Introduction to Mathematical Physics. Calculus of Variations and Boundary-value Problems

TL;DR

This book provides an introduction to mathematical physics focusing on calculus of variations and boundary-value problems, including classical methods, problem-solving techniques, and applications in physics and engineering.

Contribution

It offers a comprehensive overview of solving linear boundary-value problems with detailed analysis and sample solutions, integrating calculus of variations and special function theory.

Findings

Detailed analysis of Sturm-Liouville problems

Fourier method substantiation for boundary-value problems

Sample solutions in multiple dimensions

Abstract

This book considers posing and the methods of solving simple linear boundary-value problems in classical mathematical physics. The questions encompassed include: the fundamentals of calculus of variations; one-dimensional boundary-value problems in the oscillation and heat conduction theories, with a detailed analysis of the Sturm-Liouville boundary-value problem and substantiation of the Fourier method; sample solutions of the corresponding problems in two and three dimensions, with essential elements of the special function theory. The text is designed for Physics, Engineering, and Mathematics majors.