Landslides and erosion are some of the major environmental concerns caused by heavy rainfalls or human activities, since they can lead to risks for infrastructures and ecosystems. In this work it is proposed to use the diffusion equation (a partial differential equation) to model to describe how the land material will be moved in space and time due erosion in an intense rainfall situation. Thus, this activity is a practice exercise of an applied maths subject of the Bachelor’s Degree in Geomatic and Surveying Engineering at Universitat Politècnica de València (Spain). Its objective is double. First, to find the analytical solution of the diffusion equation and reinforce the mathematical skills of the subject, and second, to help students to become aware of the usefulness of the applied mathematical concepts studied (in this example, the relation to natural disasters prediction and mitigation).

The proposed activity also depicts an example of the application of solving mathematical problems to address real environmental challenges. With regard to them, the activity also aims to contribute to the integration of the United Nations Sustainable Development Goals (SDG) in university education. In particular, SDG 13 (Climate Action) and SDG 15 (Life on Land), within the goals to strengthen adaptive capacity to climate-related hazards and natural disasters, and restore degraded land and soil affected by floods.

At the end of the activity, a short survey is conducted to obtain the students’ feedback. It is important to highlight that more than 90% of the students appreciated this type of practical activities, and that 86% would be interested in continuing working with this type of problems.

Keywords: Partial Differential Equations, Diffusion Model, Landslides, Sustainable Development Goals, Engineering, Mathematics.