/existence-uniqueness-for-cauchy-problem-theory

Covers basics of metric spaces, normed spaces, pointwise/uniform convergence, the Banach Fixed Point Theorem and its application in the Picard-Lindelöf Theorem for existence and uniqueness of solutions to IVPs for ODEs

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Existence and Uniqueness of the Solution to Cauchy Problem

This presentation covers some key concepts in metric spaces, including Banach's fixed-point theorem, notions of convergence, normed spaces, spaces of continuous functions, and the Picard–Lindelöf theorem.

Overview

  • Metric spaces
  • Banach's fixed-point Theorem
    • Proof for uniqueness of a fixed-point
    • Proof for existence of a fixed-point
  • Pointwise and Uniform convergence
  • Normed spaces
  • Space of continuous functions
  • Picard–Lindelöf Theorem
  • References