I've been studying graduate level Linear Algebra from Steven Roman's Advanced Linear Algebra (Springer, GTM). It is a terrific book, but many of the concepts are extremely abstract so that I find it difficult to retain what I've learned. Can anyone point me to some books/reading on the...
So I've been studying advanced linear algebra and have started learning about modules. However, I am having a hard time understanding the difference between a zero divisor and a torsion elements. The definitions seem extremely similar. Can someone offer a good definition of each and an...
Is there a topologist out there that wants to explain why exactly a branched line in R2 is not not a topological manifold? I know it's because there doesn't exist a chart at the point of branching, but I don't understand why not. I'm just starting to self study this, so go easy on me :).
See this link for the given assignment.
note: on the last page the output aa4bcdd0cc1 is actually supposed to be aa3bcdd1cc1c.
I have no idea why my encoder function doesn't work. No...
Most definitions of a matrix that I have seen involve entries that are elements of a field. What if I have a unorderd set with no operations defined on it, say a set of different colored marbles or a set of historical events. Can I have a matrix whose entries are elements of such a set?
So for a function of a single variable
How can this be extended to the integration of the total differential of a multivariable function over a region (specifically one of two variables)?
That is, how do you integrate
Say over the circular region
can anyone convert the relation tan y=(Vsin(y)-gx)/Vcos(y) to an explicit function y=f(x) in terms of V, x and g?
g is a constant
V is the function V(x)= -aln(b/b-cx)-dx
a,b,c,and d are also constants.
While fiddling around with some very simple linear ODEs, I "discovered" a formula that gives a solution to ODEs of the form: ##y'+y=ax^n ##.
here it is:
i'm sure that this was discovered before, but i was just wondering if it had any official name or something.
I'm taking an online introductory chem course, and while explaing the failure of classical mechanics to describe electron behavior, the teacher brought up the following ode which is based on newton's second law and coulombs law: