Recent content by DMOC

Hi everyone, I am interested in applying to be a teaching assistant in my university's multivariable calculus class or linear algebra class. I took both of these courses already and seem to like them equally well. I will have solid recommendations and grades. Any recommendations on which...

Old topic: https://www.physicsforums.com/showthread.php?t=194725 I have a question that's the same as the one in the old topic/thread I linked to above. At the last post, I am trying to figure out how to carry out the induction process. \sum_{j=1}^n (-1)^{i+j} a_{ij} det(\alpha A_{ij})...

For closure under addition, I would suggest ------------------------- Let a<1,3,2>, b<1,3,2> \in R3, a<1,3,2> + b<1,3,2> = <a1+b1, a3+b3, a2+b2> <a1+b1, a3+b3, a2+b2> \in R3 Closure under addition holds. --------------------------- I don't know how strict your...

You'll probably catch this, but the c + 3 should really be a c + 2. A better way to write closure under addition would be the way Mark44 wrote it. Also, I recommend adding a confirmation statement such as "Closure under addition holds!" at the end of every specific property proof.

Thank you.

Yes, that should be correct ... my bad. But would the longer method be valid? i.e. mathematically legal?

y1 = x2 - x1 y2 = x3 - x2 y3 = x3 - x1 x1, x2, x3 are linearly independent in R^n Is that true for y1 y2 and y3? --- Well, normally with linear indepence problems, I can set up a matrix and check to see if the row echelon form has free variables or not, or I can calculate the...

Hey guys, I'm just curious about these REUs because I may be applying to possibly 10 or so next summer (when I'll be a rising junior, so it isn't the end of the world if I get rejected from all). Are these REU's generally one of the best ways to get a research paper or project done? As compared...

Okay guys apparently this problem has additional steps. I know this equation is right, but now I'm asked "If the advertising budget only allows $100 per day, what price should I charge (per bottle) to start having a profit in two days? So does this mean that I have to plug in 2 for t in...

The words "sep. of variables" doesn't ring a bell but the method does. I was eventually able to solve the full problem, ending up with: B(t) = \frac{Me^{\frac{-40t}{M}} - M}{-0.08} Thanks everyone. :)

When you refer to DE, you're talking about the first equation I have, right? I copied that one straight off of my notes. :) So for my solution, I have to take this D.E. I have and solve for B. Does that mean I have to do stuff like take the integrand of both sides? (so that dB/dt becomes B(t)? ).

Homework Statement A soft-drink manufacturing company introduces a new product. The company's salespeople want to predict the number of bottles per day they will sell as a function of the number of days since the product was introduced. One of the parameters will be the amount per day spent...

Wait so I can't use the alternating series test with a non alternating series ... wow I'm going to kick myself in the @%$@# for overlooking this. So I assume I just use like a comparison test for 1/ln(k+2) with 1/k (diverges) since ln makes values of k smaller so the frac. gets bigger.

Homework Statement Determine values for x where \sum \frac{(2^k)(x^k)}{ln(k + 2)} converges if k goes from 0 to infinity. Homework Equations Limit test and alternating series test. The Attempt at a Solution I used the limit comparison test to test out ak+1 and an and I ended up...

Anyone have their opinions on what I should add to the answer?