MA 2233 Lecture 01 - Orientation in 3D
Monday, August 27, 2012.
Objectives: Warm up to viewing objects in 3 dimensions.
For the most part, we will be extending concepts covered in Calculus I and II to three dimensions. Most of
these things will be related
MA 2233 Lecture 14 - Partial Derivatives and the Gradient
Wednesday, October 3, 2012.
Objectives: Review partial derivatives from labs.
Functions of two variables and partial derivatives
Weve been playing with functions of two variables in the labs. Lets
MA 2233 Lecture 13 - Curvature and the Chain Rule
Monday, October 1, 2012.
Objectives: Introduce arclength parameter and curvature.
The Chain Rule
Working with arclength parametrizations is pretty messy, so what well do is to use the chain rule and do
our
MA 2233 Lecture 15 - Directional Derivatives
Friday, October 5, 2012.
Objectives: Introduce directional derivatives
Directional derivatives
The partial derivatives fx and fy give us the slopes at a point on a surface in the x- and y-directions. Clearly,
t
MA 2233 Lecture 12 - Arclength Parameter
Friday, September 28, 2012.
Objectives: Introduce arclength parameter.
Arclength parameter s
Given a parametrization, we can dene an arclength function
t
(1)
s(t) =
v( )
d
0
that essentially measures distance along
MA 2233 Lecture 11 - Arclength
Wednesday, September 26, 2012.
Objectives: Introduce arclength of a curve.
Computing distance
Example 1. Consider this simple problem. An object is traveling at 12 feet per second for 3.5 seconds.
How far does the object tra
MA 2233 Lecture 09 - Unit Tangent and Unit Normal vectors
Friday, September 21, 2012.
Objectives: Introduce T and N.
Given a parametrization
(1)
r(t) = x(t)i + y(t)j + z(t)k,
we can dierentiate to obtain the velocity and acceleration vectors
(2)
(3)
v(t)
MA 2233 Lecture 07 - Overview of Vector Functions
Friday, September 14, 2012.
Objectives: Collect vector function concepts from labs.
Vector functions in one variable
A vector (valued) function in three dimensions, and in one variable t, will look somethi
MA 2233 Lecture 08 - Tossing Rocks
Monday, September 17, 2012.
Objectives: Use parametrizations to model a physics problem.
Tossing a rock
To give some context to what weve been talking about, lets explore a simple application of our vector
functions.
Wer
MA 2233 Lecture 03 - Intro to graphing and vectors
Friday, August 31, 2012.
Objectives: Intro to vectors and vector arithmetic
Vectors
A vector is a generalization of a number. It consists of a non-negative real number magnitude together with
a direction.
MA 2233 Lecture 02 - Orientation and Intro to graphing and vectors
Wednesday, August 29, 2012.
Objectives: Start looking at graphing and introduce vectors.
Orientation
Lets consider a simple 3D concept using dice.
A die is a cube (roughly), and it has six
MA 2233 Lecture 05 - The Cross Product
Friday, September 7, 2012.
Objectives: Continue vector arithmetic with the cross product
1. Cross product
Our third kind of vector multiplication is called the cross product. [I think Ive heard this also called the
v
MA 2233 Lecture 06 - The Gradient on a Plane
Monday, September 10, 2012.
Objectives: Introduce the gradient on a plane, normal vector, and standard equations.
Review of planes
We went over planes a bit in Lab 02. Lets look at that stu some more.
We can ta
MA 2233 Lecture 04 - More vector arithmetic
Wednesday, September 5, 2012.
Objectives: Continue with vector arithmetic
The standard unit vectors
It will be convenient to have names for the unit vectors that point in the positive x-, y-, and z -directions.
MA 2233 Lecture 10 - Unit Tangent and Unit Normal Vectors (cont.)
Monday, September 24, 2012.
Objectives: Continue T and N with some examples.
v(t)
Note on derivative of
You computed the derivative of v(t) in the quiz last time. You should have gotten
(1)