diff --git a/midterm notes b/midterm notes
index 3a08e73..b5a95a3 100644
--- a/midterm notes	
+++ b/midterm notes	
@@ -2,7 +2,18 @@ Sources of error
   Higher precision=higher accuracy for numerical approximation of analytical model
   Truncation (approx of function), roundoff error (fixed number of bits)
   
+  Roundoff error:
   11011 in base 2 = 2^4+2^3+0*2^2+2^1+2^0=27
   1.011=2^0+0*2^-1+2^-2+2^-3=1.375
   Max 8 bit integer: 2^8
   
+Trunction error:
+  Taylor series
+  
+Root finding:
+  Bracketing: incremental
+  Open: newton raphson,  modified secant
+  
+Optimization
+  if derivative is know, min max of f(x)
+  Golden ratio