Dirac delta function

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Related lectures (32)

Linear Quantum Calculus in Dirac Notation

Covers linear algebra in Dirac notation, emphasizing the scalar product and density product in quantum computations.

Dirac Delta

Covers the definition and applications of the Dirac Delta function in signal processing.

Dirac Delta Function

Introduces the Dirac delta function and discusses its properties and applications in signal processing and physics.

Dirac Delta Function and ODEs

Covers the Dirac delta function, Laplace transforms, and unimolecular reactions with convolution emphasis.

Dynamical Systems: Laplace Transform

Covers the Laplace transform, transfer functions, and properties of common functions in dynamical systems.

Real Functions: Definitions and Examples

Explores definitions and examples of real functions of a real variable.

Distributions and Laplace Transform: Key Concepts

Discusses distributions, the Laplace transform, and their applications in mathematical analysis.

Convolution of Distributions and Differential Equations

Explores the convolution of tempered distributions and solving differential equations using fundamental solutions.

Signals & Systems I: Sampling and Reconstruction

Explores ideal sampling, Fourier transformation, spectral repetition, and analog signal reconstruction.

Analysis IV: Tempered Distributions and Dirac Functional

Introduces tempered distributions, derivatives, and Dirac functional in analysis.

Particle decay rates

Explores particle decay rates through Fermi's Golden Rule and perturbation theory.

Spectral Theory: Regularity and Embedding

Explores spectral theory, emphasizing regularity properties and embedding theorems in the context of Sobolev spaces and compactly supported functions.

Continuous Variable Representation

Covers the time evolution for non-time invariant systems and continuous and discrete degrees of freedom.

Quantum Transport: Scattering Matrix Approach

Explores quantum transport using the scattering matrix approach to analyze conductance and resistance in electron movement.

Impulse-train Sampling: The Sampling Theorem

Covers impulse-train sampling, the sampling theorem, and reconstructing signals from samples in the frequency domain.

Laplace Transform: Basics

Introduces Laplace transform, ROC, and LTI systems with transfer functions and frequency response.

Fourier Transform: Diffusion Equation

Explores the derivation of the diffusion equation using Fourier transforms and discusses the significance of Dirac delta functions in mathematical analysis.

Signal Sampling and Reconstruction: Fundamentals

Covers the fundamentals of signal sampling and reconstruction, including the sampling theorem and practical reconstruction systems.

Laplace Transform: Basics

Covers the Laplace transform, region of convergence, impulse response, and multiple poles.

Signals & Systems I: Distributions and Linear Systems

Covers distributions, linear systems, impulse response, convolution, and examples of linear systems.

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