Ť

ԪŤʨ֧ ԷҾ ٧ҾժԵͧ ?

alt
繸ҧ ͹Ԫ˹觤ԪҾժԵ (Algebra) ººԧ ԷҾ ͤöѺԪŤ (Calculus) ԪŤԴѧԪҾժԵ֧˹觾ѹ ੾ҧԪŤԴѧúطҧѭҤ˭ͧªҵ 蹤ѧ ҳ (intuition) ͧӹǹͧô ӹǹٹ ͧ Ե (limit) Դ¹ѡԵʵͧҹ źԫ (Leibniz) йǵѹ (Newton) ͻҳ 400 շ
躷ͧ躺㹺ҧ觺ҧҧ褹ǧͧ


ǧԪŤҨ繵㹡Ҩ͹ ѡСѺѹ Ծѹ (integral) ǹѺͧ͹ؾѹ (derivative) ͵ͧalt ҡѺ ҡФԴ͹Ѻ ͹ؾѹͧè֧ҡѺalt ǡкǹäԴͧҡ稺§ ӵͺͧ ¹ͧǧùҹҹ 40 աԴ֡仡ҹѹǹѺѹҧ
ФԴ֡ŧ ԾѹǹѺͧ͹ؾѹ ҧ 躹ҹԴͧ ôԹ (operation) ǡ ź ٳ ͡ҡ ººԷҾ (ͤö÷ӧҹ㹪ǧҷ˹) ԪҾժԵͧ Ҩо ԪŤ᷹дԹ÷ФҧԪҾժԵͷӺǡ ź ٳ ˹觵ǴԹ (operator) ԪŤʨдԹäͧǴԹ ź㹤ǡѹ㹡óբͧ͹ؾѹ зӤٳǺǡ㹤ǡѹ㹡óբͧԾѹ
ͤͧ ôԹԪŤǹͧ͹ؾѹлԾѹöԨóѧἹҾҧҧ

alt



2. ôԹ͹ؾѹ֧ ź Ѻ ѹ
¹ҢͺͧӤѭ㹡¹͹駵ԪŤʷдѺšдѺȡ ա鹷෤Ԥ㹡͹ؾѹлԾѹҡԹ ;鹷Ѻ·ӤѭԧͧԪ ǹѧǨ֧ʹººͧôԹ÷Сǵ仹
ͤҤӵͺǢ͹ Ҩ繵ͧ鹨ҡФ¢ͧ͹ؾѹͧѧѹѹ͹ 觷駹 (ҡٵٻͧԵ) Ф (ٻ¤Ӻ) 觡ͧǡѹ͹ѹ 躷СǶ֧੾йٻٵâͧ͹ؾѹҹ
͹ؾѹͧѧѹ alt alt . . . (1)

ҡٻٵôѧ Ҩ ء駷ա͹ؾѹͧѧѹաôԹ÷ҧժԵͧ鹶֧ͧ駤 źǵ ʹԹäͧҧ 㹢зԪҾժԵͧ鹨еͧӷФ ôԹôѧҨҡ¢ͧ͹ؾѹ ѵҡ¹ŧ (rate of change) ͧѧѹͧ
ҤԴͧҷ㹡äӹdz (ԪʵҴ¡äӹdzʹͧҡ) ҷ㹡÷ӾժԵͧ駨ҡҡ͹ؾѹ ҨººԷҾͧԪҧժԵѺŤ ¹ԪŤʨջԷҾ٧(ԨóͧôԹҹ)
ҤԴͧ˹ҷҧѭҵʹѵʵͧªҵ ͡ 2000 մʡФӹdz觷ͧ ôٹ öԪҾժԵôٹ
ѡԵʵ㹻Ѩغѹҧҹ¹ҧ Ť ҡѺժԵǡԵ
ҧá Marius Sophus Lie ѡԵʵǹ ¡Ƕ֧Ԫ˹觤ԧ͹ؾѹ (Ԫ١ͧŤ) Among all mathematical disciplines the theory of differential equations is the most important. (㹺ôѡԧԵʵ ɮǡѺԧ͹ؾѹӤѭش)
¹ҹ㨢ͧ M. S. Lie Ҥ Ӥѭ 㹤ӾٴѧǹҨ¶֧ ԷҾ ¹ͧ


