antidifferentiating applications, start kinematics & light/matter ref

diff --git a/physics/light-matter-ref.md b/physics/light-matter-ref.md
new file mode 100644 (file)
index 0000000..386c83c
--- /dev/null
+++ b/physics/light-matter-ref.md
@@ -0,0 +1,15 @@
+---
+geometry: margin=2cm
+columns: 2
+graphics: yes
+author: Andrew Lorimer
+---
+
+\pagenumbering{gobble}
+
+# Light and Matter
+
+$$E=hf={hc \over \lambda}$$
+
+$$ 1 \operatorname{eV} = 1.6 \times 10^{-19} \operatorname{J}$$
+

diff --git a/physics/light-matter.md b/physics/light-matter.md
index c14d9983a7f85963172890c875ab929c47f6aa3c..6eed91fd38e83d45b7ff1c3743a49d38284f63f9 100644 (file)
--- a/physics/light-matter.md
+++ b/physics/light-matter.md
@@ -149,7 +149,7 @@ $$\sigma E \sigma t \ge {h \over 4 \pi}$$
 
 where $\sigma n$ is the uncertainty of $n$
 
 
 where $\sigma n$ is the uncertainty of $n$
 

-**$\sigma E$ and $\sigma t$ are inversely proportional$**
+**$\sigma E$ and $\sigma t$ are inversely proportional**

 
 Therefore, position and velocity cannot simultaneously be known with 100% certainty.
 
 
 Therefore, position and velocity cannot simultaneously be known with 100% certainty.
 

diff --git a/spec/calculus.md b/spec/calculus.md
index f68b82919c49a10219df39feff9141d04660c21c..ddd9011301d70a8d9681fdb5d0c0380ffc8143db 100644 (file)
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -192,8 +192,8 @@ $\int k f(x) dx = k \int f(x) dx$
 
 | $f(x)$                          | $\int f(x) \cdot dx$         |
 | ------------------------------- | ---------------------------- |
 
 | $f(x)$                          | $\int f(x) \cdot dx$         |
 | ------------------------------- | ---------------------------- |

-| $k$ (constant)                  | $kx + c$                     |
-| $x^n$         | ${1 \over {n+1}}x^{n+1} + c$ |
+| $k$ (constant) | $kx + c$ |
+| $x^n$ | ${1 \over {n+1}}x^{n+1} + c$ |

 | $a x^{-n}$ | $a \cdot \log_e x + c$ |
 | $e^{kx}$ | ${1 \over k} e^{kx} + c$ |
 | $e^k$ | $e^kx + c$ |
 | $a x^{-n}$ | $a \cdot \log_e x + c$ |
 | $e^{kx}$ | ${1 \over k} e^{kx} + c$ |
 | $e^k$ | $e^kx + c$ |


@@ -213,4 +213,18 @@ $\int k f(x) dx = k \int f(x) dx$
 
 To find stationary points of a function, substitute $x$ value of given point into derivative. Solve for ${dy \over dx}=0$. Integrate to find original function.
 
 
 To find stationary points of a function, substitute $x$ value of given point into derivative. Solve for ${dy \over dx}=0$. Integrate to find original function.
 

+## Kinematics
+
+$${dV \over dt} = {\operatorname{change in volume} \over \operatorname{respect to time}}$$
+
+`     |->--diff-->--| |-->--diff-->--|
+displacement    velocity    acceleration
+ |--<-antidiff-<---| |--<-antidiff-<-|`
+
+**displacement $x$** - change in position  
+**velocity $v$** - change in displacement  
+**acceleration $a$** - change in velocity
+
+$$v_{\operatorname{avg}}={\Delta x \over \Delta t}={{x_2 - x_1} \over {t_2 - t_1}}$$
+$$\operatorname{speed}_{\operatorname{avg}}={\Delta v \over \Delta t}$$