Advanced Mathematical Physics 1. 2026–2027 (UniTS, SISSA)
An introduction to partial differential equations in mathematical physics.
University of Trieste, Master's Degree in Mathematics. Official course page and syllabus.
Lectures
Schedule: Tuesdays 11:00–13:00 and Wednesdays 14:00–16:00.
Room: 134.
Next lectures: October 13, 14, 20, 21, 27, 28.
Materials
AI generated notes. pdf (updated October 8, 2026).
Problems. pdf (updated October 8, 2026).
Visualizations. folder.
Plan of the Course
- Introduction.
- First-order equations.
- Linear differential operators.
- The wave equation.
- The Laplace equation and harmonic functions.
- The heat equation.
- Fluid dynamics: Euler and Navier–Stokes equations.
- Selected nonlinear equations.
References
- B. Dubrovin, course notes (PDF).
- W. A. Strauss, Partial Differential Equations: An Introduction, Wiley, 2008.
- L. C. Evans, Partial Differential Equations, AMS, 2010.
- V. I. Arnold, Lectures on Partial Differential Equations, Springer, 2004.
- S. Salsa, Partial Differential Equations in Action, Springer, 2008.
- D. J. Acheson, Elementary Fluid Dynamics, Oxford University Press, 1990.