姝¤繋瑷�(f菐ng)鍟�(w猫n)鑰冪爺绉樼睄鑰冪爺缍�(w菐ng)!    鐮旂┒鐢熸嫑鐢熶俊鎭恫(w菐ng)    鑰冨崥鐪熼涓嬭級    鑰冪爺鐪熼涓嬭級    鍏ㄧ珯鏂囩珷绱㈠紩
鏂囩珷鎼滅储
   
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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€э紝鏂瑰悜?q奴)顫�?sh霉)鑸囨搴�锛岄珮闅庡亸灏�(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(w煤)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)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�(bi膩o)璁婃彌銆�
3.骞句綍鎳�(y墨ng)鐢紙骞抽潰鏇茬窔(xi脿n)鐨勫垏绶�(xi脿n)鑸囨硶绶�(xi脿n)銆佺┖闁撴洸绶�(xi脿n)鐨勫垏绶�(xi脿n)鑸囨硶骞抽潰銆佹洸闈㈢殑鍒�
骞抽潰鑸囨硶绶�(xi脿n)锛�銆�
4.妤靛€煎晱(w猫n)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�(j矛)绠楁柟娉曪紙鐩存帴绌嶅垎娉�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? ? ? 鍨嬨€�
2. 瀹氱⿳鍒嗗強鍏跺咕浣曟剰缇┿€佸彲绌嶆浠讹紙蹇呰姊濅欢銆佸厖瑕佹浠讹細 i i
x? ?? ?? 锛夈€�
鍙⿳鍑芥暩(sh霉)椤�(l猫i)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€с€佷笉绛夊紡鎬ц唱(zh矛)銆佺禃灏�(du矛)鍙⿳鎬�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�(j矛)绠�銆佸畾
绌嶅垎绗簩涓€煎畾鐞�銆�
4.鐒�(w煤)闄愬崁(q奴)闁撲笂鐨勫唬缇╃⿳鍒�銆丆anchy 鏀舵杺婧�(zh菙n)鍓�銆佺禃灏�(du矛)鏀舵杺鑸囨浠舵敹鏂�銆� ( )f x
闈�
4
璨�(f霉)鏅�(sh铆)
( )
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 鍒ゅ垾娉曘€佺劇(w煤)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厓娉曘€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�(xi脿n)寮�
闀�(zh菐ng)鑸囧姬寰垎銆佹棆杞�(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�(j矛)绠楋紙鍖栫偤绱绌嶅垎銆佹サ鍧愭(bi膩o)璁婃彌銆�
涓€鑸潗妯�(bi膩o)璁婃彌锛�銆�
2.涓夐噸绌嶅垎銆佷笁閲嶇⿳鍒嗚▓(j矛)绠楋紙鍖栫偤绱绌嶅垎銆佹煴鍧愭(bi膩o)銆佺悆鍧愭(bi膩o)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�(d貌ng)鎱i噺绛夛級銆�
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(y霉n)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(y霉n)绠楅爢搴忕殑鍙氦鎻涙€с€�
5.绗竴鍨嬫洸绶�(xi脿n)绌嶅垎銆佹洸闈㈢⿳鍒嗙殑姒傚康銆佸熀鏈€ц唱(zh矛)銆佽▓(j矛)绠椼€�
6.绗簩鍨嬫洸绶�(xi脿n)绌嶅垎姒傚康銆佹€ц唱(zh矛)銆佽▓(j矛)绠�锛汫reen 鍏紡锛屽钩闈㈡洸绶�(xi脿n)绌嶅垎鑸囪矾寰戠劇(w煤)
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▓(j矛)绠�锛屽ェ楂樺叕寮�銆丼toke 鍏紡锛�
鍏╅(l猫i)绶�(xi脿n)绌嶅垎銆佸叐椤�(l猫i)闈㈢⿳鍒嗕箣闁撶殑闂�(gu膩n)绯汇€�
涓冿級鐒�(w煤)绐礆(j铆)鏁�(sh霉)
1. 鏁�(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)
绱�(j铆)鏁�(sh霉)鍙婂叾鏂傛暎鎬�锛岀礆(j铆)鏁�(sh霉)鐨勫拰锛孋auchy 婧�(zh菙n)鍓�锛屾敹鏂傜殑蹇呰姊濅欢锛屾敹鏂傜礆(j铆)鏁�(sh霉)鍩�
鏈€ц唱(zh矛)锛涙闋�(xi脿ng)绱�(j铆)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�(cu貌)绱�(j铆)鏁�(sh霉)鐨� Leibniz 鍒ゅ垾娉�锛涗竴鑸爡(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勭禃灏�(du矛)鏀舵杺銆佹浠�
鏀舵杺鎬�銆丄bel 鍒ゅ垾娉曘€丏irichlet 鍒ゅ垾娉�銆�
2. 鍑芥暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)
鍑芥暩(sh霉)鍒楄垏鍑芥暩(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勪竴鑷存敹鏂傛€�銆丆auchy 婧�(zh菙n)鍓囥€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)鍒椼€佸嚱鏁�(sh霉)闋�(xi脿ng)绱�(j铆)鏁�(sh霉)鐨勬€�
璩�(zh矛)鍙婂叾鎳�(y墨ng)鐢�銆�
3.鍐礆(j铆)鏁�(sh霉)
鍐礆(j铆)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�(j铆)鏁�(sh霉)鐨勪竴鑷存敹鏂傛€�锛屽啰绱�(j铆)鏁�(sh霉)
5
鐨勯€愰爡(xi脿ng)鍙⿳鎬�銆佸彲寰€у強鍏舵噳(y墨ng)鐢�锛屽啰绱�(j铆)鏁�(sh霉)鍚勯爡(xi脿ng)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
绱�(j铆)鏁�(sh霉)灞曢枊(k膩i)銆乀aylor 绱�(j铆)鏁�(sh霉)銆丮aclaurin 绱�(j铆)鏁�(sh霉)銆�
4.Fourier 绱�(j铆)鏁�(sh霉)
涓夎绱�(j铆)鏁�(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�(j铆)鏁�(sh霉)灞曢枊(k膩i)銆�
Beseel 涓嶇瓑寮忋€丷iemanm-Lebesgue 瀹氱悊銆佹寜娈靛厜婊戝嚱鏁�(sh霉)鐨� Fourier 绱�(j铆)鏁�(sh霉)鐨勬敹鏂�
鎬у畾鐞嗐€�

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紝璜�(q菒ng)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(gu膩n)榛�(di菐n)锛岃垏鏈恫(w菐ng)绔欑劇(w煤)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(du矛)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(sh铆)鎬с€佸畬鏁存€�銆佸強鏅�(sh铆)鎬ф湰绔欎笉浣滀换浣曚繚璀夋垨鎵胯锛岃珛(q菒ng)璁€鑰呭儏浣滃弮鑰冿紝骞惰珛(q菒ng)鑷鏍稿(sh铆)鐩搁棞(gu膩n)鍏�(n猫i)瀹�銆�

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