ǡѺŤ

Ť ҢѡͧԵʵ觾ѲҨҡժԵ âҤԵ лѭҷҧԡ Ťյ鹡ԴҡͧǤԴѡ ѧ

ǤԴá Ťԧ͹ؾѹ (Differential Calculus) 繷ɮշҴѵҡ¹ŧ ǢͧѺ͹ؾѹͧѧѹҧԵʵ ҧ , ͤѹͧ ش˹. ɮբͧ͹ؾѹǹçѹ㨨ҡѭҷҧԡ

ǤԴͧ ŤԧԾѹ (Integral Calculus) 繷ɮշçѹ㨨ҡäӹdzҾ鹷ͻҵâͧٻçҧâҤԵҧ . ɮչҿͧѧѹ᷹ٻçҧâҤԵ ɮջԾѹ (Թõ) ѡ㹡äӹdzҾ鹷лҵ

ͧǤԴԴҡѭҷҧѹѺդѹѹ֡ ·ɮպŰҹͧŤʡ ԧǷɮշͧº͹繴ҹͧͧ­ѹǡѹ 蹤ǡѹ§ͧҹ (¤ ҡ͹ؾѹлԾѹ繿ѧѹѹͧѹСѹ). 㹡͹Ťͤ㨵Ƿɮҧ֡ áǶ֧ͧɮФѹ͹ ֡㹻ѨغѹѡСǶ֧Ťԧ͹ؾѹ͹§ҧ ͧҡҹ¡

͹ ֡Ťҧ´ҵ Դʵ ҧԵʵҡ Ե ɮաѴ 繵

ѵ

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

ûء

þѲСŤ¼᷺ءǹͧԵؤѹ繾鹰ҹͧԷʵͺءҢ੾ ԡþѲͺ ෤Ԥáҧ úԹ ෤ ͺ վ鹰ҹҨҡŤ

Ť ԧ͹ؾѹ Ťǡ Ťʢͧ¹ŧ ԧ͹ Ťԧ Ťʡԡѹ ;ԧ͹ؾѹ


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