Notes on the trigonometric Fourier series, including coefficient derivation and connection to linear algebra in Hilbert space.
Explores the Hilbert transform as an infinite matrix, linking Fourier series and block matrix multiplication.
Compares the accuracy and behavior of Fourier, Legendre, and Taylor series expansions when approximating functions with a limited number of terms.
Explains the mathematical derivation of generalized Fourier series expansions using orthogonal function bases and inner products.
Introduces linear algebra concepts like vector spaces and orthogonality as a foundation for understanding generalized Fourier series expansions.
Explores generalized Fourier series expansions using orthogonal function bases, with examples from Legendre polynomials and practical Jupyter notebook code.
