Envisioned Course Setting
• Level: 2nd–3rd year Bachelor students in Mathematics (course: Analysis 2, Ordinary
differential equations, Numerical analysis).
• Prerequisites: Basic knowledge of metric spaces, sequences, continuity, and limits.
• Language of Instruction: English.
• Lecture Type: 20-minute interactive lecture (tablet presentation).
Learning Objectives
By the end of the lecture, students should be able to:
1. Understand the concept of a contraction mapping on a complete metric space.
2. State and explain the Banach Fixed Point Theorem and outline its proof.
3. Apply the theorem to simple nonlinear equations and iterative schemes.
4. Recognize how fixed-point principles form the foundation for existence and uniqueness results in
differential equations.