1 Computer-Assisted Proofs and Interval Arithmetic
1.1 What is a Computer-assisted proof?
1.2 History

2 Interval Arithmetic
2.1 Basic Arithmetic
2.2 Automatic Differentiation
2.3 Integration
2.4 Singular integrals and integrals over unbounded domains

3 The Muskat Problem

4 The Surface Quasi-Geostrophic Equation