maths B Flashcards
What is the del operator?
What is grad?
What is the div operator?
the answer should be a scalar
What is the curl operator?
What is a scalar field?
A function that takes 2 or three values in and outputs one.
What is a vector field?
That is to say you put three values in and you get three values out
What does |a| and ||a|| denote?
|| || denotes the magnitude of a bound vector. That is to say a vector with an origin.
| denotes the magnitude of a free vector
What is the dot product equal to in terms of the angle between vectors?
A.B=|A| |B| cosα
How can you define the cross product?
AxB=|A| |B| n sinα
n is a unit vector perpendicular to both a and b pointing in the direction defined by the right hand rule.
What is the definition of the line integral of a scalar field?
How do you find the line integral of a vector field?
How can you determine whether a vector field is conservative?
if curl (f)=0 it is conservative
How do you find the scalar potential of a conservative vector field, f?
grad(φ)=f
How do you find the work done moving from one point to another when you have the scalar potential?
Calculate the potential at the two different points and the difference is the work
What is the laplace operator?
Δ=div grad
∇.∇=∇2=Δ
There is also the vector laplacian
If you have the cyclindrical co-ordiantes, ρ,Φ,z, how would you express it in cartesian co-ordinates?
r=ρcosΦi + ρsinΦj + zk
What is the formula of integration by parts?
In 3D, what is the general form from going to one set of basis to another?
If you have three vectors, how do you know if they are right handed?
You cross product two of them together to make the third
How do you evaluate a surfce integral of the first kind?
The first kind means you are integrating within a scalar field
How do you evaluate the surface integral of the second kind?
What is the parametic equation of a sphere radius r, centred at the origin?
R*cos(t)sin(s), R*sin(t)sin(s), R*cos(s)
t betweeb 0 and 2π
s between 0 and π
What is a positively oriented curve?
A positively oriented curve is a closed piecewise smooth simple (non-intersecting) curve whose interior is on the left as we traverse the curve.
This means that, in order to have a positively oriented curve, a particular parametrization r(t) : [a, b] has to be chosen so that starting at t = a, we travel, roughly speaking, in the counter-clockwise direction around the curve as t increases from a to b.
What is stoke’s theorem?
What is the Gauss divergence theorem?
The triple inegral is the exprestion for the volume of the shape.
What is grad of a vector field?
