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鹡ԴͧŤԧԾѹ͹件֧ؤաҳ⴫ ѡ繷ѡѹ㹹ͧ鹾 Ըաᨧó 觷öӹdzҾ鹷лҵԴ ѲԸաù ѲԸաê¤ӹdz 觤¤֧ѺǤԴ㹻Ѩغѹźԫ ǵѹ ѡѺѺ繼ԴŤʢ ੾Сä鹾ɮպŰҹͧŤ ᫡ ǵѹ ͷմ źԫ ա§ѹҹǵѹźԫ 繼鹾ǤԴѡͧŤʡ͹ԧ觷˭ش źԫѲѺŤ ͧ¢ͧ ѡѹ 觤Դ֧ѭѡɳ ᷹ǤԴҧԵʵҧá §ѹҧźԫ йǵѹ ¡ѡԵʵٴѧ ͡ҡѡԵʵû ҹҹ»ի觷餳Եʵѧѧûҹҹͧ·ǵѹ ͧǹ¡ҢͧźԫҧѴ ѧѹѧɨ Analytical Society ͧ¢ͧźԫȵɷ 19 ͹ѹɰҹѹ ǵѹ鹾ǤԴǡѺŤʡ͹ ҧá źԫ繼͹ءѹ繷͡ѹ 駹ǵѹźԫҧ鹾Ťʴµͧ

繼ѲԪŤʹ͡ҡ õ, Barrow, ҵ, ੾ ҵ 觺ҧѺ¡ͧ ԴŤԧ͹ؾѹ. ѡԵʵǭ ૡ ժԵ㹪ǧǡѹѺ źԫ йǵѹ 鹾ѡþ鹰ҹҧҧǡѺ ŤԧԾѹ 繷ѡšѹ㹢й ҡԴ͡ѺѡԪҡêǵѹ

Ťԧ͹ؾѹ

͹ؾѹ (derivative) ͡ҤҤ¹ŧͧ˹ ա˹¹ŧ㹻ҳҡ ҧ͹ؾѹҨ龺áç¹ ٵ ѵ = зҧ/ Ѻѵط͹ѵǤ ѵǢͧس͹ؾѹ͡¹ŧ˹˹ ԪŤʾѲҢ ͨѴáѺѭҷѺ͹繸ҵԡҹ ѵǢͧسҨ¹ŧ

ҡǶ֧´ Ťԧ͹ؾѹ ѵҡ¹ŧ㹢㴢˹ (͹ؾѹ) ҧҢͧѧѹ Ѻâͧѧѹ ԧ ͧ͹ؾѹ Եͧѵǹ㹡¹ŧ (difference quotient). ͹ؾѹ㨢ͧԷʵҾ ͹ͧǵѹ ç = × դŤ ͹ؾѹ˹ ɮ俿Ңͧ зɮçǧͧ͹䵹 (ѷҾ) Ƕ֧ҢͧŤԧ͹ؾѹ ǡѹѺɮվ鹰ҹͧǧ俿

͹ؾѹͧѧѹ Ƕ֧ҿͧѧѹ㹪ǧ 觷öҨش٧ش Шشش ͧѧѹ ҷشҹ鹡ҿТҹѺ᡹Һ ù Ťѧաûءա ºԸբͧǵѹ (Newton's Method) Ը㹡Ҥҡͧѧѹ ¡ûҳ ѧŤԧ͹ؾѹ ֧ö任ءѺҡ¤Ӷ 觶ͧԹҨԴ ҨŤʨѴ

ŤԧԾѹ

ŤԧԾѹ֡ԸաһԾѹ (Թԡ, Integral) ͧѧѹ ҨҡԵͧͧ (¡Եͧѹ) о鹤;鹷׹ᶺҿͧѧѹ ԹõԸշԸ˹㹡Ҿ鹷ҿ о鹷 лҵâͧ蹷çзçк͡

鹰ҹͧŤ

鹰ҹ觤ѴͧŤ հҹҨҡ ǤԴͧѧѹ Եѹ෤ԤͧժԵ鹰ҹ СػԧԵʵ֡Ҿ鹰ҹͧŤ ѡѹ㹪 ԧԧ 觻Сͺ 觤Ѵ к٨ͧɮբͧŤ 蹷ɮաѴ Сԧѧѹ

ɮպŰҹͧŤ ͧ

ɮպŰҹͧŤʡ ͹ؾѹСһԾѹԸա÷çѹѹ Ǥ ҧѧѹ繻Ծѹͧѧѹ˹觢 ͹ؾѹͧѧѹҧ ҡѺѧѹ ͡ҡ ѧһԾѹӡѴࢵ¡á˹Ѻҹؾѹ

ɮպŰҹͧŤ¹ٻѭѡɳ줳Եʵѧ: f 繿ѧѹդͧǧ [a, b] F 繻ҹؾѹͧ f ǧ [a, b]





Ѻء x 㹪ǧ [a, b]



ԧ͹ҡ駹ǵѹ źԫ 繡حᨹ â¼Ѿԧҧҡѧҡҹͧͧ繷ѡ.§ ö͹¹ŧ㹿ѧѹ㹪ǧ˹ ҡѵҡ¹ŧ㹢㴢˹ ¡һԾѹͧǹѧ.ɮպŰҹѧԸ㹡äӹdz ԾѹӡѴࢵ ԸշҧժԵ繨ӹǹҡ ͧԸաԵ ¡һҹؾѹ.ɮպѧ͹حҵԧ͹ؾѹ 觤÷Ǣͧѹҧ ѧѹҺ ͹ؾѹͧѹ.ԧ͹ؾѹԷʵ



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