184_notes:math_review

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184_notes:math_review [2017/08/24 16:05] – [Vector Multiplication] tallpaul184_notes:math_review [2018/05/17 13:31] – [Vector Notation] curdemma
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 +[[184_notes:defining_a_system|Next Page: Defining a System]]
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 ===== Math Review ===== ===== 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. +The following mathematical ideas are important to understand and to 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 ==== ==== Scientific Notation ====
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 ==== Vector Notation ==== ==== Vector Notation ====
  
-{{ course_planning:course_notes:3d_vector.png?300| A position vector defined in 3D space}} +[{{ course_planning:course_notes:3d_vector.png?300| A position vector defined in 3D space}}] 
-Vectors are typically drawn as an arrow. The length of the arrow represents the magnitude of the vector, and the arrow points in the same direction as the vector. The triangle end of the arrow is typically referred to as the "head" or "tip", with the other end of the arrow being the "tail". When drawn this way, a vector can easily be moved around in space as it is the difference between the tip and the tail that defines the vector itself. The tail of the arrow has no meaning besides what we assign it, for example, the location at which the vector quantities is measured.+Vectors are typically drawn as arrows. The length of the arrow represents the magnitude of the vector, and the arrow points in the same direction as the vector. The triangle end of the arrow is typically referred to as the "head" or "tip", with the other end of the arrow being the "tail". When drawn this way, a vector can easily be moved around in space as it is the difference between the tip and the tail that defines the vector itself. The tail of the arrow has no meaning besides what we assign it, for example, the location at which the vector quantities is measured.
  
 We can also define a vector in "bracket" notation: We can also define a vector in "bracket" notation:
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       *If you dot two vectors that are perfectly perpendicular, you will get zero.        *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.       *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, 
 $$\vec{a}\bullet\vec{b} = \vec{b}\bullet\vec{a}$$ $$\vec{a}\bullet\vec{b} = \vec{b}\bullet\vec{a}$$
  
  • 184_notes/math_review.txt
  • Last modified: 2020/08/24 19:30
  • by dmcpadden