education/math/MATH1060 (trig)/Vectors.md

@@ -1,57 +1,8 @@
-A vector is a mathematical concept that denotes direction and magnitude. They're often notated using an arrow ($\vec{v}$), or with a bold, lowercase letter. (**v**).
+A vector is a mathematical concept that denotes direction and magnitude. They're often notated using an arrow ($\overrightarrow{v}$), or with a bold, lowercase letter. (**v**).
 
 
-Vectors are often denoted as a matrix with two rows: $\begin{bmatrix}1 \\2\end{bmatrix}$
-# Component Form
-If $\vec{v}$ is a vector with the initial point $(x_y,\ y_i)$, and a terminal point $(x_t,\ y_t)$, we can express $\vec{v}$ in component form as $\vec{v} = \langle x_t - x_i,\ y_t, -y_i \rangle$ 
-# Magnitude
-The magnitude of a vector is $|\vec{v}| = \sqrt{a^2 + b^2}$
-
-# Direction
-The direction of a vector is $\theta = \tan^-1(\frac{b}{a})$.
-
-# Addition
-To find $\vec{u} + \vec{v}$, we can put one vector on the end of another vector. The resulting vector will share the same tail as the first vector, and the same head as the second vector.
-
-# Scalar Multiplication
-A **scalar** is just a real number. Scalar multiplication is multiplying a vector with a real number. This will scale or shrink a vector, but does not change the direction it points at.
-
-We do not multiply two vectors together.
-# Unit Vector
-A vector with a magnitude of 1 is a **unit vector**.
-
-If $\vec{v}$ is a nonzero vector, the unit vector can be found using the equation $\vec{u} = \dfrac{1}{|\vec{v}|}\vec{v}$ . In other words, to find a unit vector, divide the vector by its magnitude.
-
-# $i$, $j$ Notation
-Every 2d vector has a horizontal component and a vertical component. The horizontal unit vector could be written as $i = \langle 1, 0 \rangle$, and the vertical unit vector could be written as $j = \langle 0, 1 \rangle$ Every vector can be made up using a combination of these standard unit vectors.
-
-# Trigonometric Form
-Given a vector $\vec{v}$ with a magnitude $|\vec{v}|$ and direction $\theta$:
-
-The component form is given as:
-
-$$ \vec{v} = \langle \cos \theta,\ |\vec{v}|\sin\theta \rangle $$
-
-# Standard position
-- A vector is in standard position if the initial point is at $(0, 0)$.
-
-# The Dot Product
-The dot product of two vectors $\vec{u} = \langle a, b \rangle$ and $\vec{v} = \langle c, d \rangle$ is $\vec{u} * \vec{v} = ac + bd$.
-
-- Given that $\vec{u} = \langle -7, 3 \rangle$, and $\vec{v} = \langle -3, 4 \rangle$, find $\vec{u} * \vec{v}$.
-- $\vec{u} * \vec{v} = -7 * -4 + 3 * 4$
-
-The dot product can be used to find the angle between two vectors.
-
-If $\theta (0\degree < \theta < 180\degree)$, is the angle between two nonzero vectors $\vec{u}$ and $\vec{v}$, then
-$$ \cos\theta = \dfrac{\vec{u}*\vec{v}}{|\vec{u}||\vec{v}|} $$
-
-# Work
-The dot product can be used to compute the work required to move an object a certain distance.
-
-To compute work, you need a force and direction. If the force is applied in the same direction:
-
-$$ W = Fd $$
-
-The work $W$ is done by a constant force $\vec{F}$ in moving an object from a point $P$ to a point $Q$ is defined by:
-$$ W = \vec{F} \cdot\vec{PQ} = |\vec{F}||\vec{PQ}|\cos\theta $$Where $\theta$ is the angle between $\vec{F}$ and $\vec{PQ}$.
+$$\begin{bmatrix}
+1 \\
+2
+\end{bmatrix}
+$$

