update notes

diff --git a/chem/analysis.md b/chem/analysis.md
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+# Chemical Analysis
+
+_Salt - ionic compound formed by acid/base reaction_
+
+## Analysis methods
+
+**Quantitative** - measuring values  
+**Qualitative** - measuring categories or simple observation of characteristics
+
+### Electrical conductivity
+
+- quick and inexpensive
+- ionic salts are conductive
+- measures combined levels of dissolved salts
+- measured in EC units
+
+### Colorimetry
+
+- e.g. universal indicator (pH), or chlorine analysis
+- colour levels are compared with standards
+- colour can be natural or caused by reaction with an added chemical (dye)
+- instrumental colorimeter - compares subject with samples of known coloration
+- **complment** of a colour is the colour left after original colour is removed from white light (inverse)
+
+![](graphics/colorimeter.jpg)
+
+### Gravimetric analysis
+
+- precipitates are collected and dried
+-
+
+## Stoichiometry
+
+- analysis of ratios
+- calculations based on chemical equations
+- can predict relative amount of substances involved in chemical reactions
+- chemical equations do not indicate rate or extent of a reaction
\ No newline at end of file

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diff --git a/english/quotes.md b/english/quotes.md
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+# _Gattaca_ and _Stasiland_ quotes  
+
+### Character list  
+
+**Miriam** - married to Charlie. Tortured, escaped and rebelled as teenager.    
+**Julia** - Anna's roommate. Raped & imprisoned.    
+**Charlie** - dead husband of Miriam    
+**Hagen Koch** - wall cartographer. rebels against regime because Stasi attempted to end marriage.    
+**Herr Bohnsack** - former Stasi informant    
+**Klaus** - singer    
+**Frau Paul** - mother of Torsten who was taken away from her    
+**Herr Boch** - former Stasi professor, recruits informants  
+
+## Oppression & discrimination  
+
+[g] "never suffered from the discrimination of a 'utero'"  
+[g] society looks "so hard for any flaw that after a while that's all you see"  
+[g] "I'll never understand what possessed my mother to put her faith in God's hands"  
+[g] "I was never meant for this world"  
+[g] "everything he needed to get into Gattaca.. except the will to do so"  
+[s] "we are here to inform you today, that you don't exist any more" - re Miriam  
+[s] "in this country, any kind of printing is forbidden" - Koch  
+[s] "there is not unemployment in the GDR" - employment officer to Julia  
+[s] "I inhabit the grey end of the spectrum" - Miriam  
+[s] "a choreography of very nasty scouts"  re. Stasi informants  
+[g] "I lent you my body, you lent me your dream"
+
+## Rebellion
+
+[s] "instead of shooting cardboard figures we'd have to shoot our own peope" - Herr Bohnsack  
+[s] "I thought it was something we had to do because they were robbing us blind" - Koch, p.170  
+[s] "by 1961, about 2000 people were leaving the East each day"  
+[s] "if there's no way aroundn it, we just have to crash through somehow"  
+[s] "I have to leave here forever - I have to leave my family, and I will not see my sisters again, and I have to go to the West"  
+[s] "I have always had an acute sense of duty to obey the law" - Koch
+
+## Suffering
+
+[s] "they break you.. just like fiction" - Miriam  
+[s] "I will do whatever you ask... but that plate stays there" - Koch  
+[s] "I went to see him that time, and of course I wanted more" - Frau Paul, re Torsten  
+[s] "she told himt o go to hell and found a smallish funeral establishment" - Miriam  
+[s] "they really made sure that I didn't sleep" - Miriam  
+[s] "I was basically no longer human" - Miriam  
+[s] "I think I am definitely psychologically damaged" - Miriam  
+[g] "a child conceinved in love has a better chance of happiness"  
+[g] "I'd need an awful lot more than a drop if I was going to get anywhere" - Vincent re blood brothers  

diff --git a/methods/calculus.md b/methods/calculus.md
index 2d029fb6fe4dd67247be61f635b4e5bf93e5da46..fb19fdbbe08568cc94bf2f1e7e31b040ff08fa22 100644 (file)
--- a/methods/calculus.md
+++ b/methods/calculus.md
@@ -24,7 +24,7 @@ Average rate of change between $x=[a,b]$ given two points $P(a, f(a))$ and $Q(b,
 Tangent to a curve at a point - has same slope as graph at this point.
 Values for $\Delta$ are always approximations.
 
 Tangent to a curve at a point - has same slope as graph at this point.
 Values for $\Delta$ are always approximations.
 

-Secant - line passing through two points on a curve
+Secant - line passing through two points on a curve  

 Chord - line segment joining two points on a curve
 
 Instantaneous rate of change is estimated by using two given points on each side of the concerned point. Evaluate as in average rate of change.
 Chord - line segment joining two points on a curve
 
 Instantaneous rate of change is estimated by using two given points on each side of the concerned point. Evaluate as in average rate of change.


@@ -37,10 +37,8 @@ Each point $Q_n<P$ becomes closer to $Q_P$.
 
 ## Position and velocity
 
 
 ## Position and velocity
 

-Position - location relative to a reference point
-
-Average velocity - average rate of change in position over time
-
+Position - location relative to a reference point  
+Average velocity - average rate of change in position over time  

 Instantaneous velocity - calculated the same way as averge $\Delta$
 
 ## Derivatives
 Instantaneous velocity - calculated the same way as averge $\Delta$
 
 ## Derivatives

diff --git a/spec/calculus.md b/spec/calculus.md
index 32ea661272b11761f9e7e6403c91ffc2bdabcb41..503b19142d78c9fca9ee6258ce5f00dbd719e886 100644 (file)
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -83,8 +83,29 @@ If $f(x)=^5\sqrt{x}=x^{1 \over 5}, \quad f^\prime(x)={1 \over 5}x^{-4/5}={1 \ove
 If $f(x)=(x-b)^2, \quad f^\prime(x)=2(x-b)$
 
 $$f^\prime(x)=\lim_{h \rightarrow 0}{{f(x+h)-f(x)} \over h}$$
 If $f(x)=(x-b)^2, \quad f^\prime(x)=2(x-b)$
 
 $$f^\prime(x)=\lim_{h \rightarrow 0}{{f(x+h)-f(x)} \over h}$$

-$$=\lim_{h \rightarrow 0}

 
 ## Euler's number as a limit
 
 $$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$
 
 ## Euler's number as a limit
 
 $$\lim_{h \rightarrow 0} {{e^h-1} \over h}=1$$

+
+## Chain rule
+
+Leibniz notation:
+
+$${dy \over dx} = {dy \over du} \times {du \over dx}$$
+
+Function notation:
+
+$$(f\circ g)^\prime(x)=f^\prime(g(x))g^\prime(x),\quad \mathbb{where}\hspace{0.3em} (f\circ g)(x)=f(g(x))$$
+
+Used with only one expression.
+
+e.g. $y=(x^2+5)^7$ - Cannot reasonably expand  
+Let $u-x^2+5$ (inner expression)  
+${du \over dx} = 2x$  
+$y=u^7$  
+${dy \over du} = 7u^6$  
+
+
+$7u^6 \times$
+