Flashcards
A1
Cards in this deck (15)
- 1Define Cauchy data
- 2What is the requirement for characteristics to intersect
- 3How do you classify critical points from eigenvalues
- 4State Gronwall's inequality
- 5State Picard's existence theorem
- 6What does it mean for a solution y:[a-h,a+h] -> [b-k,b+k] to the IVP: y'(x)=f(x,y(x)) with y(a) = b, to be continuously dependent on the initial data
![What does it mean for a solution y:[a-h,a+h] -> [b-k,b+k] to the IVP: y'(x)=f(x,y(x)) with y(a) = b, to be continuously dependent on t...](https://examtimeassets.s3.amazonaws.com/uploads/media/image/43810799/desktop_c445ceb6-ab71-4479-8505-f883e3635f21.jpg)
- 7Define characteristic equations, characteristic curve, and characteristic projection
- 8Define a plane autonomous system of ODEs
- 9Show how to analyse a plane autonomous system by linearization
- 10State Bendixon-Dulac
- 11When is a second-order linear PDE hyperbolic, elliptic, and parabolic
- 12State the polynomial used to analyse a second-order linear PDE
- 13State the Contraction Mapping Theorem
- 14State and prove Picard's Existence Theorem via the Contraction Mapping Theorem and extend it to a full solution if Mh=
- 15State and prove Picard's Existence Theorem via the Contraction Mapping Theorem and extend it to a full solution if Mh=
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- uni Part A Flashcards on A1, created by Ben Tidswell on 27/12/2021.
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- Ben Tidswell
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