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鍙嬫儏鎻愮ず锛氭湰绔欐彁渚涘叏鍦�(gu贸)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�(k霉)鈥� 涓嬭級
2021骞�涓湅(gu贸)鐭虫补澶у(xu茅)鑿澅纰╁＋鐮旂┒鐢熷叆瀛�(xu茅)鑰冭│澶х侗
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鏁�(sh霉)瀛�(xu茅)锛堝柈鐛�(d煤)鑰冭│锛夊ぇ缍�
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涓€銆佽€冭│瑕佹眰
1.鍑芥暩(sh霉)銆佹サ闄�銆侀€ｇ簩(x霉)
鈶犵悊瑙ｅ嚱鏁�(sh霉)鐨勬蹇�锛屾帉鎻″嚱鏁�(sh霉)鐨勮〃绀烘硶锛屽苟鏈�(hu矛)寤虹珛鎳�(y墨ng)鐢ㄥ晱(w猫n)椤岀殑鍑�
鏁�(sh霉)闂�(gu膩n)绯�銆�
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鈶′簡瑙ｅ嚱鏁�(sh霉)鐨勬湁鐣屾€с€佸柈瑾�(di脿o)鎬�銆佸懆鏈熸€у拰濂囧伓鎬�銆�
鈶㈢悊瑙ｅ京(f霉)鍚堝嚱鏁�(sh霉)鍙婂垎娈靛嚱鏁�(sh霉)鐨勬蹇�锛屼簡瑙ｅ弽鍑芥暩(sh霉)鍙婇毐鍑芥暩(sh霉)鐨勬蹇�銆�
鈶ｆ帉鎻″熀鏈垵绛夊嚱鏁�(sh霉)鐨勬€ц唱(zh矛)鍙婂叾鍦栧舰锛屼簡瑙ｅ垵绛夊嚱鏁�(sh霉)鐨勬蹇点€�
鈶ょ悊瑙ｆサ闄愮殑姒傚康锛岀悊瑙ｅ嚱鏁�(sh霉)宸︽サ闄愯垏鍙虫サ闄愮殑姒傚康浠ュ強鍑芥暩(sh霉)妤�
闄愬瓨鍦ㄨ垏宸︽サ闄�銆佸彸妤甸檺涔嬮枔鐨勯棞(gu膩n)绯�銆�
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鈶ユ帉鎻℃サ闄愮殑鎬ц唱(zh矛)鍙婂洓鍓囬亱(y霉n)绠楁硶鍓�銆�
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鈶︽帉鎻℃サ闄愬瓨鍦ㄧ殑鍏╁€�(g猫)婧�(zh菙n)鍓�锛屽苟鏈�(hu矛)鍒╃敤瀹冨€戞眰妤甸檺锛屾帉鎻″埄鐢ㄥ叐
鍊�(g猫)閲嶈妤甸檺姹傛サ闄愮殑鏂规硶銆�
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鈶х悊瑙ｇ劇(w煤)绐皬閲忋€佺劇(w煤)绐ぇ閲忕殑姒傚康锛屾帉鎻＄劇(w煤)绐皬閲忕殑姣旇純鏂规硶锛�
鏈�(hu矛)鐢ㄧ瓑鍍�(ji脿)鐒�(w煤)绐皬閲忔眰妤甸檺銆�
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鈶ㄧ悊瑙ｅ嚱鏁�(sh霉)閫ｇ簩(x霉)鎬х殑姒傚康(鍚乏閫ｇ簩(x霉)鑸囧彸閫ｇ簩(x霉))锛屾渻(hu矛)鍒ゅ垾鍑芥暩(sh霉)闁撴柗
榛�(di菐n)鐨勯鍨�銆�
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鈶╀簡瑙ｉ€ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)鍜屽垵绛夊嚱鏁�(sh霉)鐨勯€ｇ簩(x霉)鎬�锛岀悊瑙ｉ枆鍗€(q奴)闁撲笂閫ｇ簩(x霉)