3. ôԹ㹻Ծѹ֧ ٳ Ѻ ǡ ѹ
ԸդԴ 鹨ҡͧԾѹӡѴࢵ ( definite integral) ͧ alt ҡ x = a ֧ x = b

alt . . . (2)
, alt
öѧࡵ ҧͧ͢ (2) źǡͧŤٳ 蹤 աôԹҼŤٳ͹ ҡ鹨֧´ԹҼźǡ
alt ᷹ѧ ( power ) ͧ俿ҷ㹺ҹalt ѧ Ťٳͧ alt Ѻǧalt ;ѧҹ俿 (energy) 㹪ǧҴѧ
͹Ӿѧҹ俿Ъǧ (alt ) Һǡѹ ѧҹ俿»ҳѹ ͵ͧ÷Һѧҹ俿ҷ͹ (Ҵ͹) Ҩ֧кǹâͧԵʹǧ 24
ػ һԾѹԪŤʡ ҼźǡͧŤٳͧͧҳͧ ͧкǹâͧԵ

4. §ҧ͹ؾѹлԾѹ
շɮ 2 §͹ؾѹѺԾѹҴ¡ѹ ͷɮպѡŢͧŤ (Fundamental Theorem of Calculus) йʹ§ʴ ŵҧ (ͼź) ͧͧԾѹй͹ؾѹҧ
ɮպ صalt 繿ѧѹդͧ
alt alt
ͷalt Ҩеͧ鹨ҡŵҧͧalt (alt ) ҡ 蹤 alt
alt

õʹalt
alt = ¢ͧalt 㹪ǧalt ֧
ҡѺalt alt

alt ,alt , alt ѧ
öػ繶¤ ͹ؾѹͧԾѹ(ͧѧѹ) ҡѺѧѹ
5. 觷: ͹ؾѹ Ծѹ ѺѺʹ
ͧ Ť integration ѧ һԾѹ ¹ԴҹҨջѭҵ͡÷Ӥ ԧ ·ҡ (2) ͼźǡѡԵʵ᷹ͧѭѡɳalt ( ҹ sigma ҡա) ¹ҧͧ͢ (2) дǡ ѡԵʵ֧Ѻͧ alt ״ͧ͡ alt
20-30 ҹѧѡ㨤 Integration ա óҡÔ ¶֧դʹͧѺҷ仢ͧ (2) ҧ
ѧ ¹֧դ һԾѹ ᷹ Integration ҨзԴѺʹͤҡ
㹷ӹͧǡѹ derivative ͹ؾѹ Ҩз餹ѺʹдѺ˹ ҹءѺ English Language Dictionary Collins Cobuild (1987) ͸Ժ¤ derivative 觷觴觷ѲҨҡ蹔 ºѺͧ͹ؾѹͧѧѹ价ӹͧǡѹ ;ѲҨҡѧѹ ҡͧդ ѹ ѹҧ
ҧá ¹Դ ִͧ͹ؾѹ (1) Ҩо ͹ؾѹѵҡ¹ŧ ѵҢͧŵҧ ͧѧѹ
ҵѴͧԵФԴ¹ŧ㹪ǧ˹˹¢ͧ ͹ؾѹ (differentiation) ͡Ҽŵҧ (difference) ͧ
蹹 ԧ͹ؾѹԧŵҧ ѾԧѺͧҨŴѺʹŧҧ
ش¹ ¹ ˹ҷѡ͵ͺӶӤѭº
http://www.math.psu.ac.th/html/en/Article/100-calculus.pdf

ٻҾǢͧ

Ԫ

ԴͧԪǤ٨Ҥṹҧ ԴͧԪҡ駤仡ػẺ



: antid
10 ҹ

ͧṹ ?

ҧ :


BraveheartByMeLo

ʶҹ :
俿ҡѧ