Approximating Functions with Polynomials

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Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Quadratic Approximation: Example

Covers finding the best quadratic approximation for a given function in a continuous space.

Geometric Transformations in R2 and R3: Visualizations and Rotations

Covers visualizations in orthonormal bases in R2, focusing on rotations and reflections.

Signal Representations

Covers signal representations using Fourier transforms and projection theorems in the time-frequency plane.

Distance to Origin and Constrained Domains

Covers the concept of distance to the origin and functions in constrained domains.

Projection in Vector Spaces

Explores the generalization of projection in vector spaces and its unique properties, emphasizing its role in finding the closest vector in a subspace.

Partial Derivatives: Definitions and Examples

Covers the concept of partial derivatives and their applications in mathematical analysis.

Derivatives and Continuity

Explores derivatives, reciprocal functions, and continuity of functions with examples and formulas.

Function Spaces and Hilbert Spaces

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Vibration of Diatomic Molecules

Explores the vibration of diatomic AB molecules and Fourier series, emphasizing equations of motion and Dirichlet's theorem.