MATH 0240 Lecture Notes - Lecture 4: Euclidean Vector, Ellipse, Parametric Equation
Document Summary
In this section we need to take a look at the equation of a line in section the equation ymx b. This doesn"t mean however that we can"t write down an equation for a line in 3-d space. We"re just going to need a new way of writing down the equation of a curve. So, before we get into the equations of lines we first need to briefly look at vector functions. We"re going to take a more in depth look at vector functions later. At this point all that we need to worry about is notational issues and how they can be used to give the equation of a curve. The best way to get an idea of what a vector function is and what its graph looks like is to look at an example. A vector function is a function that takes one or more variables, one in this case, and returns a vector.
of section 
youu were asked to solve equations in which the unknowns are functions. Now that we know about inverse and the identity function (see exercise 
), we can use algebra to solve 
for unknown function 
, we perform the following steps:
Problem: solve for 
Compose with 
on the right
Because 
Because 
for the indicated unknown function.
and 
