Search results

1. When the Rational Root Theorem Fails

The quartic formula! Didn't you learn it in school? :p
2. Oscillation in Dynamic Models

There are many cycles with oscillatory convergence, with the limit actually a limit cycle. The hailstone sequences come g to mind. @chiro
3. Oscillation in Dynamic Models

Oscillations in this case are more often called orbits
4. What exactly allows a differential relation form of an equation?

For f not a function of y or theta, dy= fdθ Then its just symbol pushing.
5. Professional Help Needed-Elementary Number Theory

Is it really ALL? That makes this far more interesting. Mind linking a paper or something?
6. Zeros of f(x) vs. Zeros of f'(x)

If f is a polynomial with all roots of multiplicity one, then the derivative does not have a zero in common with f. To see this, express f factored, use product rule for derivatives.
7. An identity of Ramanujan's

I'm pretty sure it is infinite. Good luck, ram was a beast
8. Indefinite Integration of function's like log(cos(x))?

I think this guy gets the u= x-pi/2 treatment. symmetry :)
9. Principal curvature used in a contact problem

Curvature is the reciprocal of the radius. Is that what is confusing you?

If the sum is divisibleby abc what does that say about the terms
11. If F is ANY field then (x^m-1)|(x^n-1) in F[x] if and only if m|n.

Ok aassuming they are: Perform division, paying attention to the form of the powers you get for the quotient
12. If F is ANY field then (x^m-1)|(x^n-1) in F[x] if and only if m|n.

What are m,n? Naturals I assume
13. Lim x to 0 x*sin(1/x)

I thought it was easily inferred...
14. Prime numbers : a math question for the pro

A lot of modern analytic number theory advances are being made using hardy's major and minor circle (arc?) Technique, but most advances just seem to be bounds improvements
15. Hi, I m trying to find out, what is imaginary unit/number. i^2

On the quaternion bit, any purely imaginary unit quaternion is a root of -1. Also they are 4D not 3 : p
16. Method of undetermined coefficients, when to raise the guess

Note the repeated roots of the characteristic equation
17. Is it possible to integrate x^2*e^(x^2)?

Let's send every rabbit in hat a to 2a...
18. Hi, I m trying to find out, what is imaginary unit/number. i^2

Bringing us to my favorite voicemail joke ever; I'm sorry the number you have dialed is imaginary.please rotate by ninety degrees and try again
19. Infinity in the complex plane

Look at how C is mapped to the riemann sphere. In this mapping there is only one point that can't quite be reached, the north pole.
20. Simple test to see if year is a leap year

Iirc a year is leap if it is divisible by four, unless it ends in two zeros then it must be divisible by sixteen.
21. Power series method

If y is a power series what does y look like?
22. The importance of determinants in linear algebra.

The book linear algebra done right avoid the use of determinants until the very end. The proofs are done without t he determinant. If det makes you uneasy, check it out!
23. Formula for lengths of a rectangle - why does it give both lengths?

I believe its a typo, his derivation is correct in the quadratic formula, the quadratic had a sign error also

25. Diagonalize Large Hermitian Matrices Efficiently?

Check out the power iteration method. The matrix must have a strictly largest ev, and this method will pick it out.
26. Diagonalize Large Hermitian Matrices Efficiently?

There are methods using matrix multiplication and fixed points to pick out the largest eigenvalue if you only need that one. Is that the case here?
27. Calculating number of possible combinations with limited repitition

Has any one set up a generating function yet? Usually those make easy work of counting problems. I have to take the girl to the dentist but I'll check it out later for you. I wonder what your marbles are : p
28. Calculus 1 (I'm taking the class in a week.)

Make sure you are comfortable with algebra and arithmetic!
29. Simplify this expression

http://en.wikipedia.org/wiki/Modular_arithmetic
30. Simplify this expression

Who knows. He didn't provide much info