Introduction to Partial Differential Equations

COURSE OBJECTIVES

Knowledge and understanding of the functional analytic foundation of PDEs and basic discretisation methods for their numerical solution.

COURSE DESCRIPTION
Many phenomena in real life applications are modeled by partial differential equations (PDEs). These mathematical models are sets of equations, which describe the essential behavior of a natural or artificial system, in order to forecast and control its evolution. We will give an overview on the derivation of PDEs from physical applications and discuss their mathematical background. The theoretical investigations will be accompanied by the introduction and implementation of numerical schemes for their actual solution. In this course, we will mainly focus on elliptic and parabolic PDEs.

LEARNING METHODS
Depending on the teaching situation in fall either direct instruction plus exercises (offline) or flipped classroom plus exercises (online).

EXAMINATION INFORMATION
Oral exam.

REFERENCES

• Finite Elements; D. Braess, 3rd edition, Cambridge University Press.
• Numerical models for differential problems; A. Quarteroni, 4th edition, Springer.
• Partial Differential Equations in action, from Modelling to Theory; S. Salsa, Springer.
• Partial Differential Equations with Numerical Methods; S. Larsson and V. Thomée, Springer.