鍑芥暩(sh霉)鐨勬€ц唱(zh矛)(鏈夌晫鎬�銆佹渶澶у€煎拰鏈€灏忓€煎畾鐞嗐€佷粙鍊煎畾鐞�)锛屽苟鏈�(hu矛)鎳�(y墨ng)鐢ㄩ€�
浜涙€ц唱(zh矛)銆�
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鈶犵悊瑙ｅ皫(d菐o)鏁�(sh霉)鍜屽井鍔殑姒傚康锛岀悊瑙ｅ皫(d菐o)鏁�(sh霉)鑸囧井鍒嗙殑闂�(gu膩n)绯�锛岀悊瑙ｅ皫(d菐o)鏁�(sh霉)鐨�
骞句綍鎰忕京锛屾渻(hu矛)姹傚钩闈㈤潰鏇茬窔鐨勫垏绶氭柟绋嬪拰娉曠窔鏂圭▼锛屼簡瑙ｅ皫(d菐o)鏁�(sh霉)鐨勭墿鐞�
鎰忕京锛屾渻(hu矛)鐢ㄥ皫(d菐o)鏁�(sh霉)鎻忚堪涓€浜涚墿鐞嗛噺锛岀悊瑙ｅ嚱鏁�(sh霉)鐨勫彲灏�(d菐o)鎬ц垏閫ｇ簩(x霉)鎬т箣闁撶殑
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闂�(gu膩n)绯�銆�
鈶℃帉鎻″皫(d菐o)鏁�(sh霉)鐨勫洓鍓囬亱(y霉n)绠楁硶鍓囧拰寰�(f霉)鍚堝嚱鏁�(sh霉)鐨勬眰灏�(d菐o)娉曞墖锛屾帉鎻″熀鏈垵
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绛夊嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)鍏紡銆備簡瑙ｅ井鍒嗙殑鍥涘墖閬�(y霉n)绠楁硶鍓囧拰涓€闅庡井鍒嗗舰寮忕殑涓嶈畩
鎬э紝鏈�(hu矛)姹傚嚱鏁�(sh霉)鐨勫井鍒�銆�
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鈶簡瑙ｉ珮闅庡皫(d菐o)鏁�(sh霉)鐨勬蹇�锛屾渻(hu矛)姹傜啊(ji菐n)鍠嚱鏁�(sh霉)鐨勯珮闅庡皫(d菐o)鏁�(sh霉)銆�
鈶ｆ渻(hu矛)姹傚垎娈靛嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)锛屾渻(hu矛)姹傞毐鍑芥暩(sh霉)鍜岀敱鍙冩暩(sh霉)鏂圭▼鎵€纰哄畾鐨勫嚱鏁�(sh霉)
浠ュ強鍙嶅嚱鏁�(sh霉)鐨勫皫(d菐o)鏁�(sh霉)銆�
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鈶ょ悊瑙ｅ苟鏈�(hu矛)鐢ㄧ緟鐖�(Rolle)瀹氱悊銆佹媺鏍兼湕鏃�(Lagrange)涓€煎畾鐞嗗拰
娉板嫆(Taylor)瀹氱悊锛屼簡瑙ｅ苟鏈�(hu矛)鐢ㄦ煰瑗�(Cauchy)涓€煎畾鐞�銆�
鈶ユ帉鎻＄敤娲涘繀閬�(d谩)娉曞墖姹傛湭瀹氬紡妤甸檺鐨勬柟娉�銆�
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鈶︾悊瑙ｅ嚱鏁�(sh霉)鐨勬サ鍊兼蹇�锛屾帉鎻＄敤灏�(d菐o)鏁�(sh霉)鍒ゆ柗鍑芥暩(sh霉)鐨勫柈瑾�(di脿o)鎬у拰姹傚嚱鏁�(sh霉)
妤靛€肩殑鏂规硶锛屾帉鎻″嚱鏁�(sh霉)鐨勬渶澶у€煎拰鏈€灏忓€肩殑姹傛硶鍙婂叾鎳�(y墨ng)鐢ㄣ€�
鈶ф渻(hu矛)鐢ㄥ皫(d菐o)鏁�(sh霉)鍒ゆ柗鍑芥暩(sh霉)鍦栧舰鐨勫嚬鍑告€�,鏈�(hu矛)姹傚嚱鏁�(sh霉)鍦栧舰鐨勬嫄榛�(di菐n)浠ュ強姘�
