Our math formulas, like xn C yn D zn, and X sin x C i are going to be

Our math formulas, like x n C y n D z n , and
n
X
sin x C i sin x C i i
sin x
i D1
are going to be using the MathTime Professional 2 fonts, but the text font is just Computer Modern (the
letters for ‘sin’ are going to come from cmr10, cmr7 and cmr5).
Here are some math formulas that should all work out OK.
A; : : : ; Z
a; : : : ; z
2A;:::;Z
22
;:::;˝
a;:::;z
A;:::;Z
€; : : : ; 
˛; : : : ; !
;:::;˝
€;:::;
˛;:::;!
;:::;˝
€;:::;
˛;:::;!
a;:::;z
@˛ @ ˇ D ˇ ” ˛ ˇ
2@˛ @ˇ Dˇ ” ˛ˇ
22
@˛ @ˇ Dˇ ” ˛ˇ
8" > ˛;
˛
28">˛;
22
jx
Œ
˛Œ "
8">˛; ˛ Œ "
aj < ı  jf .x/
2jx
22
"
lj < "
aj<ıjf .x/ lj<"
jx aj<ıjf .x/ lj<"
V
V… V
V… ! V
V…
„ ƒ‚
„ ƒ‚
„ ƒ‚
k
l
kCl
V
V… V
V…!V
V…
„ ƒ‚
„ ƒ‚
„ ƒ‚
2
2
2
k
l
kCl
V…!V
V…
V
V… V
„ ƒ‚
„ ƒ‚
„ ƒ‚
k
l
fxjx ¤ xg D ;
.A \ B/ı Aı \ B ı
.A\B/ı Aı \B ı
2fxjx¤xgD;
22
kCl
.A\B/ı Aı \B ı
fxjx¤xgD;
! D C v.x; y/ dx C w.x; y/ dy C d ~
2!DCv.x;y/ dxCw.x;y/ dyCd ~
22
!DCv.x;y/ dxCw.x;y/ dyCd ~
1
@w
@x
d! D d C
2
d!DdC
@v
@y
@w
@x
@v
@y
d!DdC @w
@x
22
dx ^ dy
dx^dy
@v dx^dy
@y
b
b C xc
xO C X
y C xyz C AE
E
O b
X Cxb
yCxyzC
c A
2xC
E
xC
O b
X Cx
byCxc
yzCA
22
Rij kl D
Rj i kl D
2Rij kl D
2
Rij lk D Rklij
Rj i kl D Rij lk DRklij
R
D Rj i kl D Rij lk DRklij
2 ij kl
.f B g/0 .x/ D f 0 .g.x// g 0 .x/
0
2.f Bg/ .x/Df
0 .g.x//g 0 .x/
.f Bg/0 .x/Df 0 .g.x//g 0 .x/
22
f .x/ D
(
jxj
x>a
jxj x a
8
<
f .x/D
:
jxj
x>a
jxj x a
f .x/D
2
22
1
Z
jxj
x>a
jxj x a
e
xx
dx D
p
1
R1
2
1
e
xx
p
dxD R1
xx dxDp
1e
22
XD
X
i
i
X
@
@
C
xj j
i
@x
@xP
P
X D i i
2
j
@
@x i
P
C j xj
@
@x
Pj
P
P
XD i i @ C j x j @
@x i
@x
Pj
22
2
Bold letters in math can be taken from the Times bold symbols:
AX .f / D X.f / D 22
X.g/
We can also get ‘calligraphic’ letters:
A; B; : : : ; Z
Compare
Xf C Xj C Xp C X t C Xy C XA C XB C XD C XH C XI C XK C XL C XM C XP C XX
with the following (with no adjustments):
Xf C Xj C Xp C Xt C Xy C XA C XB C XD C XH C XI C XK C XL C XM C XP C XX
We have the special accent
xV
and can replace
PC R
with
TC U
There are
b 1
1
A
Q
€C b
y CM
€ CM
c C xc
AO C Ay C A
A C CMO C M
y C xyz C xyzw C x C y C z C C w
and
e A
}C z
{ CM
} Cz
AL C A{ C A
A C CML C M
M Cz
xy C xz
yz C xQ
yzw C x C y C z C C w
C e
z CM
 CM
f C xf
AQ C Az C A
A C CMQ C M
y C xyz C xyzw C x C y C z C C w
and
and
x CM
S CxCyCz
MN C M
We have
0 0
B1 0
B
B
˛c 1 ˛c 0 D B 0 1
B: :
@ :: ::
0 0
0
:::
~1
~2
::
:
:::1
~n
0
1
1
versus
˛c 1 ˛c 0 D
0
1
0
0
0
::
:
1
::
:
0
0
:::
~1
~2
::
:
:::1
~n
0
C
C
C
C
C
A
1
Similarly, instead of having to rely on an extensible square root symbol, we can also get individually
designed ones:
v
u n
n
X
uX
t .y i x i /2 vs.
.y i x i /2
p
iD1
iD1
3