Final account project -Suggestions/Recommendations
Answers
(1) Give an expository account of fundamental existence and unique-
ness: provide the details of the proof, and give examples where unique-
ness and long-term existence fail.
(2) Explore the numerical methods we have been discussing in this class
in greater depth. For example, one way to improve on the methods is by
allowing for the step-size to be chosen adaptively. Explore this.
(3) Explain how to solve the two-body problem: this asks for the solution
to a system consisting of two masses interacting under Newton’s Law of
Gravitation.
(4) Give an expository account of the three-body problem.
(5) Give more details about how to compute matrix exponentials. For
example, explain how to find a Jordan basis, and explain what the matrix
exponential of a matrix in Jordan Canonical Form is.
(6) Discuss the perspective on first order ODEs that comes from thinking