骞�銆侀墰鐩村拰鏂滄几杩戠窔锛屾渻(hu矛)鎻忕躬鍑芥暩(sh霉)鐨勫湒褰�銆�
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鈶ㄤ簡瑙ｆ洸鐜�銆佹洸鐜囧湏鑸囨洸鐜囧崐寰戠殑姒傚康锛屾渻(hu矛)瑷�(j矛)绠楁洸鐜囧拰鏇茬巼鍗婂緫銆�
3.涓€鍏冨嚱鏁�(sh霉)绌嶅垎瀛�(xu茅)
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鈶犵悊瑙ｅ師鍑芥暩(sh霉)鐨勬蹇碉紝鐞嗚В涓嶅畾绌嶅垎鍜屽畾绌嶅垎鐨勬蹇�銆�
鈶℃帉鎻′笉瀹氱⿳鍒嗙殑鍩烘湰鍏紡锛屾帉鎻′笉瀹氱⿳鍒嗗拰瀹氱⿳鍒嗙殑鎬ц唱(zh矛)鍙婂畾绌�
鍒嗕腑鍊煎畾鐞�锛屾帉鎻℃彌鍏冪⿳鍒嗘硶鑸囧垎閮ㄧ⿳鍒嗘硶銆�
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鈶㈡渻(hu矛)姹傛湁鐞嗗嚱鏁�(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)鏈夌悊寮忓拰绨�(ji菐n)鍠劇(w煤)鐞嗗嚱鏁�(sh霉)鐨勭⿳鍒�銆�
鈶ｇ悊瑙ｇ⿳鍒嗕笂闄愮殑鍑芥暩(sh霉)锛屾渻(hu矛)姹傚畠鐨勫皫(d菐o)鏁�(sh霉)锛屾帉鎻＄墰闋撲竴钀婂竷灏艰尐鍏紡銆�
鈶ゆ帉鎻＄敤瀹氱⿳鍒嗚〃閬�(d谩)鍜岃▓(j矛)绠椾竴浜涘咕浣曢噺鑸囩墿鐞嗛噺(骞抽潰鍦栧舰鐨勯潰绌嶃€�
骞抽潰鏇茬窔鐨勫姬闀�(zh菐ng)銆佹棆杞�(zhu菐n)楂旂殑楂旂⿳鍙婂伌(c猫)闈㈢⿳銆佸钩琛屾埅闈㈤潰绌嶇偤宸茬煡鐨勭珛
楂旈珨绌�銆佸姛銆佸紩鍔涖€佸鍔�銆佽唱(zh矛)蹇�銆佸舰蹇冪瓑)鍙婂嚱鏁�(sh霉)骞冲潎鍊�銆�
4.澶氬厓鍑芥暩(sh霉)寰⿳鍒嗗(xu茅)
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鈶犱簡瑙ｅ鍏冨嚱鏁�(sh霉)鐨勬蹇�锛屼簡瑙ｄ簩鍏冨嚱鏁�(sh霉)鐨勫咕浣曟剰缇�銆�
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鈶′簡瑙ｄ簩鍏冨嚱鏁�(sh霉)鐨勬サ闄愯垏閫ｇ簩(x霉)鐨勬蹇�锛屼簡瑙ｆ湁鐣岄枆鍗€(q奴)鍩熶笂浜屽厓鍑芥暩(sh霉)
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鈶簡瑙ｅ鍏冨嚱鏁�(sh霉)鍋忓皫(d菐o)鏁�(sh霉)鑸囧叏寰垎鐨勬蹇�锛屾渻(hu矛)姹傚鍏冨京(f霉)鍚堝嚱鏁�(sh霉)涓€闅�銆�
浜岄殠鍋忓皫(d菐o)鏁�(sh霉)锛屾渻(hu矛)姹傚叏寰垎锛屼簡瑙ｉ毐鍑芥暩(sh霉)瀛樺湪瀹氱悊锛屾渻(hu矛)姹傚鍏冮毐鍑芥暩(sh霉)鐨�
鍋忓皫(d菐o)鏁�(sh霉)銆�
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鈶ｄ簡瑙ｅ鍏冨嚱鏁�(sh霉)妤靛€煎拰姊濅欢妤靛€肩殑姒傚康锛屾帉鎻″鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑
蹇呰姊濅欢锛屼簡瑙ｄ簩鍏冨嚱鏁�(sh霉)妤靛€煎瓨鍦ㄧ殑鍏呭垎姊濅欢锛屾渻(hu矛)鐢ㄤ簩鍏冨嚱鏁�(sh霉)鐨勬サ鍊�锛�
