Partial Differential Equations: Heat Equation in R

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Related lectures (31)

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Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems, including applications with the Fast Fourier transform (FFT) and de-noising data.

Fourier Transform and Partial Differential Equations

Explores the application of Fourier transform to PDEs and boundary conditions.

Fourier Analysis and PDEs

Explores Fourier analysis, PDEs, historical context, heat equation, Laplace equation, and periodic boundary conditions.

Numerical Methods: Boundary Value Problems

Covers numerical methods for solving boundary value problems using Crank-Nicolson and FFT.

Heat and Wave Equations: Analysis IV

Covers the study of the heat and wave equations, including the process of separating variables to find solutions.

Poisson Problem: Fourier Transform Approach

Explores solving the Poisson problem using Fourier transform, discussing source terms, boundary conditions, and solution uniqueness.

Fourier and Laplace Transforms: Concepts and Applications

Provides an overview of Fourier and Laplace transforms, their properties, and applications in signal analysis.

Fourier Transform: Concepts and Applications

Covers the Fourier transform, its properties, applications in signal processing, and differential equations, emphasizing the concept of derivatives becoming multiplications in the frequency domain.

Fourier Transform: Derivatives and Formulas

Explores Fourier transform properties with derivatives, crucial for solving equations, and introduces the Laplace transform for signal transformation.

Complex Analysis: Laplace and Fourier Transforms

Discusses complex analysis, focusing on Laplace transforms, Fourier series, and the heat equation's solutions and uniqueness.