education/nutrition/Review.md

@@ -1,116 +0,0 @@
-# Macronutrients
-- We need a larger amount
-- Provides Calories
-## Carbohydrates
-- Provides 4 calories per gram
-- The storage form of carbohydrates in the body is as glycogen (very branched sugar). Stored in muscles and in liver
-- Only **monosaccharides** can be directly absorbed. Everything else must be broken down first.
-### Simple
-- Mono/Disaccharides
-Monosaccharides include:
-- Glucose
-- Fructose (fruit sugar)
-- Galactose
-Disaccharides include:
-- Sucrose (glucose + fructose)
-- Maltose (glucose + glucose)
-- Lactose (glucose + galactose)
-### Complex
-- Polysaccharides
-Polysaccharides include:
-- Starches
-	- Amalose
-	- Amalopectin (More branched)
-- Fiber
-	- Photosynthesis +Sun + carbon + hydrogen + oxygen
-
-## Protein
-- Provides 4 calories per gram
-- Protein is composed of amino acids
-- There are **9 essential** amino acids
-- There are **11 non-essential** amino acids
-	- Donkey bridge: If it starts with the letter A, it's a non-essential amino acid
-- Protein has nitrogen alongside hydrogen, carbon, and 
-- To use protein as energy, it must be **deanimated**.
-## Lipids/Fats
-- Provides 9 calories per gram
-- Fat is composed of hydrocarbon chains
-- Tryglicerine - 3 fatty acid chains, with glycerol backbone
-### Saturated Fats
-- Saturated fats have no double bonds
-### Unsaturated Fats
-- Unsaturated fats have one or more double bond
-
-### HDL (High Density Lipoprotein)
-- We want high HDL levels
-- Takes cholesterol out of the cells to the liver to be excreted
-### LDL (Low Density Lipoprotein)
-- We want low LDL levels
-- Takes cholesterol into arteries
-### oLDL (Oxidized Low Density Lipoprotein)
-- Damaged LDL
-- Deposits plaque
-# Micronutrients
-- Smaller Amounts
-- Don't provide calories
-## Vitamins
-## Minerals
-
-## Water
-- Not a macro or micronutrient, but still one of the 6 major nutrition groups
-## Alcohol
-- While not in a food group, provides 7 calories per gram
-
-# Digestive System
-1. Mouth
-	- Digestion of carbs/starches, and fats begin here.
-	- Mechanical digestion (chewing)
-	- Chemical digestion (amalayses (starch) and lipases (fat) in the mouth)
-2. Esophagus
-	- Peristalsis is an involuntary relaxation and contraction of muscles to move food down 
-1. Gastroesophageal/Lower Esophageal/Cardiac Sphincter
-	- When this sphincter misfires, it can cause heartburn or gastroesphageal reflex disease (GERD)
-2. Stomach
-	- Protein 
-3.  Pyloric Sphincter
-4. Small Intestine (DJI)
-	1. Duodenum
-	2. Jejunum
-	3. Ilium
-5. Ilieocecal Valve
-
-# DRI (Dietary Reference Intakes)
-## EAR (Estimated Average Requirement)
-- Meet the requirements of 50% of healthy individuals
-## RDA (Recommended Daily Allowance)
-- 97.5% of healthy people
-- EAR plus a margin of safety
-## AI (Adequate Intake)
-- The average amount of nutrients a healthy population needs to consume
-## UL (Upper Limit)
-- Prevents overconsumption
-## AMDR (Acceptable Macronutrient Distribution Range)
-- Carbs: 45-65% / kCal
-- Protein: 10-35% / kCal
-- Fats: 20-35% / kCal
-## EER (Estimated Energy Requirements)
-- Average estimated caloric needs
-- Actual needs vary
-
-# Hormones
-## Insulin
-Insulin is made by the beta cells in the pancreas, and promotes absorption of glucose from the blood into liver, fat, and skeletal muscles.
-- Insulin is released when blood sugar levels are too high
-## Glucagon
-Glucagon is a peptide hormone, produced by the alpha cells of the pancreas. It's the opposite of insulin, and it increases blood sugar levels. 
-- Glucagon is released when blood sugar levels are too low
-## Ghrelin
-Ghrellin is known as the "hunger hormone", and it increases the drive to eat. It increases gastric motility and stimulates the secretion of gastric acid.
-## Leptin
-Leptin's primary role is to regulate long-term energy balance. High leptin levels indicate to the brain that energy reserves are high.
-
-# Study Types
-## Exprimental
-- A systematic way of testing a hypothesis
-## Epidemiological
-- Observations of the occurrence, distribution, and associations