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An Introduction to Partial Differential Equations
Last Updated: 2026-02-05 16:37:24
Abstract
This course aims at being an introduction to first and second order partial differential equations (in short PDEs).We will present the so called method of characteristics to solve quasilinear PDEs and some basic properties of classical solutions to second order linear PDEs.
Content
A preliminary plan is the following - Laplace equation, fundamental solution, harmonic functions and main properties, maximum principle. Poisson equation. Green functions. Perron method for the solution of the Dirichlet problem. Regularity of solutions to the Poisson Equation. - Heat equation, fundamental solution, existence of solutions to the Cauchy problem and representation formulas, main properties, uniqueness by maximum principle, regularity. - The Method of characteristics for first order equations, linear and nonlinear, transport equation, Hamilton-Jacobi equation, scalar conservation laws. -Time permitting: Wave equation, existence of the solution, D'Alembert formula, solutions by spherical means, main properties, uniqueness by energy methods.
Resources
Lecture Notes
The teacher provides the students with personal notes.
Literature
Bibliography - L.Evans Partial Differential Equations, AMS 2010 (2nd edition) - D. Gilbarg, N.S. Trudinger Elliptic Partial Differential Equations of Second Order, Springer, 1998. - E. Di Benedetto Partial Differential Equations, Birkauser, 2010 (2nd edition). - W. A. Strauss Partial Differential Equations. An Introduction, Wiley, 1992. -Q. Han, A Basic Course in Partial Differential Equations, Graduate Studies in Mathematics Volume: 120; 2011.
Learning Materials (Links)
- Main link
- Webpage of the course
- Additional links
- Link zur Homepage von Prof. Francesca Da Lio
General Information
- Language
- English
- Levels
- BSC , MSC
- Frequency
- Yearly recurring
Examination
- Type
- session examination
- Mode
- oral 20 minutes
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture |
An Introduction to Partial Differential Equations
Starts in the second week of the semester. The missing three lecture hours from the first week are planned to take place Thu 8-9 (exact dates to be announced).
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3 h weekly |
Offered In
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Selection: Analysis ((so far) no course offering)
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Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
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