MATHEMATICAL PHYSICS I (part II)
The syllabus and lecture notes presented below are related to the academic
years 2004/05, 2005/06 and 2006/07. The lecture notes have been sectioned into
independent downloadable PDF and PostScript files. They do not necessarily
follow the order and content presented at the lectures in every detail.

## Syllabus

- Lagrange multipliers
- Euler-Lagrange equation
- Principle of least action
- Laplace's equation in cartesian, cylindrical and spherical coordinates
- Bessel's equation and the properties of Bessel functions of the first and second kind
- Legendre's equation and Legendre polynomials
- The associated Legendre's equation and associated Legendre polynomials
- Spherical harmonics

## Lecture notes

- Lagrange Multipliers
(PDF)
- Calculus of Variations (I)
(PDF)
- Calculus of Variations (II)
(PDF)
- The Principle of Least Action
(PDF)
- Gradient, Divergence and Curl in Curvilinear Coordinates
(PDF)
- Laplace's Equation in Cylindrical Coordinates and Bessel's Equation (I)
(PDF)
- Laplace's Equation in Cylindrical Coordinates and Bessel's Equation (II)
(PostScript)
(PDF)
- Laplace's Equation in Spherical Coordinates and Legendre's Equation (I)
(PostScript)
(PDF)
- Laplace's Equation in Spherical Coordinates and Legendre's Equation (II)
(PostScript)
(PDF)

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