M 427J Differential Equations with Linear Algebra (Spring 2016)
I was the TA for Differential Equations. Some class materials are provided here.
- All quizzes and solutions: .tar.xz, .tar.gz, .zip
- Quiz 1 (quiz, solution): Separable differential equations, first order linear differential equations, initial-value problems.
- Quiz 2 (quiz, solution): Picard iteration, making differential equations exact using an integrating factor.
- Quiz 3 (quiz, solution): Judicious guesses for solutions of differential equations, complex differential equations, variation of parameters.
- Quiz 4 (quiz, solution): Correspondence of higher-order differential equations and matrix differential equations, reduced row echelon form (RREF) of matrices, solving homogeneous matrix equations using RREF.
- Quiz 5 (quiz, solution): Vector space bases, showing a subset is a vector space, kernels of linear operators.
- Quiz 6 (quiz, solution): Eigenvalues of a matrices, solving matrix differential equations using generalized eigenvalues and eigenvectors, derivative of a solution to a matrix differential equation is also a solution to the same equation.
- Quiz 7 (quiz, solution): Asymptotic stability of solutions to matrix differential equations using eigenvalues and characteristic polynomials, separable solutions to the 2D heat equation, decay of Fourier coefficients.