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Applied Functional Analysis
Engineering & Social Sciences Program
Madrid, Spain
Dates: early Sep 2025 - mid Dec 2025
Applied Functional Analysis
OVERVIEW
CEA CAPA Partner Institution: Universidad Carlos III de Madrid
Location: Madrid, Spain
Primary Subject Area: Mathematics
Instruction in: English
Course Code: 18281
Transcript Source: Partner Institution
Course Details: Level 400
Recommended Semester Credits: 3
Contact Hours: 42
Prerequisites: Integration and measure, Complex variables, Ordinary differential equations, Partial differential equations
DESCRIPTION
1. Infinite dimensional vector spaces: Banach and Hilbert spaces.
2. Geometry of Hilbert spaces.
3. Orthonormal bases and Fourier analysis.
4. The problem of best approximation and other applications.
5. Linear operators on Hilbert spaces.
6. Self-adoint and unitary operators on Hilbert spaces: The Fourier transform.
7. The spectral theorem.
8. Applications to signal theory: sampling.
9. Applications to physical theories: quantum mechanics.
10. Applications to numerical analysis: Sobolev spaces.
2. Geometry of Hilbert spaces.
3. Orthonormal bases and Fourier analysis.
4. The problem of best approximation and other applications.
5. Linear operators on Hilbert spaces.
6. Self-adoint and unitary operators on Hilbert spaces: The Fourier transform.
7. The spectral theorem.
8. Applications to signal theory: sampling.
9. Applications to physical theories: quantum mechanics.
10. Applications to numerical analysis: Sobolev spaces.