鎺屾彙鐢ㄦ媺鏍兼湕鏃ヤ箻瀛愭硶姹傛浠舵サ鍊肩殑鏂规硶锛岃兘澶犳眰绨�(ji菐n)鍠鍏冨嚱鏁�(sh霉)鐨勬渶
澶у€煎拰鏈€灏忓€�锛岃兘澶犺В姹轰竴浜涚啊(ji菐n)鍠殑鎳�(y墨ng)鐢ㄥ晱(w猫n)椤屻€�
鈶や簡瑙ｄ簩閲嶇⿳鍒嗙殑姒傚康鍜屽熀鏈€ц唱(zh矛)锛屾帉鎻′簩閲嶇⿳鍒嗙殑瑷�(j矛)绠楁柟娉�-鐩�
瑙掑潗妯�(bi膩o)鏂规硶鍜屾サ鍧愭(bi膩o)鏂规硶銆�
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鈶犱簡瑙ｅ井鍒嗘柟绋嬪強鍏堕殠銆佽В銆侀€氳В銆佸垵濮嬫浠跺拰鐗硅В绛夋蹇点€�
鈶℃帉鎻¤畩閲忓彲鍒嗛洟鐨勫井鍒嗘柟绋嬪強涓€闅庣窔鎬у井鍒嗘柟绋嬬殑瑙ｆ硶锛屾渻(hu矛)瑙ｉ綂
娆″井鍒嗘柟绋�銆�
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鈶㈡渻(hu矛)鐢ㄩ檷闅庢硶瑙ｄ笅鍒楀舰寮忕殑寰垎鏂圭▼锛�y(n) f(x),y (x) f(x,y
" ')鍜�
f(x,y
)銆�
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鈶ｇ悊瑙ｄ簩闅庣窔鎬у井鍒嗘柟绋嬭В鐨勬€ц唱(zh矛)鍙婅В鐨勭祼(ji茅)妲�(g貌u)瀹氱悊銆�
鈶ゆ帉鎻′簩闅庡父绯绘暩(sh霉)榻婃绶氭€у井鍒嗘柟绋嬬殑瑙ｆ硶锛屽苟鏈�(hu矛)瑙ｆ煇浜涢珮浜庝簩
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闅庣殑甯哥郴鏁�(sh霉)榻婃绶氭€у井鍒嗘柟绋�銆�
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鈶ユ渻(hu矛)瑙ｈ嚜鐢遍爡(xi脿ng)鐐哄闋�(xi脿ng)寮�銆佹寚鏁�(sh霉)鍑芥暩(sh霉)銆佹寮﹀嚱鏁�(sh霉)銆佷綑寮﹀嚱鏁�(sh霉)浠ュ強瀹�
鍊戠殑鍜岃垏绌嶇殑浜岄殠甯哥郴鏁�(sh霉)闈為綂娆＄窔鎬у井鍒嗘柟绋�銆�
鈶︽渻(hu矛)鐢ㄥ井鍒嗘柟绋嬭В姹轰竴浜涚啊(ji菐n)鍠殑鎳�(y墨ng)鐢ㄥ晱(w猫n)椤�銆�
6.琛屽垪寮�
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鈶犱簡瑙ｈ鍒楀紡鐨勬蹇碉紝鎺屾彙琛屽垪寮忕殑鎬ц唱(zh矛)銆�
鈶℃渻(hu矛)鎳�(y墨ng)鐢ㄨ鍒楀紡鐨勬€ц唱(zh矛)鍜岃鍒楀紡鎸夎(鍒�)灞曢枊瀹氱悊瑷�(j矛)绠楄鍒楀紡銆�
7.鐭╅櫍
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鈶犵悊瑙ｇ煩闄ｇ殑姒傚康锛屼簡瑙ｅ柈浣嶇煩闄�銆佹暩(sh霉)閲忕煩闄�銆佸皪(du矛)瑙掔煩闄ｃ€佷笁瑙掔煩
闄�銆佸皪(du矛)绋辩煩闄ｃ€佸弽灏�(du矛)绋辩煩闄ｅ拰姝ｄ氦鐭╅櫍浠ュ強瀹冨€戠殑鎬ц唱(zh矛)銆�
鈶℃帉鎻＄煩闄ｇ殑绶氭€ч亱(y霉n)绠�銆佷箻娉曘€佽綁(zhu菐n)缃互鍙婂畠鍊戠殑閬�(y霉n)绠楄(gu墨)寰�锛屼簡瑙ｆ柟
闄ｇ殑鍐垏鏂归櫍涔樼⿳鐨勮鍒楀紡鐨勬€ц唱(zh矛)銆�
