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Lecture# Waves and Diffusion: Fundamentals

Description

This lecture covers the fundamentals of waves, diffusion, and convection, focusing on the concepts of propagation, initial conditions, and boundary conditions. The instructor discusses the mathematical equations and numerical methods used to solve wave and diffusion problems.

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Instructors (2)

MATH-251(b): Numerical analysis

The students will learn key numerical techniques for solving standard mathematical problems in science and engineering. The underlying mathematical theory and properties are discussed.

Related concepts (35)

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In mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.

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Explores waves in inhomogeneous media, covering initial and boundary conditions, numerical stability, eigen modes, and propagation principles.