Review of Vector Functions
rt ex.
te , lnt , 5 . Find v 1 and a t .
t
2
vt
ex.
1 1 t
2, 2, 2 .
, t 2 , sint 2
. Find
rt
if
r0
r Do: Let t
cost,sint,3t
. Determine if v t is always
orthogonal to a t . Also, find the speed of a particl
UNIT 10: Components of Acceleration and Curvature
Reminders:
is is our last unit of new material. However, you have three deadlines le in order to complete the
course. Please do not forget them:
Quiz
:
due by
Review for Test :
Test :
due by
Review for Fin
UNIT 9: Variable Acceleration, Arc Length, and The Unit
Tangent Vector
Variable Acceleration
In Unit , we covered projectile motion problems in which the acceleration was due to gravity, and was a
constant amount. In these rst few examples from Unit , we
UNIT 8: Velocity, Acceleration, and Projectiles
Vector-valued Functions
A vector-valued function takes a single number (o en time) as an input, and gives a vector as an output.
For example, f (t ) = t , t , sin t is a vector-valued function.
When we di er
UNIT 7: Lines and Planes
In two dimensions, we used the familiar equation y = mx + b to represent a line segment. e value of
m told us the direction in which the line travelled, and the value of b told us the position where the line
was located relative t
UNIT 5: Introduction to Vectors
What is a vector?
A vector is a way of representing a straight line segment by describing the motion of the segment
without reference to its speci c endpoints. We can use vectors to represent any measurement that has
both a
UNIT 4: Complex Numbers
What is a Complex Number?
In high school, you learned that the imaginary number i was de ned to be the square root of , and
that certain quadratic equations had imaginary roots.
At the time, it may not have made much sense why one
UNIT 3: Polar Coordinates
Review
e polar coordinate system is an alternate way of identifying points in the plane. In this system, a
point P is represented by a coordinate pair (r , ), where r denotes the distance from the point to the
origin (or, the len
UNIT 9: Variable Acceleration, Arc Length, and The Unit
Tangent Vector
Variable Acceleration
In Unit 8, we covered projectile motion problems in which the acceleration was due to gravity, and was a
constant amount. In these first few examples from Unit 9,
UNIT 10: Components of Acceleration and Curvature
Reminders:
This is our last unit of new material. However, you have three deadlines left in order to complete the
course. Please do not forget them:
Quiz 10:
due by
Review for Test 3:
Test 3:
due by
Review
UNIT 2: Parametric Equations (continued)
Review: What is parameterization?
In a parametrically-de ned relationship, we introduce a third variable called a parameter (o en t , but
sometimes a di erent letter is used). is third variable acts as a seed for t