SU-MATH53 Homework Index
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SU-MATH53 JAN082024
Last edited: August 8, 2025Key Sequence
Notation
New Concepts
Important Results / Claims
Questions
Interesting Factoids
SU-MATH53 JAN102024
Last edited: August 8, 2025Key Sequence
Notation
New Concepts
Important Results / Claims
- division method
- general solution to y’(t) = ry(t)
- IMPORTANT: one and exactly one solution exist for every point of an IVP
Questions
Interesting Factoids
SU-MATH53 JAN122024
Last edited: August 8, 2025Key Sequence
Notation
New Concepts
Important Results / Claims
Questions
Interesting Factoids
SU-MATH53 JAN172024
Last edited: August 8, 2025Key Sequence
Notation
New Concepts
- tying into Separated Equations: \(y’ = f(t,y)\) which are the most nicest. Recall that there was two special cases: seperable and autonomous ODEs.
- if we can write in terms of elementary function, good times
- if we can’t do it in terms of elementary functions, we can use qualitative analysis t(slope field, etc.)
- recall again Newton’s Law of Cooling
- phase line and stability (ODEs)
Important Results / Claims
- autonomous First Order ODEs’ solutions do not cross; as in, if there are two solutinos \(y_1\) and \(y_2\), their curves never intersect.
- one and exactly one solution exist for every point of an IVP
- autonomous ODEs level off at stationary curves