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This is a basic rough sketch of the argument ...there are a few gaps that need to be filled in by yourself to be rigorous... Since [a,b] is a closed and bounded interval, note that f(x) is uniformly continuous on this interval. So given any epsilon > 0 , then there must exist a delta such...

Okay I get that the all of the ideals of Z are of the form mZ for some integer m, but I am still not sure how n*1F implies that the kernel must be a prime ideal of Z?

Homework Statement Assuming the mapping Z --> F defined by n --> n * 1F = 1F + ... + 1F (n times) is a ring homomorphism, show that its kernel is of the form pZ, for some prime number p. Therefore infer that F contains a copy of the finite field Z/pZ. Also prove now that F is a finite...

Its t^1, so n = 1 when you plug into the transform for t^n.

You should check the laplace transform for 7t. L{t^n} = (n!)/(s^(n+1)) therefore L{t} = L{t^1} = (1!/(s^(1+1)) L{7t} should look more like 7*(1/s^2) or (7/s^2)

also... can I use cylindrical coordinates for the volume of the cylinder then use spherical coordinates for the volume of the cap and add them together?

Homework Statement Compute the flux of vector field (grad x F) where F = (xz+x^2y + z, x^3yz + y, x^4z^2) across the surface S obtained by gluing the cylinder z^2 + y^2 = 1 (x is > or eq to 0 and < or eq to 1) with the hemispherical cap z^2 + y^2 (x-1)^2 = 1 (x > or eq to 1) oriented in...

im not quite sure I understand where to plug in x^r .

Solve by method of variation of parameters (x^2)y'' - (4x)y' + 6y = x^4*sinx (x > 0) Hey, I know how to solve problems using variation of parameters but only when the corresponding homogenous equation has constant coefficients... y'' - (4/x)y' + (6/x^2)y = 0.. the bit I am confused about...

No unfortunately the professor has mentioned anything about it and gave us this web assignment anyways... also we don't use a textbook just his lectures...which why I am utterly confused.. if someone can point me in the direction of a good link that might explain the general methods that would...

I have other problems of similar form such as 4y'' - 81y = 0 and 2500y'' + 9y = 0 Should I go about solving these using the same method?

oh, okay thanks, that's what I found confusing it makes sense now.

Can you please explain to me how you got to this step: This gives us two different solutions phi1 = e^t*phi2 = e^(-t) Thanks

I am trying to find y as a function of t (Determine y(t) = _____________) and y'' - y = 0 The two IV given are y(0) = 7, and y(1) = 5 .. Remark: the initial condition involves values at two points. Well since y = {y,y''} and the independent variable t does not appear, I went about it by...

2nd order diff Eq with t missing I am trying to find y as a function of t and y'' - y = 0 The two IV given are y(0) = 7, and y(1) = 5 .. Remark: the initial condition involves values at two points. Well since y = {y,y''} and the independent variable t does not appear, I went about it by...