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鈶㈢悊瑙ｉ€嗙煩闄ｇ殑姒傚康锛屾帉鎻￠€嗙煩闄ｇ殑鎬ц唱(zh矛)浠ュ強鐭╅櫍鍙€嗙殑鍏呭垎蹇呰
姊濅欢锛庣悊瑙ｄ即闅ㄧ煩闄ｇ殑姒傚康锛屾渻(hu矛)鐢ㄤ即闅ㄧ煩闄ｆ眰閫嗙煩闄�銆�
鈶ｄ簡瑙ｇ煩闄ｅ垵绛夎畩鎻涚殑姒傚康锛屼簡瑙ｅ垵绛夌煩闄ｇ殑鎬ц唱(zh矛)鍜岀煩闄ｇ瓑鍍�(ji脿)鐨勬
蹇�锛岀悊瑙ｇ煩闄ｇ殑绉╃殑姒傚康锛屾帉鎻＄敤鍒濈瓑璁婃彌姹傜煩闄ｇ殑绉╁拰閫嗙煩闄ｇ殑鏂�
娉�銆�
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鈶犵悊瑙� n缍悜閲忋€佸悜閲忕殑绶氭€х祫鍚堣垏绶氭€ц〃绀虹殑姒傚康銆�
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鈶簡瑙ｅ悜閲忕祫鐨勬サ澶х窔鎬х劇(w煤)闂�(gu膩n)绲勫拰鍚戦噺绲勭殑绉╃殑姒傚康锛屾渻(hu矛)姹傚悜閲忕祫
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鈶ｄ簡瑙ｅ悜閲忕祫绛夊児(ji脿)鐨勬蹇�锛屼簡瑙ｇ煩闄ｇ殑绉╄垏鍏惰(鍒�)鍚戦噺绲勭殑绉╃殑
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鈶や簡瑙ｅ収(n猫i)绌嶇殑姒傚康锛屾帉鎻＄窔鎬х劇(w煤)闂�(gu膩n)鍚戦噺绲勬浜よ(gu墨)鑼冨寲鐨勬柦瀵嗙壒
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鈶犳渻(hu矛)鐢ㄥ厠鎷夐粯娉曞墖姹傝В绶氭€ф柟绋嬬祫銆�
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鈶＄悊瑙ｉ綂娆＄窔鎬ф柟绋嬬祫鏈夐潪闆惰В鐨勫厖鍒嗗繀瑕佹浠跺強闈為綂娆＄窔鎬ф柟
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鈶㈢悊瑙ｉ綂娆＄窔鎬ф柟绋嬬祫鐨勫熀绀�(ch菙)瑙ｇ郴鍙婇€氳В鐨勬蹇�锛屾帉鎻￠綂娆＄窔鎬ф柟
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鈶ｇ悊瑙ｉ潪榻婃绶氭€ф柟绋嬬祫鑹茶В鐨勭祼(ji茅)妲�(g貌u)鍙婇€氳В鐨勬蹇�銆�
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鈶犵悊瑙ｇ煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚戦噺鐨勬蹇靛強鎬ц唱(zh矛)锛屾渻(hu矛)姹傜煩闄ｇ殑鐗瑰緛鍊�
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鈶＄悊瑙ｇ浉浼肩煩闄ｇ殑姒傚康銆佹€ц唱(zh矛)鍙婄煩闄ｅ彲鐩镐技灏�(du矛)瑙掑寲鐨勫厖鍒嗗繀瑕佹浠讹紝
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鈶㈢悊瑙ｅ(sh铆)灏�(du矛)绋辩煩闄ｇ殑鐗瑰緛鍊煎拰鐗瑰緛鍚戦噺鐨勬€ц唱(zh矛)銆�
