Mathematics Flashcards
Vector
A quantity with both direction and magnitude
Usually drawn as an arrow, it’s direction is visible and its length is its magnitude
Written as a letter with an arrow over it
What is cosine?
The ratio of the adjacent to the acute angle to the hypotenuse
It can help in finding the difference between two vectors
What is the purpose of a Differential equation?
A differential equation relates a function with its derivatives
Functions usually represent physical quantities and derivatives represent their rates of change
Differential equations define a relationship between the two
Zenos Dichotomy
The invention of the Limit
To leave a room you must walk 1/2 way. Then from there you must walk 1/2. You repeat this but you never actually escape
Fundamental Theory of Calculus
Two ‘flavours’
Differentiation allows you to break down a property and describe its rate of change
(Position > velocity > accel. > jerk)
Integration allows you to ‘walk up’ from a rate of change to describe a position
(Jerk > accel. > velocity > position)
What does x’ and x’’ mean?
x and y represent the position of a quantity
x’ is the first derivative of x with respect to time (dx/dt) which describes how fast it is moving in x direction
x’’ is the second derivative of x and it represents acceleration. (Means acceleration in x direction)
Angular Velocity
ω
How fast something rotates relative to another point.
What is Brownian Motion
Brownian motion is the conclusion (ending position) of a random walk model.
Brownian motion models unpredictable behaviour that evolves over time, with each change being independent of the previous ones
Divergence
A measure of the quantity of flux emanating from any point in a vector field
Positive means something is entering the vector field, negative means something is leaving the vector field
Incongruent
Not the same, incompatible
