Perturbative Methods for Modelling (M2)

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Ordinary Differential Equations

• Atelier Variation of parameters
• Atelier Green function

Difference Equation

• Atelier Gamma function

Approximate Solution of Linear Differential Equations

• Atelier Singular points
• Atelier Airy functions
• Atelier Frobenius method
• Atelier Irregular singular points
• Atelier Bessel functions

Approximate Solution of Nonlinear Differentiale Equations

• Atelier Critical points

Asymptotic Expansion of Integrals

• Atelier Watson's lemma
• Atelier Laplace's method
• Atelier Path deformation
• Atelier Steepest descent method
• Atelier Stationnary phase method

Perturbation Series

• Atelier Perturbation of an eigenvalue problem

Boundary Layer Theory

• Atelier Boundary layer

WKB Theory

• Atelier Schrödinger equation
• Atelier Sturm-Liouville problem
• Atelier Airy equation
• Atelier Turning point

Multi-Scale Analysis

• Atelier Periodic solutions
• Atelier Mathieu equation