Day 228: The Banach Fixed-Point Theorem

Learning Objectives

• •**Define** contraction mappings and verify the contraction property
• •**State and prove** the Banach fixed-point theorem
• •**Apply** fixed-point iteration to solve equations
• •**Understand** convergence rates and error bounds
• •**Use** the theorem to prove existence/uniqueness for differential equations
• •**Connect** fixed-point methods to self-consistent field calculations in QM

Today's Schedule (7 hours)