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--- 184_notes:math_review [2017/08/24 16:00] – [Scientific Notation] tallpaul
+++ 184_notes:math_review [2018/05/15 14:15] – curdemma
@@ Line 1: / Line 1: @@
+[[184_notes:defining_a_system|Next Page: Defining a System]]
 ===== Math Review =====
 The following mathematical ideas are important to understand and be able to use as we will rely on them fairly heavily in this course. These notes will provide a review of these ideas with links to more thorough resources if you feel like you need more information about a topic.
 ==== Scientific Notation ====
-[[https://en.wikipedia.org/wiki/Scientific_notation|Scientific notation]] is particularly useful to represent very large and very small numbers, which will show up in E&M frequently (e.g., charges are very small objects, but the forces they experience are very strong!). The basic form of a number in scientific notation is: $number*10^{exponent}$. For example, if you have a length of $x=5,430,000 m$ then in scientific notation, $x=5.43 \cdot 10^{6} m$.
+[[https://en.wikipedia.org/wiki/Scientific_notation|Scientific notation]] is particularly useful to represent very large and very small numbers, which will show up in E&M frequently (e.g., charges are very small objects, but the forces they experience are very strong!). The basic form of a number in scientific notation is: $number \cdot 10^{exponent}$. For example, if you have a length of $x=5,430,000 m$ then in scientific notation, $x=5.43 \cdot 10^{6} m$.
 Scientific notation also ties into [[https://en.wikipedia.org/wiki/Unit_prefix|unit prefixes]], which are commonly used in physics.  For example, we could write the length of $y=.00000458m$ as $y=4.58 \cdot 10^{-6}m$ or as $y=4.58 \mu m$ (micro-meters). The common prefix names, symbols and scientific notation are shown below.
@@ Line 70: / Line 72: @@
       *If you dot two vectors that are perfectly perpendicular, you will get zero.
       *If you dot two vectors that point directly opposite each other, you will get the //negative// of the magnitudes multiplied together.
-   *The order of the dot product does not matter. This means that $\vec{a} \cdot \vec{b}$ will give you the same answer as $\vec{b} \cdot \vec{a}$, that is,
+   *The order of the dot product does not matter. This means that $\vec{a} \bullet \vec{b}$ will give you the same answer as $\vec{b} \bullet \vec{a}$, that is,
-$$\vec{a}\cdot\vec{b} = \vec{b}\cdot\vec{a}$$
+$$\vec{a}\bullet\vec{b} = \vec{b}\bullet\vec{a}$$
 There are a couple of ways to calculate the dot product:
@@ Line 78: / Line 80: @@
 - **Using vector components** - If you have two vectors given by $\vec{a}=\langle a_x, a_y, a_z \rangle$ and $\vec{b}=\langle b_x, b_y, b_z\rangle$, then you can calculate the dot product by multiplying each component together and adding them together:
-$$\vec{a} \cdot \vec{b} = a_x b_x+a_y b_y+a_z b_z$$
+$$\vec{a} \bullet \vec{b} = a_x b_x+a_y b_y+a_z b_z$$
 - **Using whole vectors and angles** - You can also calculate the dot product by using the magnitudes of the two vectors and the angle between them. Using this method, it is much easier to visualize taking the parallel part of one vector and multiplying by the other vector. It doesn't matter whether you take the part of $\vec{a}$ that is parallel to $\vec{b}$ or the part of $\vec{b}$ that is parallel to $\vec{a}$, you will get the same answer.
-$$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| cos(\theta) = |\vec{a}|cos(\theta)|\vec{b}|$$
+$$\vec{a} \bullet \vec{b} = |\vec{a}| |\vec{b}| cos(\theta) = |\vec{a}|cos(\theta)|\vec{b}|$$
 === Cross Product ===