glitches

Author: smidl

docs/src/lecture_12/lecture.md

@@ -132,8 +132,14 @@ which trivially applies to sum: ``x_1+x_2=N(\mu_1+\mu_2, \sqrt{\sigma_1^2 + \sig
 
 
 ## Vector uncertainty
-The approach above competely ignores the covariances between variables
+The approach above competely ignores the covariances between variables. While it is possible to do it linearnly in the same fashion, the approach suffer from a loss of precision under non-linearity.
 
+A more sophisticated approach is based on decomposition of the covariance matrix 
+
+
+# Manipulating ODEs
+
+So far, we have considered first-order ODEs. Many ODEs are defined in higher order form, e.g. 
 
 
 - check Chris Raucausacc latest blog

docs/src/lecture_12/ode.jl

@@ -77,4 +77,5 @@ GX=solve(f,[GaussNum(1.0,0.1),GaussNum(1.0,0.1)],[0.1,0.2,0.3,0.2],0.1,1000)
 M,V=MV(GX)
 plot(M',errorbar=V')
 using Measurements
-GX=solve(f,[1.0±0.1,1.0±0.1],[0.1,0.2,0.3,0.2],0.1,1000)
+MX=solve(f,[1.0±0.1,1.0±0.1],[0.1,0.2,0.3,0.2],0.1,1000)
+plot(MX[1,:])