ѵ Ť http://203.172.204.162/intranet/1023_mc41/content/charles.01.htm

Ť

Ť Ң˹觢ͧԵʵ觾ѲҨҡժԵâҤԵ ԴҡѹͧͧǤԴѡ ǤԴá Ťԧ͹ؾѹ (Differential Calculus) ͷɮշҴѵҡ¹ŧ ǢͧѺ͹ؾѹ 觾ٴ֧ѧѹҧԵʵ, , Фѹͧ ش˹ ǤԴͧ ŤԧԾѹ (Integral Calculus) ǢͧѺǤԴ㹡Թõ ǤԴ鹰ҹǡѺ鹷¡ҿͧѧѹ ǤԴǡѺҵ

ҡͧǤԴԴ ѧѹԹ ͸Ժ´ ɮպŰҹͧŤ Щй 㹡͹ŤʤáǶ֧ͧҧ͹ ֡㹻ѨغѹѡСǶ֧Ťԧ͹ؾѹ͹

ѵ (History)

鹡ԴͧŤԧԾѹ͹件֧ؤաҳ ⴫ ѡ繷ѡѹ㹹ͧ鹾 Method of Exhaustion 觷öӹdzҾ鹷лҵ Դ ѲԸաù ѲԸաê¤ӹdz 觤¤֧ѺǤԴ㹻Ѩغѹ źԫ ǵѹ ѡѺѺ繼ԴŤʢ ੾Сä鹾ɮպŰҹͧŤ

ա§ѹҹǵѹźԫ繼鹾ǤԴѡͧŤʡ͹ ԧ 觷˭شźԫѲѺŤʤͧ¢ͧ ѡѹ觤Դ֧ѭѡɳ᷹ǤԴҧԵʵ ҧá §ѹҧźԫйǵѹ ¡ѡԵʵٴѧ͡ҡѡԵʵûҹҹ» 觷餳Եʵѧѧûҹҹ ͧ·ǵѹ鹤ͧǹ¡ҢͧźԫҧѴ ѧѹѧɨ Analytical Society ͧ¢ͧźԫȵɷ 19 ͹ ѹɰҹѹҹǵѹ鹾ǤԴǡѺŤʡ͹ ҧá źԫ繼͹ ءѹ繷͡ѹ 駹ǵѹźԫҧ鹾Ťʴµͧ

繼ѲԪŤʹ͡ҡ Barrow, Descartes, de Fermat, Huygens Wallis ੾ de Fermat 觺ҧѺ¡ͧ ԴŤԧ͹ؾѹ ѡԵʵǭ Kowa Seki ժԵ㹪ǧǡѹѺ źԫ йǵѹ ѧ鹾ѡþ鹰ҹҧҧǡѺ ŤԧԾѹ 繷ѡšѹ㹢й ҡԴ͡ѺѡԪҡêǵѹ

Ťԧ͹ؾѹ (Differential Calculus)͹ؾѹ (derivative) ͡ҤҤ¹ŧͧ˹ ա˹¹ŧ㹻ҳҡ ҧ͹ؾѹ龺áç¹ٵ ѵ=зҧ/ Ѻѵط͹ѵǤ ѵǢͧس͹ؾѹ͡¹ŧ˹˹ ԪŤʾѲҢͨѴáѺѭҷѺ͹繸ҵԡҹ ѵǢͧسҨ¹ŧ

ҡǶ֧´ Ťԧ͹ؾѹ ѵҡ¹ŧ㹢㴢˹ (͹ؾѹ) ҧҢͧѧѹ Ѻâͧѧѹ ԧͧ͹ؾѹԵͧѵǹ㹡û¹ŧ ͹ؾѹ㨢ͧԷʵҾ ͹ͧǵѹ ç=× դŤ ͹ؾѹ˹ ɮ俿Ңͧ зɮçǧͧ͹䵹 (ѷҾ) Ƕ֧ҢͧŤԧ͹ؾѹ ǡѹѺɮվ鹰ҹͧǧ俿

͹ؾѹͧѧѹǶ֧ҿͧѧѹ㹪ǧ 觷öҨش٧شШششͧѧѹ ҷشҹ鹡ҿТҹѺ᡹Һ ù Ťѧաûءա ºԸբͧǵѹ Ը㹡Ҥҡͧѧѹ¡ûҳ ѧŤԧ͹ؾѹ֧ö任ءѺҡ¤Ӷ觶ͧԹҨԴҨŤʨѴ

ŤԧԾѹ (Integral Calculus)

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

鹰ҹͧŤ (Foundation)

鹰ҹ觤ѴͧŤհҹҨҡǤԴͧѧѹԵ ѹ෤ԤͧժԵ鹰ҹСػԧʵ ֡Ҿ鹰ҹͧŤѡѹ㹪͡ԧԧ 觻Сͺ¹觤Ѵк٨ͧɮբͧŤ 蹷ɮաѴ Сԧѧѹ

ɮպŰҹͧŤ (Fundamental theorem of calculus)

ɮպŰҹͧŤʡҡ͹ؾѹ СһԾѹ ԸաáѺѹ ҡ´ ҹؾѹöӹdz¡һԾѹӡѴࢵ

ԧ͹ҡ駹ǵѹźԫ 繡حᨹâ¼Ѿԧҧҡѧҡҹͧͧ繷ѡ §ö͹¹ŧ㹿ѧѹ㹪ǧ˹觨ҡѵҡ¹ŧ㹢㴢˹ ¡һԾѹͧǹѧ ɮպŰҹѧԸ㹡äӹdzһԾѹࢵԸշҧժԵ繨ӹǹҡ ͧԸաԵ ¡һҹؾѹ ɮպѧ͹حҵԧ͹ؾѹ 觤÷Ǣͧѹҧ ѧѹҺ ͹ؾѹͧѹ ԧ͹ؾѹԷʵ

ɮպŰҹͧŤ 1: ͹ؾѹ(Ծѹ(f(x))) ͧ x x

ɮպŰҹͧŤ 2: Ծѹ(f(x)) b 繢ͺࢵ a 繢ͺࢵҧ ҡѺ F(b)-F(a) F(x) 繻ҹؾѹͧ f(x)

ûء (Application)

þѲСŤ¼᷺ءǹͧԵؤ ѹ繾鹰ҹͧԷʵͺءҢ੾ ԡ þѲͺ ෤Ԥáҧ úԹ ෤ͺ վ鹰ҹҨҡŤ

Ť ԧ͹ؾѹ Ťǡ Ťʢͧ¹ŧ ԧ͹ Ťԧ Ťʡԡѹ ;ԧ͹ؾѹ

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