Recent content by thrill3rnit3

Hello all. I am preparing to take my math department's preliminary qualifying exam for pure math. It covers analysis and linear algebra. I have a good number of past papers but I was wondering if there is a good source, maybe a book or a website, for problems of similar difficulty. Thanks.

\frac{1}{n+1} = \frac{1}{\sqrt{(n+1)^2}} = \frac{1}{\sqrt{n^2+2n+1}} < \frac{1}{\sqrt{n^2+2n}} < \frac{1}{\sqrt{n^2}} = \frac{1}{n} In short, we've sandwiched \frac{1}{\sqrt{n^2+2n}} between \frac{1}{n+1} and \frac{1}{n}

My post above yours answers that question.

Hm, I think it would be nice to have an systematic approach to this proof. What do we want to show? We want to show that for any point p (x,y) there exists a radius δ > 0 such that, for any point q, if the distance from p to q is less than δ, ie. if l p - q l < δ where l l represents the [...

Momentum is defined as mass times velocity. Acceleration is defined as the change in velocity divided by the change in time. net force = mass times acceleration

If you say that the acceleration of gravity is 10m/s/s, then it is constant. Your 2nd table does not reflect that.

What is P0? You need to make sure every detail in your proof is accounted for.

Note that "10m/s/s" is not "gravity"; rather, it is the acceleration [ magnitude ] due to gravity. Now, with that said, which one is constant and which one changes with time: acceleration or velocity? I'm assuming that you know the definition of these terms. If not then go back to your...

An object's momentum is in the same direction as its velocity.

Can you link momentum with Newton's 2nd law?

Think about it this way, for intuition, which you can then formalize to create your "proof". You want to make sure that for all points in that given set S, you can create a "disk", or "neighborhood" [ with radius δ > 0 ], around each one of them, in such a way that all the points inside this...

A multivariable calculus book that I like that is at a higher level than your run-off-the-mill calculus books is the one by Williamson, Crowell, and Trotter. I believe it's called Calculus of Vector Functions. Get the 3rd edition [ or older ], and not the 4th [ which I believe is renamed as...

I suggest going back and re-reading (and understand?) the formal definition. What you have said above is not quite accurate. The structure of the proof (ie. what you have to do) comes really from the definition itself.

You want that delta to work for any choice of ε > 0.

Not really, if he's gone through an analysis textbook already, and know enough linear algebra.