Perturbation Methods II

• Course Outline

 
• Handouts
• Formularies
  • Essential series expansions
  • Essential trigonometric identities
  • Solutions to 1st and 2nd order ODEs
  • Classification of damped oscillations
  • Asymptotic expansions of special functions
  • Laplace integrals
    
    
• Valuable Notes
  • Special Class Notes
  • Lecture on algebraic equations
  • Lecture on rescaling
  • Lecture on the Method of Averaging
  • Lecture on the Laplace Method
   
• Important Contributors
• Milton. Van Dyke
• Ali Nayfeh
• Julian D. Cole
• James Murdock
• L. D. Landau
• Erdelyi
• Others
  
  
• Some References
  • On Perturbation Theory
    • Singular Perturbation Theory --R.S. Johnson
    • Advanced Mathematical Methods for Scientists and Engineers --Sean Mauch
    • Mathematical Methods in Physics and Engineering --Cap
    • Some Asymptotic Methods for Strongly Nonlinear Equations --Ji-Huan He
    • Modelling and Perturbation Methods --Mattheij, Rienstra and ten Thije Boonkkamp
    • Perturbation Theory of Dynamical Systems --Berglund
    • Laplace Transform: Theory and Application --Schiff
    • Advanced Mathematical Methods for Scientists and Engineers --Bender
       
  • Mathematical Handbooks
    • Handbook of Mathematical Functions --Abramowitz and Stegun
    • Handbook of Exact Solutions for ODEs --Polyanin
    • Handbook of Linear PDEs --Polyanin
    • Handbook of Integral Equations --Polyanin
    • Handbook of Differential Equations --Zwillinger
      
      
• Some Tutorials and Tools in Symbolic Programming (Mathematica)
  • Nayfeh's Package (contents) Book (To download Mathematica notebooks below use Save Link As)
    • Chapter 1 Global Rules
    • Chapter 2 Duffing, Lindtedt-Poincaré, Multiple Scales, Variation of Parameters, Averaging
    • Chapter 3 Quadratic & Cubic Nonlinearities, Multiple Scales, General Method of Averaging, Krylov-Bogoliubov-Mitropolsky, Method of Normal Forms
    • Chapter 4 Forced Oscillations, Multiple Scales, Resonance, Averaging, Normal Forms
    • Chapter 5 Higher Order Approximations for Systems with Internal Resonances
    • Chapter 6 Forced Oscillators with Finite Degrees of Freedom
    • Chapter 7 Continuous Systems with Cubic Nonlinearities, Solvability Conditions and the Concept of Adjoint, Time-Averaged Lagrangian
    • Chapter 8 Continuous Systems with Quadratic and Cubic Nonlinearities
    • Chapter 9 Higher Order Approximations of Continuous Systems with Two-to-One Internal Resonances
       
  • Kaufmann's Package
     
  • Introductory to Symbolic Programming
    • Getting Started with Mathematica --Erickson
    • An Introduction to Mathematica --Ramsden and Kent
    • A Brief Introduction to Mathematica --Moretti
       
  • Specialized Mathematica
    • Differential equations with Mathematica --Abell and Braselton
    • Partial Differential Equations and Mathematica --Kythe
    • Nonlinear Physics with Mathematica for Scientists and Engineers --Enns and McGuire
    • Exploring Analytic Geometry with Mathematica --Vossler
    • The Mathematica Book 5th Edition --Wolfram