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28 Cards in this Set
- Front
- Back
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T =
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v/lvl
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at =
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<a,T>
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lal^2 =
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at^2+an^2
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k =
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la X vl/lvl^3
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an =
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klvl^2
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a =
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atT+anN
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B =
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T X N
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m<n?
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A is never one to one.
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m>n?
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A is sometimes one to one.
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what two things qualify a basis?
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1) the span of the vectors is the Vector space
2) the vectors are linearly independent. |
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what is det(A) in terms of the eigenvalues of A?
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The product of the eigenvalues.
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A^x =
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SD^xS^-1
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length of a curve?
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Slr'ldt
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which are the only open and closed sets?
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The null set and Rn
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what does compact mean?
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a set that is closed and bounded.
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L is a limit of f(y) as y approaches x if...
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0 < ly-xl < sig
then, lL -f (y)l < ep |
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f(x) is cont. at x if...
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lf(y)-f(x)l<ep whenever lx-yl<sig
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Dvf(x) =
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lim f(x+hv)-f(x)
h->0 h |
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a func. is diff if...
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lim lf(x+v)-f(x)-<grad.f, v>l = 0
v->0 lvl |
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o(v) =
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f(x+v)-f(x)-<grad.f(x), v>
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lim sin(x)/x =
x->0 |
1
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hyperboloid of two sheets
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z^2/a^2-x^2/b^2-y^2/c^2=1
shape: bowl w/ reflection |
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hyperboloid of one sheet
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x^2/b^2+y^2/c^2-z^2/a^2=1
shape: corset |
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hyperbolic paraboloid
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z=x^2/b^2-y^2/c^2
shape: curvy tunnel |
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elliptic paraboloid
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z=x^2/b^2+y^2/c^2
shape: cup |
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ellipsoid
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x^2/b^2+y^2/c^2+z^2/a^2=1
shape: football |
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elliptic cone
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z^2/a^2=x^2/b^2+y^2/c^2
shape: inverted cone w/ reflection |
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if y' =ay then what does y = ?
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y(t)=ce^at
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