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)