Notes on Basic Singular Perturbations For
Elliptic, Parabolic, Hyperbolic PDE Click here Click here
Rough notes on more advanced material
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Notes on Strong Localized Peterturbation Theory
Click here: Review of
Green's functions Click here
Review of Legendre Polynomials Click here Two Worked Problems in 2-D Click here
Further Notes on Applications of Strong
Localized Perturbation Theory: Ostwald Ripening
Click here Biharmonic Equation
Click here Low Reynolds Number Flow
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Notes on Interface Dynamics in 1-D
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Notes on Interface Dynamics in Multi-Dimemsions:
Tangential-Normal Coordinates and Derivation of Mullins-Sekerka Flow from Cahn-Hilliard
Click here Surface Diffusion
in a Chemotaxis model with volume filling
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Notes on Homogenization Theory
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Basic Notes on Pattern Formation: Turing Stability Analysis
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Notes on Pattern Formation: Case Study of
Brusselator
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Notes on Pattern Formation: Localized
Pulse Solutions
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Condensed Notes on Pulse Solutions for an RD
System
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Notes on Singularities in PDE: Blow-Up Behavior
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Notes on WKB For PDE's
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Homework 1 (Due Jan. 21: ): Assignment
Click here: Solutions
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Homework 2 (Due: Feb. ): Assignment
Click here: Solutions
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Homework 3 (Due: Feb. ): Assignment
Click here: Solutions
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Homework 4 (Due: March): Assignment
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Homework 5 (Due: March) : Assignment
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Homework 6 (Due: April) : Assignment
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Project (Due: April ) : Instructions
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Convection-Diffusion Asymptotics and Strong Localized Perturbation Theory:
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Homogenization References:
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Weakly Nonlinear and Localized Pattern Formation
References:
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WKB For PDE's References:
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