Perturbative Methods for Modelling (M2)

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• Méthodes perturbatives pour la modélisation / Perturbative Methods for Modelling

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  Olivier THUAL, INP Toulouse

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    Résumé / Summary Page
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• Reference materials for the course
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    Exercices structuring the course (POLYCOP) Fichier
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    Reference Book (pdf format) Fichier
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    Reference Book (.djvu format) Fichier

• Ordinary Differential Equations
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    Variation of parameters Atelier
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    Green function Atelier

• Difference Equation
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    Gamma function Atelier

• Approximate Solution of Linear Differential Equations
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    Singular points Atelier
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    Airy functions Atelier
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    Frobenius method Atelier
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    Irregular singular points Atelier
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    Bessel functions Atelier

• Approximate Solution of Nonlinear Differentiale Equations
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    Critical points Atelier

• Asymptotic Expansion of Integrals
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    Watson's lemma Atelier
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    Laplace's method Atelier
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    Path deformation Atelier
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    Steepest descent method Atelier
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    Stationnary phase method Atelier

• Perturbation Series
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    Perturbation of an eigenvalue problem Atelier

• Boundary Layer Theory
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    Boundary layer Atelier

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

• Multi-Scale Analysis
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    Periodic solutions Atelier
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    Mathieu equation Atelier