Perturbation Methods I

• Course Outline
   
• Assignments
  • Problem Set I
    • Preliminary Concepts and Gauge Functions
  • Problem Set II
    • Proper Scaling and Regular Perturbations
  • Problem Set III
    • Transcendental Equations and Successive Approximations
  • Problem Set IV
    • Singular Perturbations, Lindstedt's Technique
  • Problem Set V
    • Method of Strained Coordinates, PLK and Pritulo
  • Problem Set VI
    • Boundary Layers and Matched Asymptotic Expansions
  • Problem Set VII
    • Method of Multiple Scales
    
    
• Handouts
  • Formularies
    • Essential series expansions
    • Essential trigonometric identities
    • Solutions to 1st and 2nd order ODEs
    • Classification of damped oscillations
    • Classification of regular and singular perturbations by Milton Van Dyke
      
      
  • Special Notes
    • Class notes (acquired by a fellow student)
    • Introduction, gauge functions and asymptotic expansions
    • Finding roots of polynomials
    • Perturbation techniques for ODEs --Tzitzouris
    • Boundary layer problems with constant coefficients
    • Boundary layer problems with variable coefficients
    • Strained coordinates, Duffing's equation, linear oscillator
    • Multiple scales
       
• Historical Contributors
  • Von Karman's approach to research--as described by Bill Sears
  • Ludwig Prandtl
  • Leonhard Euler
  • Blaise Pascal and René Descartes
  • Isaac Newton
  • Other contributors
     
• Other
  • Course notebook
  • Interesting video titles
  • Expanding websites
  • Basic terms
  • Wolfram Alpha