MATHS 2106 Lecture Notes - Lecture 5: Xz, Gkn
17 Jun 2021
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43 : - rate at which mass gathers in each vessel : Null clines :yi=o= - %- (cid:15482) yz=2y y;=0=y% - (cid:15482) (cid:15482) ye=2y, 44 : - my"+cy"+ky=flt) ,bty,=y&y=y" system of egns : y. A system of n 1st- order odes can be written in vector form as y 4,31 where y=cy, vectors. 43 , a vector can be written as : yi-f-ct. gl where g- (g) f- (4) =/ - -1:o) (cid:15482) - (cid:15482) 2 :-[ i an initial value problem can be written as : 1101=19,1 where yiol-9andy. co/ =3 n e ar s y s t e m s. A system of linear 1st- order odes can be written as : given coefficients yj-amltlyy-ayztlyzt-n-tamtlyn-g. it y-iazyltlygazzctlyzt-n-azntlyn-g. lt) + annltlyntgnt) given functions in vector form : yj-a~lty~i-g. lt) where a~ltl-a. it/a,iti---a. na-iandg~lti--git1 ifg~ltt-oi-g. lt) if a- is not a function of t. Azyct) azzctl a. net: system has constant coeffs .
