Differential Equations

복수전공하고 있는 수학과의 학부 졸업시험에 미분방정식이 있는 줄 알고, 시험 준비도 할 겸 복학할 때 “상미분방정식” 과목을 신청했습니다. 나중에 알고보니 미분방정식은 졸업시험 과목이 아니었습니다… OTL… 그래도 이왕 시작한 것 포기란 없습니다!! 💪 으랏차!!

Textbooks

• Morris, Differential Equations, Dynamical Systems & An Introduction to Chaos 3rd Edition
  • 학교 도서관에서 e-book으로 다운 받을 수 있길래 그걸로 공부 했습니다 🙂
• Gerald Teschl, Ordinary Differential Equations and Dynamical Systems
• Terence Tao, Chapter 1 of “Nonlinear dispersive equations: local and global analysis”

First order ODE

• Logistic Population Model
• Poincare Map

Planar Linear Systems

Nothing to write

Phase Portraits for Planar Systems

• Zero Eigen Value on Systems of ODEs
• Jordan Block Case on Systems of ODEs
  • Generalized Eigen Values의 내용을 참고할 것
• Insights for Solving 2nd Order ODE System with Repeated Roots

Classification of Planar Systems

(Empty)

• Duhamel’s Theorem

The Existence and Uniqueness

• Lipschitz Constant
  • Locally Liipschitz
• Picard Iteration 👋
• Gronwall’s Inequality
  • Differential Form
  • Integral Form
• Banach Space
  • Completeness
    • Completeness of Real Numbers
  • Hibert Space
  • Banach Space
    • Norm Space vs. Inner Product Space