃灏嶆敹鏂傘€佹浠�
鏀舵杺鎬�銆丄bel 鍒ゅ垾娉�銆丏irichlet 鍒ゅ垾娉�銆�
2. 鍑芥暩(sh霉)闋呯礆鏁�(sh霉)
鍑芥暩(sh霉)鍒楄垏鍑芥暩(sh霉)闋呯礆鏁�(sh霉)鐨勪竴鑷存敹鏂傛€�銆丆auchy 婧栧墖銆佷竴鑷存敹鏂傛€у垽鍒ユ硶锛圡-
鍒ゅ垾娉�銆丄bel 鍒ゅ垾娉�銆丏irichlet 鍒ゅ垾娉曪級銆佷竴鑷存敹鏂傚嚱鏁�(sh霉)鍒�銆佸嚱鏁�(sh霉)闋呯礆鏁�(sh霉)鐨勬€�
璩�(zh矛)鍙婂叾鎳�(y墨ng)鐢�銆�
3.鍐礆鏁�(sh霉)
鍐礆鏁�(sh霉)姒傚康銆丄bel 瀹氱悊銆佹敹鏂傚崐寰戣垏鍗€(q奴)闁�锛屽啰绱氭暩(sh霉)鐨勪竴鑷存敹鏂傛€�锛屽啰绱氭暩(sh霉)
5
鐨勯€愰爡鍙⿳鎬�銆佸彲寰€у強鍏舵噳(y墨ng)鐢�锛屽啰绱氭暩(sh霉)鍚勯爡绯绘暩(sh霉)鑸囧叾鍜屽嚱鏁�(sh霉)鐨勯棞(gu膩n)绯汇€佸嚱鏁�(sh霉)鐨勫啰
绱氭暩(sh霉)灞曢枊銆乀aylor 绱氭暩(sh霉)銆丮aclaurin 绱氭暩(sh霉)銆�
4.Fourier 绱氭暩(sh霉)
涓夎绱氭暩(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)绯荤殑姝ｄ氦鎬с€�2? 鍙� 2l 鍛ㄦ湡鍑芥暩(sh霉)鐨� Fourier 绱氭暩(sh霉)灞曢枊銆�
Beseel 涓嶇瓑寮�銆丷iemanm-Lebesgue 瀹氱悊銆佹寜娈靛厜婊戝嚱鏁�(sh霉)鐨� Fourier 绱氭暩(sh霉)鐨勬敹鏂�
鎬у畾鐞嗐€�
鍏嶈铂鑱叉槑锛氭湰鏂囩郴杞�(zhu菐n)杓夎嚜缍�(w菐ng)绲�(lu貌)锛屽鏈変镜鐘紝璜嬭伅(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€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�銆佸畬鏁存€�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€鑰呭儏浣滃弮鑰冿紝骞惰珛鑷鏍稿鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�
|
鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
