https://github.com/danielpancake/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
https://github.com/danielpancake/existence-uniqueness-for-cauchy-problem-theory

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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

• Host: GitHub
• URL: https://github.com/danielpancake/existence-uniqueness-for-cauchy-problem-theory
• Owner: danielpancake
• Created: 2023-08-05T20:44:36.000Z (over 1 year ago)
• Default Branch: master
• Last Pushed: 2023-08-06T11:38:16.000Z (over 1 year ago)
• Last Synced: 2025-02-10T12:16:41.774Z (2 months ago)
• Topics: presentation-slides
• Language: TeX
• Homepage:
• Size: 127 KB
• Stars: 0
• Watchers: 1
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# 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