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鍑芥暩(sh霉)鐨勬蹇靛強琛ㄧず娉曪細鍑芥暩(sh霉)鐨勬湁鐣屾€с€佸柈瑾�(di脿o)鎬�銆佸懆鏈熸€у拰濂囧伓鎬�锛�
寰�(f霉)鍚堝嚱鏁�(sh霉)銆佸弽鍑芥暩(sh霉)銆佸垎娈靛嚱鏁�(sh霉)鍜岄毐鍑芥暩(sh霉)锛屽熀鏈垵绛夊嚱鏁�(sh霉)鐨勬€ц唱(zh矛)鍙婂叾鍦�
褰�锛屽垵绛夊嚱鏁�(sh霉)锛屽嚱鏁�(sh霉)闂�(gu膩n)绯荤殑寤虹珛銆�
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鏁�(sh霉)鍒楁サ闄愯垏鍑芥暩(sh霉)妤甸檺鐨勫畾缇╁強鍏舵€ц唱(zh矛)锛屽嚱鏁�(sh霉)鐨勫乏妤甸檺鑸囧彸妤甸檺銆�
鐒�(w煤)绐皬閲忓拰鐒�(w煤)绐ぇ閲忕殑姒傚康鍙婂叾闂�(gu膩n)绯�銆傜劇(w煤)绐皬閲忕殑鎬ц唱(zh矛)鍙婄劇(w煤)绐皬
閲忕殑姣旇純锛屾サ闄愮殑鍥涘墖閬�(y霉n)绠�銆傛サ闄愬瓨鍦ㄧ殑鍏╁€�(g猫)婧�(zh菙n)鍓囷細?ji菐n)鎻(di脿o)鏈夌晫婧�(zh菙n)鍓囧拰
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澶鹃€兼簴(zh菙n)鍓�銆傚叐鍊�(g猫)閲嶈妤甸檺锛�
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鍑芥暩(sh霉)閫ｇ簩(x霉)鐨勬蹇�锛屽嚱鏁�(sh霉)闁撴柗榛�(di菐n)鐨勯鍨嬶紝鍒濈瓑鍑芥暩(sh霉)鐨勯€ｇ簩(x霉)鎬�锛岄枆鍗€(q奴)
闁撲笂閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)
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灏�(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑姒傚康,灏�(d菐o)鏁�(sh霉)鐨勫咕浣曟剰缇╁拰鐗╃悊鎰忕京,鍑芥暩(sh霉)鐨勫彲灏�(d菐o)鎬ц垏
閫ｇ簩(x霉)鎬т箣闁撶殑闂�(gu膩n)绯�锛屽钩闈㈡洸绶氱殑鍒囩窔鍜屾硶绶氾紝灏�(d菐o)鏁�(sh霉)鍜屽井鍒嗙殑鍥涘墖閬�(y霉n)绠�锛�
鍩烘湰鍒濈瓑鍑芥暩(sh霉)鐨勫皫(d菐o)鏁�(sh霉)锛屽京(f霉)鍚堝嚱鏁�(sh霉)銆佸弽鍑芥暩(sh霉)銆侀毐鍑芥暩(sh霉)浠ュ強鍙冩暩(sh霉)鏂圭▼鎵€纰�
瀹氱殑鍑芥暩(sh霉)鐨勫井鍒嗘硶銆傞珮闅庡皫(d菐o)鏁�(sh霉)锛屼竴闅庡井鍒嗗舰寮忕殑涓嶈畩鎬�锛屽井鍒嗕腑鍊煎畾
鐞�锛屾礇蹇呴仈(d谩)(L'HoSpital)娉曞墖銆傚嚱鏁�(sh霉)鍠(di脿o)鎬х殑鍒ゅ垾锛屽嚱鏁�(sh霉)鐨勬サ鍊�锛屽嚱
鏁�(sh霉)鍦栧舰鐨勫嚬鍑告€�銆佹嫄榛�(di菐n)鍙婃几杩戠窔銆傚嚱鏁�(sh霉)鍦栧舰鐨勬弿绻�锛屽嚱鏁�(sh霉)鐨勬渶澶у€艰垏
鏈€灏忓€�锛屽姬寰垎鏇茬巼鐨勬蹇�锛屾洸鐜囧湏鑸囨洸鐜囧崐寰�銆�
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鍘熷嚱鏁�(sh霉)鍜屼笉瀹氱⿳鍒嗙殑姒傚康锛屼笉瀹氱⿳鍒嗙殑鍩烘湰鎬ц唱(zh矛)锛屽熀鏈⿳鍒嗗叕寮�.
