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 Ordinary Differential Equations Partial Differential Equations What we want to understand: qualitative behaviors and values writing it as an elementary function is lame Linear ODEs SU-MATH53 JAN082024 SU-MATH53 JAN102024 SU-MATH53 JAN122024 SU-MATH53 JAN172024 SU-MATH53 JAN192024 SU-MATH53 JAN222024 Linear Second Order ODEs (and how to first-order them) SU-MATH53 JAN262024 SU-MATH53 JAN292024 SU-MATH53 FEB022024 SU-MATH53 FEB052024 Non-linear ODEs SU-MATH53 FEB072024 SU-MATH53 FEB092024 Linear Non-Constant Coefficient ODEs SU-MATH53 FEB122024 SU-MATH53 FEB142024 SU-MATH53 FEB162024 Fourier Series SU-MATH53 FEB212024 SU-MATH53 FEB232024 SU-MATH53 FEB252024 SU-MATH53 FEB282024 SU-MATH53 MAR042024 Fourier Transform SU-MATH53 MAR062024 SU-MATH53 MAR082024 SU-MATH53 MAR112024 Midterm Sheet SU-MATH53 Midterm Sheet Other Stuff Bessel’s Equation