Differential Equations. math53.stanford.edu.
Logistics
Prof. Rafe Mazzeo
TAs
- Rodrigo Angelo
- Zhenyuan Zhang
Assignments
- Pre-lecture reading + questionnaire
- PSets: Wed 9A
- 2 Midterms + 1 Final: wk 4 + wk 7, Thurs Evening; Tuesday 12:15
Review
- it suffices to study First Order ODEs because we can convert all higher order functions into a First Order ODEs
- homogeneous linear systems \(y’=Ay\) can be solved using eigenvalue, matrix exponentiation, etc. (recall that special cases exists where repeated eigenvalues, etc.)
- inhomogeneous systems \(y’ = Ay +f(t)\) can be solved using intergrating factor or variation of parameters method
- general analysis of non-linear \(y’=f(y)\): we can talk about stationary solutions (1. linearize each \(y_0\) stationary solutions to figure local behavior 2. away from stationary solutions, use Lyapunov Functions to discuss), or liapenov functions
- for variable-coefficient ODEs, we decry sadness and Solving ODEs via power series
Content
What we want to understand:
- qualitative behaviors and values
- writing it as an elementary function is lame
Linear ODEs
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