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2銆佹帉鎻″拰鐞嗚В妤甸檺鐞嗚珫鍜屾柟娉�锛岀敱姝よ€岀敘(ch菐n)鐢熺殑閫ｇ簩(x霉)鎬с€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
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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€�
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2.
2
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浠ュ強涓婅堪姒傚康鍜屽畾鐞嗗湪
n
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3. 鍑芥暩(sh霉)銆佹槧灏�銆佽畩鎻涙蹇靛強鍏跺咕浣曟剰缇╋紝闅卞嚱鏁�(sh霉)姒傚康锛屽弽鍑芥暩(sh霉)鑸囬€嗚畩鎻�锛�
鍒濈瓑鍑芥暩(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)鍒楁サ闄愩€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�銆佹湁鐣屾€с€佷繚铏熸€�銆佷笉绛�
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€с€佸柈瑾�(di脿o)鏈夌晫鍘熺悊銆佹暩(sh霉)鍒楁敹鏂傝垏鍏�
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1
lim (1 )
n
n
e
n? ?
? ?
鍙婂叾鎳�(y墨ng)鐢�銆�
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鎬�銆佷笉绛夊紡鎬ц唱(zh矛)銆佽揩鏂傛€э級锛屽叐鍊嬮噸瑕佹サ闄�
sin 1
0
lim 1, lim (1 )
xx
x x
x x
e
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鍙婂叾鎳�(y墨ng)鐢�锛�
瑷堢畻涓€鍏冨嚱鏁�(sh霉)妤甸檺鐨勫悇绋柟娉曪紝鐒＄灏忛噺鑸囩劇绐ぇ閲�銆侀殠鐨勬瘮杓�锛岃铏� O 鑸� o 鐨�
鎰忕京锛屽鍏冨嚱鏁�(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�
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€�銆佷繚
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€с€佹渶澶у€兼渶灏忓€煎畾鐞�銆佷粙鍊煎畾鐞嗐€�
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)绯汇€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�銆佹礇蹇呴仈锛圠'Hospital锛�
娉曞墖銆�
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�锛屼簩鍏冨嚱鏁�(sh霉)涓€煎畾鐞嗚垏 Taylor 鍏紡銆�
2. 闅卞嚱鏁�(sh霉)锛堢祫锛夋眰灏�(d菐o)鏂规硶銆佸弽鍑芥暩(sh霉)绲勮垏鍧愭璁婃彌銆�
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)娉曘€�
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�銆佷笉瀹氱⿳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�銆佸彲绌嶅嚱鏁�(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�
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�
璨犳檪
( )
a
f x dx
??
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Dirichlet 鍒ゅ垾娉�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�銆佹サ鍧愭璁婃彌銆�
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⿳锛�銆�
4.鍚弮閲忔甯哥⿳鍒嗗強鍏堕€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€�.
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�
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э紝绱氭暩(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讹紝姣旇純鍘熷墖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 鍒ゅ垾娉曘€�
2.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€э紝鍐礆鏁�(sh霉)
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�銆佸嚱鏁�(sh霉)鐨勫啰
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