Credits: 7.5

Type: bridging

Objectives:

• To understand the physical origin and interpretation of the classical equations
• To understand the characteristic traits of different equation types and the main basic techniques used in their study.

Knowledge:

• Classification. Examples of equations.
• Elliptic equations. Laplace 's equation. Average value formulas. Maximum principle. Green's function. Energy methods.
• Parabolic equations. Heat equation. Maximum principle. Properties of solutions.
• Hyperbolic equations. Wave equation. Spherical averages.
• Energy methods.
• Finite difference methods.

Subject-specific competences:

• To understand the basic tools used in the study of partial differential equations.
• To solve classical equations in simple domains.