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Forum: General Questions - University/Tertiary
Welcome to the General Questions - University/Tertiary forum!
Questions from any subject, at the university/tertiary/4-year college level.

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Orthogonality by zee on 2009-11-23 17:26:18
Find all vectors in R^3 that are orthogonal to ( 1 , 1 , 1) and ( 1, -1, 0 ). Produce an orthonormal basis from these vectors (mutually orthogonal unit vectors). Thanks for any feedback.
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Article in Mathworld by curious on 2009-11-22 20:03:11
I was reading an article in Wolfram Mathworld about second order differential equations.
Here is the link: http://mathworld.wolfram.com/Second-OrderOrdinaryDifferentialEquation.html

The author tries to transform (9) into constant coefficients by doing the wierd substitution z=y(x). Note that (d^2 y)/(dz^2) = 0 and dy/dz = 1, adn eq (14) becomes and ALGEBRAIC equation with solution y = -A/B.

Does this mean that there is something wrong?? It seems that the explanation is weak.. What do you think?
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Special Riccati Equation by curious on 2009-11-20 14:09:44
I am trying to solve this 1st order special Riccati ODE:

(dy/dx) + P(x)y^2 + Q(x) = 0

Is this equation solvable in general? If yes please explain the method. If not, for what P(x) and Q(x) is it solvable?

I am also interested in P(x) and Q(x) that are sines and cosines, so I would like to know if it is solvable or not in this case?

Thanks.
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solving a trig equation by oeivinr on 2009-11-20 11:14:41
hi,

I would be most grateful if somebody could help me with solving the following trig equation:

tan(t+1) = t

Thanx Oivind Reinemo
[ reply | up ]
Linear Transformations by zee on 2009-11-17 14:26:08
Suppose A is a linear transformation from the x-y plane to itself. Why does A^(-1) (x+y)=A^(-1)x+A^(-1)y ? If A is represented by the matrix M, explain why A^(-1) is represented by M^(-1) ? For the first part, I think the linear transformation A is satisfying the rule of linearity. Can you give me some feedback? Thanks.
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