PHYS GU4019

Linear algebra, operator theory, Hilbert spaces, distribution theory, fourier transforms, complex analysis, Green's functions, all from the point of view of physics and physics applications

I learnt multiple mathematical skills which are very useful for Physics students.

A rough intro to Fourier analysis, ODEs, PDEs, Complex analysis, Path integrals in QM, etc

some intro abstract algebra, spectral decomposition/ diagonalization of operators, hermitian operators, Hilbert spaces, functionals, distributions, Fourier transforms, complex analysis (contour integrals, branch cuts, green's functions)

Lots of useful math techniques for Physics

I came in with a general knowledge of complex analysis and special functions, but the approach by the professor was really helpful and the examples were very interesting. I think through the course I learned some new math, but more than that I really workedthrough some applications tht made me think about what the matth really *meant*.

Vector spaces, operators, diagonalization, distributions, complex analysis, Fourier transforms, etc...

I recommend this course to anyone who feels like they are behind in math and struggle in other Physics classes. Even if you don't struggle, this course is interesting and closes any gaps that you might have had. Some of the homework assignments can be long but it's worth it. 1 Columbia University: Arts & Sciences Fall 2021 Course: PHYSGU4019_001_2021_3-MATHEMATICLMETHODSOFPHYSICS : PHYSGU4019_001_2021_3 - MATHEMATICL METHODS OF PHYSICS Instructor: Yury Levin

Linear operators, complex analysis, and fourier transforms

So much maths. Operators, infinite dimensional vectors, hilbert space, distributions, complex analysis, Green's functions