Differences
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision | |||
linear_first-order_ode_system [2014/03/21 11:11] 127.0.0.1 external edit |
linear_first-order_ode_system [2017/01/17 01:06] nikolaj |
||
---|---|---|---|
Line 3: | Line 3: | ||
| @#55CCEE: context | @#55CCEE: $ A:\mathbb R\to\mathrm{Matrix}(n,\mathbb R) $ | | | @#55CCEE: context | @#55CCEE: $ A:\mathbb R\to\mathrm{Matrix}(n,\mathbb R) $ | | ||
| @#55CCEE: context | @#55CCEE: $ b:\mathbb R\to\mathbb R^n $ | | | @#55CCEE: context | @#55CCEE: $ b:\mathbb R\to\mathbb R^n $ | | ||
- | |||
| @#FFBB00: definiendum | @#FFBB00: $ y \in \mathrm{it} $ | | | @#FFBB00: definiendum | @#FFBB00: $ y \in \mathrm{it} $ | | ||
- | |||
| @#55EE55: postulate | @#55EE55: $ y:C^k(\mathbb R,\mathbb R^n) $ | | | @#55EE55: postulate | @#55EE55: $ y:C^k(\mathbb R,\mathbb R^n) $ | | ||
- | |||
| @#55EE55: postulate | @#55EE55: $ y'(t)=A(t)\ y(t)+b(t) $ | | | @#55EE55: postulate | @#55EE55: $ y'(t)=A(t)\ y(t)+b(t) $ | | ||
- | ==== Discussion ==== | + | ----- |
=== Theorems === | === Theorems === | ||
There exists a matrix $S(t,s)$ such that the solution of the equation above is of the form | There exists a matrix $S(t,s)$ such that the solution of the equation above is of the form | ||
Line 40: | Line 37: | ||
=== Reference === | === Reference === | ||
Wikipedia: [[http://en.wikipedia.org/wiki/Dyson_series|Dyson series]] | Wikipedia: [[http://en.wikipedia.org/wiki/Dyson_series|Dyson series]] | ||
- | ==== Parents ==== | + | |
+ | ----- | ||
=== Context === | === Context === | ||
[[Square matrix]] | [[Square matrix]] | ||
=== Subset of === | === Subset of === | ||
[[ODE system]] | [[ODE system]] |