Admin:
  1) Up-to-date syllabus on website (link in blackboard)
  2) Lab 2 due next week.
    - Format not critical.
	- Include all measurements somewhere.
	- Repeated (>5) measurements in separate file (xls,mat,m,txt,json,xml,...).
    - Final measurements with errors in standard form in pdf.
    - Images in pdf or as separate file.
    - Graphs in pdf. 	
	- rule of thumb: anything you discuss in text should be in pdf. 
  3) Probably only 6 labs.  12 point for free.
  
Review:  
  1) Error <=> Uncertainty
    - Unavoidable
	- Not mistakes
  2) Individual error estimates:
    - Visual Scale
    - Repeated measurement: range or std
  3) Standard form:
    - Significant figures of best estimate +/- Significant figures of centered error
  4) Error propagation:
    - N measurements: x1 +/- Dx1,...,xN +/- DxN
	- q(x1,...,xN) +/- sqrt[(dq/dx1 Dx1)^2+...+(dq/dxN DxN)^2] 
    - +- errors add in quadrature
    - */ fractional errors add in quadrature
    - q=Bx => Dq=abs(B)Dx
  5) Quadrature
  6) Error in the mean
	- plug in <x>=(1/N)*(x1+...+xN); Dx1...DxN=Dx==std(x); D<x>=Dx/sqrt(N);
    - Conditions: random (symmetric) and uncorrelated

Statistics of uncertainties:
  1) Mean: <x>=(1/N)*(x1+...+xN);
  2) STD: Measured Dx=<Dx>=std(x)=sqrt[(x1-<x>)^2+...+(xN-<x>)^2]/(N-1)
  3) Random vs systematic
  4) +/- std(x) covers 68% of error
  5) Use mean to decrease random error: D<x>=Dx/sqrt(N)
  6) Can not eliminate systematic
    - D<x>_tot = sqrt(D<x>^2+D_sys<x>^2)

Rejecting data:
  1) Read section, but don't do it
  
Least-Squares-Fitting:
  1) Measure x,y points on a function y(x)
  2) chi-squared = X^2= [(y(x1;P1...PN)-y1)^2+...+(y(xN;P1...PN)-yN)^2]/std(y)
  3) Find minimum X^2 over P1...PN	
  4) a=polyfit(x,y,N);
  5) yfit=polyval(a,x);
  6) fminsearch(@(P) chi(P,x,y),[P1,P2]);  % non-linear 
  7) Change to linear
    - Exponential: y = A exp(B x) => log(y) = log(A) + B x 
	  - linear in log(y),x 
	  - P1=log(A),P2=B
	- Power law: y = A x^B => log(y) = log(A) + B log(x) 
	  - linear in log(y), log(x) 
	  - P1=log(A), P2=B
	- Logrythmic: y = A log(x^B) => y = exp(A) + B log(x)
	  - linear in y, log(x)
	  - P1=exp(A), P2=B