Recent content by jessawells

Homework Statement let x^{(1)} = \left( \begin{array}{ccc}1\\1\\1\end{array} \right) , x^{(2)} = \left( \begin{array}{ccc}1\\t\\t^2\end{array} \right) , x^{(3)} = \left( \begin{array}{ccc}1\\t\\t^3\end{array} \right) a) Find the Wronskian W(x^{(1)}, x^{(2)}, x^{(3)}) b) You are...

Homework Statement solve the initial value problem: x(2-x)y'' - 6(x-1)y' - 4y = 0 y(1)=1 y'(1) = 0 hint: since the initial condition is given at x_0 = 1 , it is best to write the solution as a series centered at x_0 = 1 . Homework Equations I have attempted the question, but...

Hi, I'm trying to answer a question that I'm stuck on. The question is as follows: -------------------------------------------------------------- If the Gibbs free energy change (deltaG) for ATP hydrolysis in a cell is -57 kJ/mol and the free energy change for transporting a proton from...

yes, f is continuous

1. use the inverse function theorem to prove that any function f: R^2 -> R cannot be one-to-one. hint: let g(x,y) = (f(x,y), y) near an appropriate point. 2. prove #1 using the implicit function theorem. 3. generalize part 2) to show that no function f:R^n -> R^m, with n>m...

an additional piece of info in the question, which i forgot to type, is: g is onto - that is, for every y in R, there is an x such that g(x) = y. anyway, i tried reparameterizing according to arclength. let s1, s2, s3 = arclength of f, g, and h. functions are f = f(t), and g = g(b)...

hi, i was wondering if anyone could tell me how i should approach this problem: Let f:R->R^3 be a differentiable, vector-valued function and g:R->R be a strictly increasing vector-valued function. Let h = fog:R->R^3. Show that the paths traced by f and h are equal and that h'(t) =...

Hi, I have to solve this problem: Suppose that f is a continuous, vector-valued function and that T is a linear transformation on R^3. Show that "T o f" (stands for T composite f) is continuous and that INTEGRAL[T o f] = T(INTEGRAL[f])...

how about taking math as a minor? it would involve less courses and therefore less stress, and you'll still be able to put it on your application.

can someone help me with this problem: "show that a point is traveling along the surface of a sphere if and only if its velocity vector is orthogonal to its position vector." I know that it is true intuitively - since in centripetal motion, the velocity is always directed toward the...

hi, yes, its the second case - simplifying the expression. I'm not sure at all how to approach it. I've thought about using the fact that both terms are squared - eg. making it \sqrt{x^3 + (1+x^3)} but i know that's wrong. other than that, I've been trying to expand the \sqrt{1+x^3} term...

no, that's the problem. i don't have it "=0". i just have one to simplify the expression.

hi, can anyone show me how to solve this: \sqrt{x^3} + \sqrt{1+x^3} i want to get it to so that there's only 1 term of x. but i don't know how to expand the squared root. any help is appreciated.

hi, can anyone show me how to solve this: x^(3/2) + (1+x^3)^(1/2) i want to get it to so that there's only 1 term of x. but i don't know how to expand the squared root. any help is appreciated.

Hi, i'm having trouble with a thermal physics problem relating to the partition function and i was wondering if anyone could help me out. the problem is as follows: (a) Consider a molecule which has energy levels En=c|n| , where n is a vector with integer components. Compute the partition...