From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 11 Sep 2018 06:57:41 +0000 (+1000)
Subject: general additions
X-Git-Tag: yr11~41
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/1b07812d144dd0fb7c3e54423a7200eab0135a54?hp=--cc

general additions
---

1b07812d144dd0fb7c3e54423a7200eab0135a54
diff --git a/chem/acids-bases.md b/chem/acids-bases.md
index 32a0d25..50c0919 100644
--- a/chem/acids-bases.md
+++ b/chem/acids-bases.md
@@ -81,3 +81,12 @@ $$[H_3O^+] \times [OH^-] = 10^{-14} \quad \text{(hydrolysis constant)}$$
 Ionic bases dissolving in $H_2O$ - ionic compounds dissociate into constituent ions. Not ionised.
 
 e.g. $NaOH_{(s)}\stackrel{\mathrm{H_2O}}{\longrightarrow}Na^+_{(aq)}+OH^−_{(aq)}$
+
+## pH values
+
+Acid/base/neutral not equivalent to pH (logarithmic scale)
+
+In water at 25C: $[H_3O^+] \times [OH^-]=10^{-7} \therefore \text{pH}=7$
+
+$$\text{pH} = -\log[H_3O^+]=-\log[H^+]$$
+$$[H_3O^+]=10^{-\text{pH}}$$
diff --git a/english/persuasive.md b/english/persuasive.md
new file mode 100644
index 0000000..e69de29
diff --git a/methods/stuff.md b/methods/stuff.md
index 9335409..1eb560c 100644
--- a/methods/stuff.md
+++ b/methods/stuff.md
@@ -1,4 +1,6 @@
-# Index laws
+# random methods shit
+
+## Index laws
 
 $a^m \times a^n = a^{m+n}$  
 $a^m \div a^n = a^{m-n}4$  
@@ -6,6 +8,10 @@ $(a^m)^n = a^{_mn}$
 $(ab)^m = a^m b^m$  
 ${({a \over b})}^m = {a^m \over b^m}$
 
-# Fractional indices
+## Fractional indices
+
+$^n\sqrt{x}=x^{1/n}$
+
+## Logarithms
 
-$^n\sqrt{x}=x^{1/n}$
\ No newline at end of file
+$$\log_b (x) = n \quad \operatorname{where} \hspace{0.5em} b^n=x$$
diff --git a/spec/calculus-ref.md b/spec/calculus-ref.md
new file mode 100644
index 0000000..88ad371
--- /dev/null
+++ b/spec/calculus-ref.md
@@ -0,0 +1,100 @@
+---
+geometry: margin=2cm
+<!-- columns: 2 -->
+graphics: yes
+tables: yes
+author: Andrew Lorimer
+---
+
+# Spec - Calculus
+
+## Gradients
+
+$$m \operatorname{of} x \in [a,b] = {{f(b)-f(a)}\over {b - a}} = {dy \over dx}$$
+
+## Limit theorems
+
+1. For constant function $f(x)=k$, $\lim_{x \rightarrow a} f(x) = k$
+2. $\lim_{x \rightarrow a} (f(x) \pm g(x)) = F \pm G$
+3. $\lim_{x \rightarrow a} (f(x) \times g(x)) = F \times G$
+4. ${\lim_{x \rightarrow a} {f(x) \over g(x)}} = {F \over G}, G \ne 0$
+
+
+## First principles derivative
+
+$$f^\prime(x)=\lim_{h \rightarrow 0}{{f(x+h)-f(x)} \over h}$$
+
+
+## Tangents & gradients
+
+**Tangent line** - defined by $y=mx+c$ where $m={dy \over dx}$  
+**Normal line** - $\perp$ tangent ($m_{\operatorname{tan}} \cdot m_{\operatorname{norm}} = -1$)  
+**Secant** $={{f(x+h)-f(x)} \over h}$
+
+## Derivatives
+
+| $f(x)$ | $f^\prime(x)$ |
+| ------ | ------------- |
+| $kx^n$ | $knx^{n-1}$ |
+| $g(x) + h(x)$ | $g^\prime (x) + h^\prime (x)$ |
+| $c$    | $0$ |
+| ${u \over v}$ | ${{v{du \over dx} - u{dv \over dx}} \over v^2}$ |
+| $uv$ | $u{dv \over dx} + v{du \over dx}$ |
+| $f \circ g$ | ${dy \over du} \cdot {du \over dx}$ |
+| $\sin ax$ | $a\cos ax$ |
+| $\sin(f(x))$ | $f^\prime(x) \cdot \cos(f(x))$ |
+| $\cos ax$ | $-a \sin ax$ |
+| $e^{ax}$ | $ae^{ax}$ |
+| $\log_e {ax}$ | $1 \over x$ |
+| $\log_e f(x)$ | $f^\prime (x) \over f(x)$ |
+
+
+
+## Product rule for $y=uv$
+
+$${dy \over dx} = u{dv \over dx} + v{du \over dx}$$
+
+## Logarithms
+
+$$\log_b (x) = n \quad \operatorname{where} \hspace{0.5em} b^n=x$$
+
+## Integration
+
+$$\int f(x) dx = F(x) + c$$
+
+- area enclosed by curves
+
+| $f(x)$ | $\int f(x) \cdot dx$ |
+| --------------- | ------------------ |
+| $k$ (constant) | $kx + c$ |
+| $x^n$ | ${1 \over {n+1}}x^{n+1} + c$ |
+| $a x^{-n}$ | $a \cdot \log_e x + c$ |
+| $e^{kx}$ | ${1 \over k} e^{kx} + c$ |
+| $e^k$ | $e^kx + c$ |
+| $\sin kx$ | $-{1 \over k} \cos (kx) + c$ |
+| $\cos kx$ | ${1 \over k} \sin (kx) + c$ |
+| ${f^\prime (x)} \over {f(x)}$ | $\log_e f(x) + c$ |
+| $g^\prime(x)\cdot f^\prime(g(x)$ | $f(g(x))$ (chain rule)|
+| $f(x) \cdot g(x)$ | $\int [f^\prime(x) \cdot g(x)] dx + \int [g^\prime(x) f(x)] dx$ |
+| ${1 \over {ax+b}}$ | ${1 \over a} \log_e (ax+b) + c$ |
+| $(ax+b)^n$ | ${1 \over {a(n+1)}}(ax+b)^{n-1} + c$ |
+
+
+## Definite integrals
+
+$$\int_a^b f(x) \cdot dx = [F(x)]_a^b=F(b)-F(a)_{}$$
+
+## Kinematics
+
+**position $x$** - distance from origin or fixed point  
+**displacement $s$** - change in position from starting point (vector)  
+**velocity $v$** - change in position with respect to time  
+**acceleration $a$** - change in velocity  
+**speed** - magnitude of velocity  
+
+| | no |
+| - | -- |
+| $v=u+at$ | $s$ |
+| $s=ut + {1 \over 2} at^2$ | $v$ |
+| $v^2 = u^2 + 2as$ | $t$ |
+| $s= {1 \over 2}(u+v)t$ | $a$ |
diff --git a/spec/calculus-ref.pdf b/spec/calculus-ref.pdf
new file mode 100644
index 0000000..d2ede04
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