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F16 PH 333 1.1-1.2.3
Transcript of F16 PH 333 1.1-1.2.3
1.1.1 : Vector Operations
1.1.2 : Vector Algebra
1.1.3 : Triple Products
1.1.4 : Position, Displacement and Separation Vectors
1.1.5 : Vector Transformations
1.2.1 : "Ordinary Derivatives
1.2.2 : Gradient
1.2.3 The Del Operator
Turn to your neighbor and work these out.
Vector Algebra: Components
What is the angle between these two vectors?
D I could do it, but no calculator
E No idea, review please
Just go look them up, here are some
one of your homework will come from here.
Position, Displacement, and Separation vectors
What is the direction of force of attraction between these two charges?
What about these two?
the vector between
In Cartesian coordinates this is messy. but the representation is the same
Vectors Got it!?!
Define (length and direction)
But, components of what, and direction with regard to what?
Define (made of 3 components in 3D)
The key to a vector is to transform from one coordinate system to another.
rotate by o
how was the quiz?
how was the reading?
"Can you explain tensor a little better?"
"Could you go over gradients?"
"Would you give us some of the application of cross product and dot product ?."
"For the separation vector, is it easier to use cartesian coordinates?"
"I have a hard time remembering that r is the point at which we're measuring and r' is the point where the source is located. I tend to mix them up. Any suggestions on how I can keep these two straight"
"It was hard for me to understand how matrices related to vector transformation. Also, I think that I would like to review in more detail the del operator. "
z to y & -y to z
y to z & -z to y
x to z & -z to x
z to x & -x to z
y to x & -x to y
x to y & -y to x
x to z, y to x, z to y
z to x, y to z, x to y
Find me the transform matrix that takes rotations around these axis:
but when they do, they can cause other things to change.
when anything changes we call it
if it is a variable (like x) then
if they are associated with each other the derivative, ,tells you the proportionality factor.
if it is a function (like f) then
Example position,velocity, and time
Changes in a Vector
What if that function depends on 3 (or more) quantities. If one of them change, how does it affect the function.
The rate of change in elevation and hence the change in elevation itself, depends upon the direction you take
This is where partial derivatives come in, and they aren't that bad.
We define this term to be called the gradient.
points in direction of biggest change
magnitude gives the rate of change
What is the gradient of
E Not sure, please review some more
The nabla symbol is called the Del operator, it 'acts' on things, and is not a vector by itself.
We define vector multiplication in three ways
The del operator is the same
Vector operations of Del
- easy, dot, cross
- again, but in components
- look them up
- useful later
- bit of math, but nice to have
- what a derivative is
- partial derivative, def. of Grad
- vector operator
"I’ve never learned about triple products or tensors"