Calculus 141, section 9.7 Alternating Series, Absolute ...

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ESSENTIAL KILLING FIELDS OF PARABOLIC GEOMETRIES

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Complex inner products (6.7 supplement) u 6= 0 and

b) The dimension of the eigenspace for each eigenvalue λ equals the multiplicity of λ as a root of the characteristic polynomial of A. c) The eigenspaces are mutually orthogonal, in the sense that eigenvectors corresponding to different eigenvalues are orthogonal.

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Theorem (The Monotone Convergence Theorem)

However in the case of monotone sequences it is. 2. Definitions: • We say {a n} is monotonically (monotone) increasing if ∀n,a n+1 ≥ a n. • We say {a n} is monotonically (monotone) decreasing if ∀n,a n+1 ≤ a n. • A sequence is monotone if it is either. 3. Theorem (The Monotone Convergence Theorem): If {a n} is monotone and ...

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Riemann problem for Burgers' equation u t + 1 2 u 2 x = 0 ; ut + uu x = 0 : f (u ) = 1 2 u 2; f 0(u ) = u: Consider Riemann problem with states u ` and u r. Forany u `; ur, there is a weak solution consisting of this discontinuity propagating at speed given by the

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