Assume that f is a continuous, real-valued function defined on a metric space X. If {xn} is a sequence in X converging to x, prove that Limn→∞f(xn) = f(x).
Here is my attempt, but I am not sure if it is correct.
My professor never really went over this concept clearly in Advanced Calculus.
The definition of an equivalent metric from my lecture slides:
Two metrics: d1 and d2 on a metric space X are called equivalent when there exists M >= 1 such that M-1d1(x,y) <= d2(x,y) <= Md2(x,y)
I am trying to...
Just a question, do all universities require students (especially math majors) to take an intro to mathematical proof class in order to take advanced, proof based math classes?
These courses are at two different colleges that I plan on going to (whichever picks me). I think that discrete math is more relevant for Computer Scientists and the other for Math majors. But both look similar (for the bridge to advance math course, it does teach you to write proofs, something...
Hi, I am currently an undergraduate student and I plan on taking advanced math courses such as Abstract Algebra, Real Analysis, Complex Analysis, etc. There are two courses which I think could help me prepare for the courses above as they are proof intensive: discrete math and bridge to advance...
I haven't really went deep into physics because I just started Physics, but definitely plan on taking more advanced physics courses, but from what I researched, people divide physics into experimental and theoretical, the latter being more math. Also, from what I heard, physicists are not...
Thanks for your reply. So essentially a proof based Linear Algebra course would be the same level of difficulty as an Abstract Algebra and the proofs, though different, are not so difficult.
As for physics, I would think proof based math classes like Abstract Algebra are not that useful in...
I know both are different courses, but what I mean is, will a proof based Linear Algebra course be similar to an Abstract Algebra course in terms of difficulty and proofs, or are the proofs similar? Someone told me that there isn't that much difference between the proofs in Linear or Abstract...
Ok maybe every chemistry course uses it. For my organic chemistry class, I just needed to know a few elements, electronegativity, and atomic numbers, but other than that, there was no use of the periodic table. Gen Chem II, It was the same thing. but we never looked at the periodic table. I...
So far, I have taken General Chemistry I and II, and Organic Chemistry I. Out of these classes, only General Chemistry I seems to make use of the periodic table, but it is mostly just going through the basics of the periodc table. Not so much in Gen Chem II or Orgo I. I mean they give it to you...
Just a quick question, I was solving sin(x)=0 and cos(x)=0. I was trying hard to find out the solutions and the solutions were: for sin(x)=0------>x=0, pi, 2pi for cos(x)=0-------->x=pi/2, 3pi/2
But my question is why are those the solutions?
Homework Statement
Solve Laplace Transform L{tsin(2t)sin(5t)}
Homework Equations
cos(bt)=s/s^2+b^2
trig identity (product identity): sin(a)sin(b)=1/2[cos(a-b)-cos(a+b)
t^nf(t)=(-1)^nd^n/ds^nF(S)
(the template is complicated for me to use. Srry for the inconvinience)
The Attempt at a Solution...
Homework Statement
Homework Equations
The Attempt at a Solution
I am not asking to find the answer, just wanted to know whether to use the variation of parameters or undetermined coefficients. Because this was on a test problem and I used variation of parameters instead. I know it is a...
My professor did not go in dept. I just know know:
if a constant: yp=A
if x: yp=Ax+B
if x^2: yp=Ax^2+Bx+C
if cos(x) or sin(x): yp=Acos(x)+Asin(x)
if e^x: yp=Ae^x
Or something like that???
But I need to know why instead of using yp=ae^4x, you have to use yp=axe^4x (sorry, the template to write the equation like you did is very complicated for me)
Homework Statement
y''-16y=2e^4x. Find general solution
Homework Equations
The Attempt at a Solution
I have the homogenous equation which is c1e^-4x+c2e^4x, but I'm trying to find the particular solution for 2e^4x. I did yp=ae^4x, yp'=4ae^4x, yp''=16ae^4x, then plugged it into the equation...
Homework Statement
Sketch the curve with the given vector equation. Indicate with an arrow the direction in with 't' increases
r(t)=<t, 2-t, 2t>
Homework Equations
parametric equation (can't type the equation, too confusing to use the template)
The Attempt at a Solution
So far, I have <1...
Sketch the curve with the given vector equation. Indicate with an arrow the direction in with 't' increases
r(t)=<t, 2-t, 2t>
So far, I have <1, -1, 2> and points (0, 2, 0). Am I even correct? And how do I sketch the graph. I know it's suppose to be in the xyz graph, but how do I graph the...
Thank you for the link. It translates automatically into any language so it's ok. I wanted to know the whole steps on how to solve the integral: sin(3x)/cos^2(3x) (I found the template, but don't know how to use it yet. I don't go on that much on these forums for help. It's my first time using...
Why, is Greek complicated? :oldeyes:. It does all sound confusing and intimidating to people who are just beginning Orgo.
From what I heard from others taking it, you have to be able to both memorize and understand why. There are people who just memorize without understanding anything at all...
For Organic Chemistry, all I can think of is having to remember: methane, hexane, butane, propane, octane, pentane, nonane, decane, ethylene, methylene, etc, etc o0) You also have to remember the formula and have to draw a very complicated spider web-like bonding structure :oldeek:. I feel like...
So the topics I need to really focus on for Organic Chemistry are:
General Chemistry I: Electronic Structure of Atoms, Periodic Properties of Elements, Basic Concepts of Chemical Bonding, Molecular Geometry and Bonding Theories.
General Chemistry II: Chemical Kinetics, Chemical Equilibrium...
I've heard from a lot of people who took Organic Chemistry in my college as well as on other forums that there is not that much General Chemistry involved in Organic and it only involves bonding, electronegativity and more on memorization and understanding how chemical reactions work than in...