Exam Questions Flashcards
are two vectors orthogonal
dot product = 0
evaluate the normal to the plane
n(hat) = b x c /|b x c|
if vectors are in the same plane
a . (b x c) = 0
fourier series conditions
periodic
derive
L(g’(t)) = -g(0) + sL(g(t))
L(g’(t)) = (∞ ∫ 0) g’(t) e^(-st) dt
integration by parts
solve the differential equation via Laplace differential equation
take the Laplace of the differential equation
substitute known Laplace transform values
the divergence theorem
the outward flux of a vector field through a closed surface is equal to divergence of the vector field integrated over the enclosed volume.
parameterise
means change r = (x,y,z) into cylindrical or spherical r
laplace transformation exists for
s < s(0)
prove the identity
f(x-a) = F^-1[exp(-ika) F(f(x))]
conditions for a Fourier transform to exist
FT exists if
(∞ ∫ -∞) |f(x)|^2 dx must be finite for all times t
f(x) -> 0 for x -> ± ∞
what is the weight of a function y = 3-x^2 and p(x,y) = 5y
A = ∫∫p(x,y) dxdy
Length of L centered round the origin
limits of L/2 to -L/2
stokes theorem
the integral of the microscopic circulation of a vector field over the region S inside a closed curve C is equal to the total circulation of a round C.
line integral
L = (B ∫ A) a.dS
LHS of stoke’s theorem
