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Concept

List of periodic functions

Related lectures (32)

Periodic Functions: Integrals and Approximations

Discusses periodic functions, integrals, and approximations using trigonometric polynomials and proofs of related theorems.

Unbounded and Bounded Systems: Fourier Methods

Explores the spectral properties of unbounded and bounded systems using Fourier methods and emphasizes the importance of choosing the correct representation for different boundary conditions.

The DTFT as a change of basis

Explores the DTFT as a change of basis, localizing functions, and the Dirac delta functional.

Periodic Functions and Extrema Analysis

Explores periodic functions and extrema analysis in functions.

Parametric Resonance: Standard Base MOOC: Lagrangian Mechanics

Covers parametric resonance, standard base, linearly independent solutions, and periodic functions in mechanics.

Real Functions of Real Variables: Properties and Domains

Covers the properties of real functions, domains, and types of functions, including periodicity.

Sampling Theorem and Control Systems

Explores the Sampling Theorem, digital control, signal reconstruction, and anti-aliasing filters.

Fourier Series: Properties and Applications

Explores Fourier series properties, periodic functions, and coefficient calculation for signal processing and mathematics.

Derivatives of Trigonometric Functions

Explores the derivatives of trigonometric functions and their reciprocals.

Wave Propagation: General Solutions

Explores the general solutions for wave propagation and Fourier transforms in periodic functions.

Fourier Series: Understanding Periodicity and Coefficients

Explores t-periodic functions in Fourier series, discussing intervals, propositions, and variable changes for coefficient calculation and series convergence.

Fourier Series: Understanding Signals and Transformations

Explores Fourier series, left and right limits, theorem proofs, and exam formats.

Algebraic Operations MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

Explores algebraic operations on functions, even and odd functions, and periodic functions.

Fourier Series: Odd and Even Functions

Explores odd and even functions in Fourier series applications, including half-range series and cosine/sine series.

Fourier Series: Sinusoidal Functions and Coefficients Log in to Mediaspace to watch this video

Explains the Fourier series representation of periodic functions using sinusoidal functions and coefficients.

Characterization of Sequences Log in to Mediaspace to watch this video

Explores the convergence criteria and the importance of continuity in sequences near a point xo.

Elastic Collisions and Rotational Motion Log in to Mediaspace to watch this video

Explores elastic collisions, rolling cylinders, and ballistic pendulums.

Fourier Coefficients of Periodic Functions Log in to Mediaspace to watch this video

Explores computing Fourier coefficients of periodic functions, discussing convergence and reconstruction of the original signal.

Interference Patterns Analysis Log in to Mediaspace to watch this video

Analyzes interference patterns from a device with six slits to determine the relation between slit width and distance, showcasing mathematical expressions and graphical representations.

Uniform Convergence of Fourier Series Log in to Mediaspace to watch this video

Covers the concept of uniform convergence of Fourier series and Dirichlet's theorem application.