Prove that equation have a unique solution through the point
(0,1). With the knowledge acquired can...
Prove that equation have a unique solution through the point
(0,1). With the knowledge acquired can you exhibit explicitly that
unique solution for a and b?
Uniqueness theorem
Prove that the solution to the Laplace’s equation in a spatial
region is unique if the potential is specified on the surface of
the region.
Use a fixed-point iteration to determine the solution (in
[0,1])ofthe equation x = 1.5cos(x). Use a starting value of 0.5.
How many iterations does it take before you have an answer which is
accurate in the first 2 digits? ...in the first 3 digits?...in the
first 4 digits? What happens if you change the starting value to
0.7?...to 0.0?
Does the fixed-point iteration converge? If not, modify the
equation so that x = cos(x)/30 + 44x/45. Does the iteration
converge...
Plot the Trapezoid Method approximate solution on [0,1] for the
differential equation y = 1 + y2 and initial condition (a) y0 = 0
(b) y0 = 1, along with the exact solution (see Exercise 6.1.7). Use
step sizes h = 0.1 and 0.05 (Code In Matlab)
Plot the Euler’s Method approximate solution on [0,1] for the
differential equation
y* = 1 + y^2 and initial condition (a) y0 = 0 (b) y0 = 1, along
with the exact solution (see
Exercise 7). Use step sizes h = 0.1 and 0.05. The exact solution is
y = tan(t + c)
For a unique solution to the wave equation, what boundary
conditions must be satisfied.
a) Boundary conditions are not needed for a medium with no
interfaces.
b) This is a trick question; all boundary conditions must be
satisfied.
c) The tangential boundary conditions
d) The normal boundary conditions
e) Continuity in solution across the boundary must be
satisfied.
T F (1)The loss tangent is related to the ratio of the
conduction current density to the convection current density in the...
The equation of the line that goes through the point (3,2) ( 3 ,
2 ) and is parallel to the line going through the points (−2,3) ( −
2 , 3 ) and (5,6) ( 5 , 6 ) can be written in the form ?=??+?
where:
m=
b=
Find the equation of the line through the point P = (0,2,−1)
that is perpendicular to both ⃗v = 〈3,0,1〉 and ⃗w = 〈1,−1,2〉.
v and w are vectors by the way