Lectures related to Fourier Analysis: Stokes Theorem

Fourier Analysis: Series and Divergence Theorem

Covers Fourier analysis, series convergence, divergence theorem, and vector analysis.

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

Covers the properties of signal/data representations using Fourier transformations and matrices.

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Transformations and Inversions: Laplace and Fourier

Discusses Laplace and Fourier transformations, focusing on their inversion formulas and applications in solving differential equations.

Vector Spaces and Scalar Products

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

Dot Product: Properties and Applications

Explores the properties and applications of the dot product in vector spaces.

Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Fourier Transform: Analysis IV

Covers the Fourier transform in Analysis IV, discussing Fourier series and solutions for various problems.

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Orthogonality and Least Squares Method

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Linear Algebra: Dot Product and Pre-Hilbertian Spaces

Explores pre-Hilbertian spaces, focusing on dot product properties and algebraic bases.

Euclidean Spaces: Properties and Concepts

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Fourier Series: Understanding Coefficients and Periodicity

Explores Fourier series coefficients, periodicity, and series relations.

Vector Operations and Geometry

Covers mathematical concepts related to vector operations and geometry, including scalar product and vector norms.

Linear applications and eigenvalues

Covers the representation of linear applications through matrices, diagonalizable matrices, bases, dot product, orthogonality, and orthogonal vectors.

Signal Representations

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Matrix Operations: Determinants and Vector Spaces

Covers strategies for matrix operations and the concept of vector spaces.

Orthogonality and Scalar Product

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Hermitian Forms: Definition and Properties

Explores the definition and properties of Hermitian forms in complex vector spaces.