memo
pChem

 - 1st law of thermo dynamics
   dU = q + w
   dU: internal energy change
   q : heat to the system
   w : work to the system
 - isothermal expansion
   q = -w; heat to the system is equal to work done by environment
   give 10kJ work to system, w = 10kJ
   system did 10kJ work, w = -10kJ
   give 10kJ heat to system, q = 10kJ
   system lose 10 kJ heat, q = -10kJ
   T = fixed
   dU= 0
   P_i*V_i=P_f*V_i

 - adiabatic expansion
   q = 0
   w = -du
   Pi*Vi^gamma=Pf*Vf^gamma, gamma=Cp/Cv

math
   x^n * e^(^ax) dx = n!/(a^(n+1))
   scalar projection a onto b = |a| dot b_unit, |b_unit|=1
   lim sin(t)/t=1
   t->0

cheating sheet for TI89

tan'x=sec^2 x
csc'x=-cscxcotx
sec'x=secxtanx
cot'x=-csc^2 x
sin-1'x=1/sqrt(1-x^2)
cos-1'x=-1/sqrt(1-x^2)
tan-1'x=1/(1+x^2)
csc-1'x=-1/(x sqrt(x^2-1))
sec-1 x=1/( x sqrt(x^2-1))
cot-1'x=-1/(1+x^2)
int secx dx=ln|secx+tanx|
int tanx dx=ln|secx|
int dx/(x^2+a^2)=(1/a)tan-1(x/a)
int dx/(x^2-a^2)=1/(2a)ln|(x-1)/(x+a)|
int cscx dx=ln|cscx-cotx|
int cotxdx=ln|sinx|
int dx/sqrt(a^2-x^2) dx=sin-1(x/a)
int dx/sqrt(x^2+-a^2)=ln|x+sqrt(x^2+-a^2)|

int udv=uv-int vdu

sin(x+y)=sinxcosy+cosxsiny
sin(x-y)=sinxcosy-cosxsiny
cos(x+y)=cosxcosy-sinxsiny
cos(x-y)=cosxcosy+sinxsiny
tan(x+y)=(tanx+tany)/(1-tanxtany)
tan(x-y)=(tanx+tany)/(1+tanxtany)

sinAcosB=1/2{sin(A-B)+sin(A+B)}
sinAsinB=1/2{cos(A-B)-cos(A+B)}
cosAcosB=1/2{cos(A-B)+cos(A+B)}

sin2x=2sinxcosx
cos2x=cos^2x-sin^2x=2cos^2x-1=1-2sin^2x
tan2x=2tanx/(1-tan^2x)

a^2=b^2+c^2-2bccosA