瀹氱⿳鍒嗙殑姒傚康鍜屽熀鏈€ц唱(zh矛)锛屽畾绌嶅垎涓€煎畾鐞嗭紝绌嶅垎涓婇檺鐨勫嚱鏁�(sh霉)鍙婂叾灏�(d菐o)
鏁�(sh霉)锛岀墰闋撲竴钀婂竷灏艰尐(Newton鈥�Leibniz)鍏紡锛屼笉瀹氱⿳鍒嗗拰瀹氱⿳鍒嗙殑鎻�
鍏冪⿳鍒嗘硶鑸囧垎閮ㄧ⿳鍒嗘硶锛屾湁鐞嗗嚱鏁�(sh霉)銆佷笁瑙掑嚱鏁�(sh霉)鐨勬湁鐞嗗紡鍜岀啊(ji菐n)鍠劇(w煤)鐞嗗嚱
鏁�(sh霉)鐨勭⿳鍒�锛屽畾绌嶅垎鐨勬噳(y墨ng)鐢�銆�
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甯稿井鍒嗘柟绋嬬殑鍩烘湰姒傚康锛岃畩閲忓彲鍒嗛洟鐨勫井鍒嗘柟绋�锛岄綂娆″井鍒嗘柟绋�銆�
涓€闅庣窔鎬у井鍒嗘柟绋嬶紝鍙檷闅庣殑楂橀殠寰垎鏂圭▼銆傜窔鎬у井鍒嗘柟绋嬭В鐨勬€ц唱(zh矛)
鍙婅В鐨勭祼(ji茅)妲�(g貌u)瀹氱悊锛屼簩闅庡父绯绘暩(sh霉)榻婃绶氭€у井鍒嗘柟绋�锛岄珮浜庝簩闅庣殑鏌愭甯�
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5.澶氬厓鍑芥暩(sh霉)寰⿳鍒嗗(xu茅)
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澶氬厓鍑芥暩(sh霉)鐨勬蹇�锛屼簩鍏冨嚱鏁�(sh霉)鐨勫咕浣曟剰缇�銆備簩鍏冨嚱鏁�(sh霉)鐨勬サ闄愯垏閫ｇ簩(x霉)鐨�
姒傚康锛屾湁鐣岄枆鍗€(q奴)鍩熶笂浜屽厓閫ｇ簩(x霉)鍑芥暩(sh霉)鐨勬€ц唱(zh矛)銆傚鍏冨嚱鏁�(sh霉)鐨勫亸灏�(d菐o)鏁�(sh霉)鍜屽叏寰�
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6.琛屽垪寮�
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琛屽垪寮忕殑姒傚康鍜屽熀鏈€ц唱(zh矛)锛岃鍒楀紡鎸夎(鍒�)灞曢枊瀹氱悊銆�
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鐭╅櫍鐨勬蹇�锛岀煩闄ｇ殑绶氭€ч亱(y霉n)绠�锛岀煩闄ｇ殑涔樻硶锛屾柟闄ｇ殑鍐�锛屾柟闄ｄ箻绌�
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鍒嗗鐭╅櫍鍙婂叾閬�(y霉n)绠�銆�
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鍚戦噺鐨勬蹇�,鍚戦噺鐨勭窔鎬х祫鍚堝拰绶氭€ц〃绀猴紝鍚戦噺绲勭殑绶氭€х浉闂�(gu膩n)鑸囩窔
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绶氭€ф柟绋嬬祫鐨勫厠鎷夐粯(Cramer)娉曞墖銆傞綂娆＄窔鎬ф柟绋嬬祫鏈夐潪闆惰В鐨勫厖
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鏂囩珷鎼滅储
鎮ㄧ従(xi脿n)鍦ㄧ殑浣嶇疆锛� 
