Advanced Mathematics Equations and Constants, Exams of Physics

A collection of advanced mathematics equations and constants, including trigonometric functions, integrals, derivatives, and physical constants. It covers topics such as calculus, differential equations, and thermodynamics.

Typology: Exams

2021/2022

Uploaded on 09/07/2022

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bg1
( , ) sin ( )
m
y x t y k x t

2
k
22f
T


v

22
1
2
avg m
P v y

( , ) [2 sin ]cos
m
y x t y kx t
1,2, 3,....
2
vv
f n n
L
cos( )
m
s s k x t

sin ( )
m
p p k x t
vB
mm
p v s


1,2, 3,4,...L

0.5,1.5,2.5,...L

2
L

2
4
s
P
Ir
22
1
2m
I v s

(10 )log
o
I
dB I
D
S
vv
ff
vv
1,3,5,...
4;f n n
L
v

273
C
o
TT
932
5
o
FC
TT
L L T
;3V V T
Q Lm
Q cm T
int
E Q W
f
V
Vi
W dW PdV

4
rad
P AT

4
abs env
P AT

HC
cond
Q T T
P kA
tL

PV nRT NkT
ln f
i
V
W nRT V
3
rms
RT
vM
3
2
avg
K kT
V
Q
CnT
P
Q
CnT
PV
C C R
int V
E nC T
=
3;
2V
p
V
C
C
CR
1
TV Constant
PV Constant
f
i
dQ
ST

ln




 f
i
T
S mc T
ln ln
V
ff
ii
VT
S nR nc
VT
HL
W Q Q
HL
HL
QQ
TT
H
W
Q
L
Q
W
K
11
LL
c
HH
QT
QT
HL
LL
c
HL
QT
KQ Q T T


12
2
1
4o
qq
Fr

2
1
4o
q
Er

2o
E
.E dA
o
F
Eq
3
4o
q
Er
R




o encnet q
Ep
o
E
p qd
.UEp
U q V
2o
Er

Es
f
fi
i
if
V V V d
UW
11
1
4
nn
i
i
ii
oi
q
VV
r




1
4o
q
Vr

;;
x y z
V V V
E E E
x y z
12
1
4
o
qq
Ur

q CV
22
1
22
q
U CV
C

2
1
2o
uE
2ln
o
L
Cba

oA
Cd
4-
o
ab
Cba

air
CC
dq
idt
()
d
J ne v
.i J dA
1

E
J
P iV
VL
RiA

()
o o o
TT
t RC
o
q q e
1t RC
q C e

ot RC
q
ie
RC

t RC
ie
R
B

B
F q v B
NiA

B
F i L B
.UB


4
oi
BR

2
4
ˆ
oi
dB r
ds r
2
oi
BR
.
o enc
B d s i
o
B ni
2
o a b
ba
Li i
Fd
2 2 2
B L v
PR
.
net B dA
B
d
N
dt

BLv
2
2 2 2
2
;
1
; ; 2
21
0; 2
r
o o o
mv
F ma F R
v v at x v t at v v a x
k U K mv
CONSTANTS
12 22
8.854 10 C N m
o

23 1
6.022 10 mole
A
N
824
5.6704 10 W / m K

52
1 1.01 10 N / matm 
19
1 1.602 10 JeV

343 m / s
air
v
19
1.602 10 Ce

12 2
10 W / m
o
I
7
4 10 T m A
o


31
9.11 10 kg
e
m
27
1.673 10 kg
p
m

2
9.8 m / sg
8.314 J / mole.KR
33
1 10 mL
23
1.381 10 J Kk

1 4.1868Jcal
FOR WATER
4187 J / kg.Kc
3
1000 /kg m
2256 kJ / kg
V
L
g333 kJ / k
F
L
PREFIXES
3
10k kilo
3
10m milli

6
10Mmega
6
10micro

9
10G giga
9
10n nano

12
10T tera
12
10p pico


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y x t( , )  ym sin ( k x  t)

2 k

2 2 f T

v   

P avg   v ym

( , ) [2 cos ]sin ( 2) 2

y ^ x t  y m  kx  t 

y ( , )^ x t [2 ym sin kx] cos t

v v f n n  L

s  sm cos ( k x  t)

 p  p (^) m sin ( k x  t)

v  B  ^ p^ m^ ^ ^ v^ sm

L 1, 2, 3, 4,... L 0.5,1.5, 2.5,...

