Lecture		Topic(s)

 1		Intro, course overview, online resources
 2		Linear vector spaces, dimension, basis, scalar product
 3		Linear operators, matrices, coordinate transformations

 4		Linear equations, eigenvalues, diagonalization
 5		Application: normal modes; diagonalizability
 6		LU and SV decomposition, applications

 7		Numerical diagonalization, examples and applications
 8		Complex functions, analytic functions, Cauchy's theorem
 9		Cauchy integral formula and applications; Taylor series

10		Laurent series, poles, the residue theorem
11		Applications of the residue theorem

12		Jordan's lemma; more applications of the residue theorem
13		Examples; quantum mechanical scattering integrals
		
14		Review; more on QM scattering integrals
		

15		MID-TERM (October 24)
16		2nd order linear ODEs; singular points, series solutions
17		Series and second solutions to ODEs; Fuchs's theorem

18		Greens fuctions; self-adjoint operators
19		Sturm-Liouville theory; eigenfunctions; Fourier expansion
20		Mean square convergence; Fourier series

21		Numerical solution of ODEs, IV problems, RK methods
22		Numerical solution of ODEs, RK methods (continued)
23		Predictor-corrector schemes, time reversibility

24		Symplectic integrators; Bulirsch-Stoer methods
25		BV problems, shooting, relaxation
26		Integral transforms, Fourier series and transforms, examples

27		Fourier transforms, applications, convolution

28		Laplace transforms (brief), Discrete Fourier Transforms
29		The Fast Fourier transform
30		Applications of FFTs