Analytical Methods in Physics

This textbook is based on lectures for a third-year course on mathematical methods in physics taught in the Department of Physics at the University of Oslo.

This textbook contains 26 lectures organized into five topics: i) Complex Analysis, ii) Variational Calculus, iii) Ordinary Differential Equations, iv) Integral Transformations, and v) Partial Differential Equations. For each topic, basic fundamental theorems and mathematical techniques are introduced and applied to solving problems. This resource is intended as concise and well-structured, making it suitable for a one-semester course. It is aimed at second- or third-year undergraduate students with background in mathematics and physical science.

A concise primer on analytical methods and applied math for the physical sciences Introduces complex analysis and variational calculus Covers Green's function method and integral transforms for solving differential equations

Autorentext

Luiza Angheluta is a Professor of Physics at the University of Oslo. She received the Fridtjof Nansen Award for Young Researchers in 2012 and HM the King's Gold Medal in 2011. Her research uses theoretical statistical physics and computational physics to understand emergence phenomena and pattern formations in systems with topological defects, including superfluids, crystals, liquid crystals, and active matter. This is an interdisciplinary research that aims to better our understanding of the material properties and functionalities of geomaterials, biological systems, and bio-inspired materials.

Inhalt

Complex Analysis.- Variational Calculus.- Ordinary differential equations.- Fourier Series.- Integral transforms.- Partial differential equations.