2

L   

  2 4

I^ P^ s r

I   v sm (10^ ) log o

I

dB I

D

S

v v f f v v

1,3,5,... 4

f n ;n

L

v  

C^273

o T  T

o TF  TC

L  L  T V^ ^ V^ ^ T^ ;^ ^ ^3 

Q Lm Q  cm T

 E (^) int  Q W

Vf

Vi

W   dW PdV

4 P rad  AT

4 P abs  ATenv

H C cond

Q T T

P kA t L

PV  nRT NkT ln

f

i

V

W nRT V

rms

RT

v M

K avg  kT

V

Q

C

n T

P

Q

C

n T

CP  CV R  E (^) int  nCV T

=

2 V

p V

C

C

C  R 

1 TV Constant

   PV Constant

 

f

i

dQ S T

   ln

       

  f i

T

S mc T

ln (^) Vln

f f

i i

V T

S nR nc V T

W  QH QL

H L

H L

Q Q

T T

H

W

Q

  L

Q

W

K 

c^1 L^1 L H H

Q T

Q T

H L

L L c H L

Q T

K

Q Q T T

1 2 2

(^4) o

q q F  r

2

(^4) o

q E  r

(^2) o

E

   E dA. 

o

F

E

q

3 (^4) o

q E r R

o  (^) net qenc

 p E

o

E

p qd U  p.E

U  q V (^2) o

E

r



E s

f

f i i

V if  V  V    d U  W

1 1

1

4

n n i i i (^) o i i

q V V  (^)   r

(^4) o

q V  r

x ;^ y ; z

V V V

E E E

x y z

o

q q U  r

q CV

2 (^12)

2 2

q U CV C

u  oE

ln

o

L

C

b a

  o^

A

C

d

 o

ab

C

b a

 C  Cair

dq i dt

 J^ (^ ne v)^ d i^ ^ J dA.

1  

E J

 

P iV

V L R i A

  

   (^) o   o ( T To) q q eot RC

t RC q C  e

    o^ 

q t RC i e RC

  

 

t RC i e R

    B

FB  q  v B^  NiA

FB  i  L B U      .B

4

B oi R

2 4

 o i^  dB r

^ d s^ r

B oi R

  B d s.  o enci

B  oni

2

o a b ba

Li i F d

2 2 2 B L v P R

 ^ net B dA.

N^ d B dt

 ^ BLv

2

2 2 2

2

;

1 ; ; 2 2 0; 1 2

 

       

    

r

o o o

F ma F mv R

v v at x v t at v v a x

k U K mv

CONSTANTS 12 2 2 o 8.854 10 C N m

    23 1 6.022 10 mole

 NA 

  5.6704  10 ^8 W / m^2 K^4

1 atm  1.01 10 N / m^5

1 eV  1.602  10 ^19 J 343 m / s vair  19 e 1.602 10 C

  

12 2 Io 10 W / m

  7 o 4  10 T m A

31 me 9.11 10 kg

   27 mp 1.673 10 kg

   g  9.8 m / s^2

R 8.314 J / mole.K 1 L  10 ^3 m^3

k  1.381  10 ^23 J K^1 cal^ 4.1868 J FOR WATER

c 4187 J / kg.K  1000 kg /m^3

LV 2256 kJ / kg LF 333 kJ / kg PREFIXES k  kilo 103 m  milli  10 ^3 6 M  mega 10   micro 10 ^6

G  giga 109 9 n  nano  10  12 T  tera 10 p  pico  10 ^12