Homework Statement
Suppose we have a rope of length L and total mass M. Suppose we x its ends at points
(xA; yA) and (xB; yB). We want to determine the shape the rope makes, hanging under the
influence of gravity. The rope is motionless, with a shape parametrised by y(x) or equivalently,
x(y)...
Thanks Bill.
Would you consider this textbook good as a standalone text? If so, which chapters would you recommend going through in order to learn Galois Theory. I alreadyknow that a semester course in abstract algebra is not required even though I'm planning to take it next semester.
I am looking for an accessible textbook in group theory. The idea here is to use it to learn basic group theory in order to take up Galois Theory.
My background includes Calculus I-IV, P/Differential Equations, Discrete Mathematics including some graph theory, Linear algebra, and am currently...
Homework Statement
Recall that F is the vector space of functions from ℝ to ℝ, with the usual operations of addition and scalar multiplication of functions. For each of the following subsets of F, write down two functions that belong to the subset, and determine whether or not the subset is a...
Will be doing that once I find such a provider. It would've been great if Indian institutions offered their units to Westerners, though. They seem respectable considering that their open university grads do post-grad studies in the West.
Hello all,
I'm enrolled at an Australian university that offers mathematics. However, I want to fast track my education by enrolling in units over the holidays ( late Nov to early March). The problem, however, is that my institution does not offer advanced second or third year units. I'm...
I am using R studio for a practical and I need to load a survey. It suggests that I place the following into the R template that I was provided:
survey=read.csv("http://www.maths.usyd.edu.au/u/UG/IM/STAT2012/r/survey.csv")
attach(survey)
pulse.sf=pulse[smoke==1 & sex==2]
pulse.sf
Template...
Delta Q is a fixed variable and rather k, t depend on it as they are floating variables.
MATLAB is a bit different from python in that its arrays aren't indexable. Say x = [1,2,3,4,5], I can't use x[0] = 1, x[3] = 4, etc.
Homework Statement
Modelling the following equation:
k = Delta Q / t
Homework Equations
Q = T2 - T1 = -40 (fixed)
t = Delta Q / k. I need to find t.
k can be floating so I suppose 0 to 10 minutes with 0.5 increments
The Attempt at a Solution
I don't have MATLAB on me at the moment...
k is just an integer that belongs to set Z.
As for b, I think f is surjective because h is. Since f is an input of g, I'm not exactly sure how I can re-utilise my proof from part a.
Homework Statement
Let
f: X ----> Y and g: Y ----> Z
be functions and let
h = g o f: X ----> Z
Homework Equations
a. If h is surjective then g is surjective
b. If h is surjective then f is surjective.
The Attempt at a Solution
Here
h: X ----> Z
a.
Suppose h: x ---> z is surjective...
Yes, for the first part, I essentially grabbed a sub-matrix and showed that its determinant is zero. To go any further than that would probably be quite tricky.
Thanks Ray
Oh that makes sense. Now what I even more puzzling is that I'm supposed to find a min floating point such that, it plus 1 should not return 1. Interestingly, the output I am getting when adding min float and 1 is 1.
I just tried out sys. and got the following:
>>> sys.float_info.epsilon
2.220446049250313e-16
>>> sys.float_info.min
2.2250738585072014e-308
I am looking for the smallest floating point number. Oddly, I was expecting the smallest floating point number to be greater than machin epsilon.
PS...
I'm finding it difficult to find the exact value of epsilon on python? Moreover, I am also supposed to find the smallest floating point number as well.
Wikipedia tells me that the machine epsilon is 2−52 ≈ 2.22e-16 for 64-bit
IEEE 754 - 2008? Is this the exact value on Python?
Outside of...
Homework Statement
Let
A =
4 -4 -1
4 -4 0
4 0 0
Use the criterion from the lectures to show that A does not have an LU factorisation such that A = LU with lower and upper triangular matrices L and U.
How can you re-arrange the matrix rows...
So the array x = 0:0.01:1 is actually a loop? I can see that, but how would I nest a counter into that?
Moreover, why would I have to initialise i = 0 in the beginning of the c loop?
Reformed code...
x = 0:0.1:1; <--- Acts as a loop from 0 to 1, 0.1 increments
i = i + 1;
for c = 1:1:4...
Homework Statement
Plotting the exponential exp(-cx), 0 ≤ x ≤ 1 with c = 1, 2, 3, 4. Use a for loop.
Homework Equations
The Attempt at a Solution
for c = 1:1:4;
for x = 0:1;
F = exp(-cx);
end
end
plot(x,F)
I'm not really sure where to start..
Help is appreciated.
I just noticed that by tinkering around with the function, I was able to get the velocity function to work. Unfortunately, the height function doesn't work and I've tried modifying it once again...
for p in range(21):
H[p] = (1/2)*g*(p**2)+(velocity0*p)+height0
return H
The...
Homework Statement
Enter a minimum height and velocity into plot function and return a velocity-height plot.
Homework Equations
The Attempt at a Solution
# Find length of general list
n = len(K)
# Build a list for time [0,20] seconds ( Global)
time = n*[0.0]
# Acceleration of gravity
g =...
Homework Statement
As a submarine dives, the pressure on its hull..
a. remains constant
b. increases
c. depends on the decrease in volume of the submarine
d . decreases
e. depends on the thickeness of the walls of the submarine
Homework Equations
P = F / A
The Attempt at a Solution
Not a...
Homework Statement
Analyse the physical world around you in terms of Circular Motion/ Energy/ Momentum / Pressure/ Buoyancy/ Bernoulli's Equation.
Choose one aspect you would like to investigate further.
Homework Equations
e.g. why some potatoes float and other do not
The Attempt at a...