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Partial Differential Equations
Engineering & Social Sciences Program
Madrid, Spain
Dates: 1/16/25 - 6/4/25
Partial Differential Equations
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Mathematics
Instruction in: English
Course Code: 18277
Transcript Source: Partner Institution
Course Details: Level 300
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Besides the Basic Core matters: Vector calculus (year 1, semester 2), Integration and measure (year 2, semester 1), Ordinary differential equations (year 3, semester 1).
DESCRIPTION
1. Introduction to PDEs. First concepts. Fundamental equations.
2. Fourier series. Motivation. Convergence and regularity of Fourier series. Sturm-Liouville problems. Generalized Fourier series. The Fourier transform.
3. Elliptic equations. Laplace equation. Properties of harmonic functions. Poisson equation . Green representation. Green function in different domains. Eigenvalue problem.
4. Parabolic equations. Heat equation in bounded domains. Green representation. Heat equation in the whole space. Gauss kernel. Selfsimilarity.
5. Hyperbolic equations. Wave equation in bounded domains. Resonance. Green representation. Wave equation in the line. D'Alembert formula. Wave propagation in dimensions 3 and 2, Green function. Huygens principle.
2. Fourier series. Motivation. Convergence and regularity of Fourier series. Sturm-Liouville problems. Generalized Fourier series. The Fourier transform.
3. Elliptic equations. Laplace equation. Properties of harmonic functions. Poisson equation . Green representation. Green function in different domains. Eigenvalue problem.
4. Parabolic equations. Heat equation in bounded domains. Green representation. Heat equation in the whole space. Gauss kernel. Selfsimilarity.
5. Hyperbolic equations. Wave equation in bounded domains. Resonance. Green representation. Wave equation in the line. D'Alembert formula. Wave propagation in dimensions 3 and 2, Green function. Huygens principle.