Analytical Methods in Physics

TL;DR

This lecture notes collection provides a comprehensive introduction to analytical methods in physics, covering mathematical tools like complex analysis, differential geometry, and PDEs for upper-level students.

Contribution

It compiles and expands foundational mathematical techniques essential for advanced physics education into an accessible textbook format.

Findings

Covers complex numbers, matrix algebra, and vector spaces.

Includes calculus on complex plane and approximation methods.

Discusses differential geometry and PDEs in physics.

Abstract

This set of lecture notes constitutes the free textbook project I initiated towards the end of Summer 2015, while preparing for the Fall 2015 Analytical Methods in Physics course I taught to upper level undergraduates at the University of Minnesota Duluth. During Fall 2017, I taught Differential Geometry and Physics in Curved Spacetimes at National Central University, Taiwan; and this gave me an opportunity to expand on the text. Topics currently covered include: complex numbers, matrix algebra, finite and infinite dimensional vector spaces, calculus on the complex plane, special/approximation methods in calculus, differential geometry in curved space(time)s, and partial differential equations.