analysis,calculus difference - eq to differential - eq 599

... the sequence converges and lim n→∞ a n = B. Similar results hold for sequences which are monotone decreasing. Monotone sequence theorem Suppose the sequence {a n } is monotone. If the se- quence ... monotone increasing if a n ≤ a n+1 for all n. We say a sequence {a n } is monotone decreasing if a n ≤ a n+1 for all n. We say a sequence is monotone if it is either monotone increasing or monoton...

Ngày tải lên: 12/05/2014, 03:31

... such an immersion exists, to what extent is it unique? As shown in Theorems 1. 6-1 and 1. 7-1 , the answers turn out to be remarkably simple to state (but not so simple to prove, especially the first ... expected to appear by virtue of the chain rule). Such a task is required for example if we wish to write a system of partial differential equations whose unknown is a vector fiel...

Ngày tải lên: 17/03/2014, 14:24

...         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … !-2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3 … !-2 x 2 x n … … … … … -2 x n x 1 !-2 x n x 2 !-2 x n x 3 … ! r 2 -2 (x n ) 2         -x 2 x 1 0 0 … 0 ... 1 r 4         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … !-2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3...

Ngày tải lên: 17/03/2014, 14:28

...         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … -2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3 … -2 x 2 x n …………… -2 x n x 1 -2 x n x 2 -2 x n x 3 …  r 2 -2 (x n ) 2           -x 2 x 1 0 0 … 0 ... 1 r 4         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … -2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3 … -2...

Ngày tải lên: 27/03/2014, 11:52

Ngày tải lên: 27/03/2014, 11:54

... vectors onto? Exercise 2.3. Find a 1-form which (1) projects vectors onto the line dy = 2dx and scales by a factor of 2. (2) projects vectors onto the line dy = 1 3 dx and scales by a factor ... scales by a factor of 1 5 . (3) projects vectors onto the dx-axis and scales by a factor of 3. (4) projects vectors onto the dy-axis and scales by a factor of 1 2 . (5) does both of the two preceding...

Ngày tải lên: 31/03/2014, 15:39

Ngày tải lên: 31/03/2014, 15:56

...         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … !-2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3 … !-2 x 2 x n … … … … … -2 x n x 1 !-2 x n x 2 !-2 x n x 3 … ! r 2 -2 (x n ) 2         -x 2 x 1 0 0 … 0 ... 1 r 4         r 2 -2 (x 1 ) 2 -2 x 1 x 2 -2 x 1 x 3 … !-2 x 1 x n -2 x 2 x 1 r 2 -2 (x 2 ) 2 -2 x 2 x 3...

Ngày tải lên: 24/04/2014, 17:08

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Ngày tải lên: 20/08/2012, 12:26