azumat@post.kek.jp - PowerPoint PPT Presentation

Title: azumat@post.kek.jp


1
????????????

• 2006?6?7? (? ????????)
• ???(?????????????)
• azumat_at_post.kek.jp
• http//www2.yukawa.kyoto-u.ac.jp/azuma/index.html

• ??
• ???? p2
• ???????? p5
• ???????? p15
• ???????? p18
• ??? p24

2
1 - ????
??????? ? ??????????????

• ??????????????????
• ????????????????

????????????
?????????????????!? ??????2????--?????
????????????????????6???????????? ???????????2????
??????????????????? ??????????????????????????????
?? ???????????????????????????? (???? 2006?2?7?
???????)
3
?????? ???????????????????????? ??????
??????????? ? ??????????
???????? (???????) ?????????????????????????????
(???? ???????????)
4
???? ????????????? ? ??????????????????? ??III,
C??? ?????????????IIIC ? ISBN
4410105930 ??????? ????????? (???????) ??? ISBN
4-480-08675-7 ?????????(??????) ???? ASIN
4781909817 ????????????(???????) ????? ISBN
4924460893
5
2- ????????
????(differential and integral calculus)?????

• 1st step ????????? (??II)
• 2nd step ?????(???????????)??????(??III)
• 3rd step ??????????????
• Taylor?????????????????
• (Fourier??????????)

() ???????????????????????? ???????????????????
????
6
?????????
?? ????????????
?? ?????????????
S
h
a
b
O
???????????
7
???????
??m, ??v
x0
8
?? ?????? (uniformly-accelerated motion)
??m??????????(free-falling motion)
t0??x0????????(v0)??????? ????x(t0)0,
v(t0)0?
??(gravity) mg
t????????
x
??
??
a
v
??t??tdt???? ??v?gdt?????
??t??tdt???? ??x?vdt?????
vgt
xgt2/2
t
t
t
tdt
tdt
t
9
??III???????????
????(trigonometric function)
????(Napier)?
????(exponential function)
log a??(basis)?e????????(natural logarithm)
????(logarithmic function)
????(composed function)
???(inverse function)
yf(x)??????xf-1(y)
10
??????(air resistance)??????????(falling motion)
v
g/k
x
O
t
??????? ???????????????

• ?????????v0???????????????
• ????????????????????
• ????????0????????????

11
?????? ????????????????
Newton?????? (equation of motion)
???????????????(separation of variables)???????
??????????????(C?????)
????
???t0??????(v0)??????
???????????????????????????
12
Taylor?? ????????????
?? f(x)????????????
x????(a0)????????????
13
?? ???(pendulum)???
??????????
????
?
?ltlt1???sin??...
r
?????
??(tension) mg cos ?
mg sin ?
??(gravity) mg
??????(period)
???????????
14
?? ???(harmonic oscillation)
?????????????
????(spring constant) k
??m
x
O
x ????????????????(equation of motion)????

• ??

• ??

15
3- ????????

• ???? (linear algebra)?????
• ??(matrix)?????(linear transformation)??????
• ??C ??22????????
• ???? ???NN???????????

• ?????? (??)
• ????1??????????
• ????????????????????
• (eigenvalue(???)??????????????Dirac????)
• NN???????????????????????????
• (????6?25??????????)

16
?? ????????
?????CO2???????????????????
????k
????k
?? x1
?? x3
?? x2
???? ??m
???? ??M
???? ??M
?????
(
??????)
xiAi cos (wta) (i1,2,3)????????????????
??(amplitude)?????????
17
??A1,A2,A3??A1A2A30???????????? ??????(determi
nant)???????
????????????
?????????
18
4- ????????
???? (?) ??????????????? http//www.suken.net/jap
an.html
2006?????? 7?23? (???? 6?20?)?11?5?(????10?2?)
???? (?1??1???) 1??? (??????)
????7???????????????60????????70 2??? (??????)
2????2?????4?????????????
????120????????60 (1????2????????????)
???1??1??????
19
???1?????
1???(??????)????
??? x-2ltx/2 ???????
?? 4/3ltxlt4
????
????????????????????
?? ???
??
???????
??
20
2???(??????)????
???t1,-3????y0??????C?x?????? ???(3,0)?(11,0)???
? ??????????????????????????
?? ???(x,y)???t??????????????
??????????????
?????S????????
t -1 0
dx/dt - - - 0
dy/dt - 0
x ?? 3 ?? 2 ??
y ?? -4 ?? -3 ??
21
??1?????
1???(??????)????
???
???????
?? -12
?????
??????????
??????
??
22
2???(??????)????
??????(???????)
?? ?????A????????????????
????????????????????k4???????
???k3????????????????
k5?????????????????????
k4????????????????
23
??????(??????????)
?? ??????????????????
??????????????????????????
????????
????
???????f(1)??????????g(x)?????????????g(x)??????x
lt1??????????????g(x)????0,1(x1???)??????????
24
5- ???
??????????????????????????
??????????????????????????????
??????????????1??1?????
?????????????????????