Advanced Mathematics

Advanced Mathematics for Theoretical Chemistry

"The interplay between mathematics and physics needs no emphasis. What may need to be emphasized is that mathematics is not merely a tool with which the presentation of physics is facilitated, but the only medium in which physics can survive. Just as language is the means by which humans can express their thoughts and without which they lose there unique identity, mathematics is the only language through which physics can express itself and without which it loses its identity. And just as language is perfected due to its constant usage, mathematics develops in the most dramatic way because of its usage in physics."

-from the preface of Mathematical Physics:

A modern introduction to its foundation

by Sadri Hassani

Course Syllabus

Chapters one and four from my book

Problem Sets


Mathematica Notebooks

diagonalization.nb: Some basic matrix manipulation

eulerangles.nb: Construction of the Euler rotation matrix and visualiztion of its action on a vector in three-space

mapping.nb: Maps lines from the complex z-plane to the complex w-plane.

phasecolor.nb: Displays the modulus of a function colored according to the phase of the function. Several examples.

viewcomplex.nb: Displays the real, imaginary, modulus and phase of a complex function. Sevaral examples.

showfourier.nb: Displays the real and imaginary parts of both the original function and its Fourier transform.

causal.nb: Superimposes the real and imaginary parts of causal functions and their Fourier transforms.

chirp.nb: Investigates linearly chirped pulses and their Fourier transforms.

doubleexp.nb: Illustrates the complementary nature of time and frequency domain techniques for biexponential decay.

2dnmr: Generates COSY free induction decay signals and the corresponding COSY spectra.