7/29/2019 Formula Sheet QMA

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ECON 1202/2291 QABE: Selected Formulae

aman = am+n

am

an= amn

(am)n = amn

ln(mn) = ln m + ln n

lnm

n

= ln m ln n

ln(mr) = r ln m

ln1 = 0

I = P rt

S = P(1 + r)n

S = P ert

N P V = F0 + F1(1 + r)1 + ... + FT(1 + r)

T

s =a(1 rn)

1 r

A = R 1 (1 + r)n

r

S = R (1 + r)n 1

r

A = (1 + r)

R

1 (1 + r)n

r

S = (1 + r)

R

(1 + r)n 1

r

(AT)T = A

(A+B)T = AT +BT

(AB)T = BTAT

A(BC) = (AB)C)

A(B+C) = AB+AC

(A+B)C = AC+BC

IA = A

AI = A

(AB)1 = B1A1

(A1)1 = A

(AT)1 = (A1)T

(A+B)1 = A1 +B1

|A2| = a11a22 a12a21

|A3| = a11(a22a33 a32a23)

a12(a21a33 a31a23)

+ a13(a21a32 a31a22)

A1 =1

|A|adj(A)

nPr =n!

(n r)!

nCr =n!

r!(n r)!

P(A B) = P(B) P(A | B)

P(Ai | Bj) =P(Ai)P(Bj | Ai)

P(A1)P(Bj | A1) + ... + P(An)P(Bj | An)

Xn = TXn1 = TnX0

Q = TQ

f(x) = limx0

f(x + x) f(x)

x

(q) = pq

dqdp

xa =1

a + 1xa+1 + c, (a = 1)

1

xdx = ln |x| + c

eaxdx =

1

aeax + c

axdx =

1

ln aax + c, (a > 0, a = 1)

ba

f(x)dx = F(x)]ba = F(b) F(a)

ba

f(x)dx =

ab

f(x)dx

aa

f(x)dx = 0

ba

kf(x)dx = k

ba

f(x)dx

ca

f(x)dx =

ba

f(x)dx +

cb

f(x)dx

N(t) = Aekt

N(t) = M Aekt

N(t) =M

1 + Aekt

z

t=

z

x

dx

dt+

z

y

dy

dt

L = f(x, y) + [c g(x, y)]

|H| =

0 gx gygx Lxx Lxygy Lyx Lyy