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1. ### Uniform convergence problem

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...
2. ### Finite Fields and ring homomorphisms HELP

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?
3. ### Finite Fields and ring homomorphisms HELP

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...
4. ### Leplace transform

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

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)
6. ### Flux of Vector Field Across Surface

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?
7. ### Flux of Vector Field Across Surface

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...
8. ### Variation of Parameters

im not quite sure I understand where to plug in x^r .
9. ### Variation of Parameters

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...
10. ### 2nd order diff Eq help

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...
11. ### 2nd order diff Eq help

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?
12. ### 2nd order diff Eq help

oh, okay thanks, that's what I found confusing it makes sense now.
13. ### 2nd order diff Eq help

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
14. ### 2nd order diff Eq help

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...
15. ### 2nd order diff Eq help

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...