▼ IMPORTANT ▼ In this video we will see an exercise (example) solved of an equation in partial derivatives (partial differential equation) of heat in one dimension with conditions at the zero boundary (thin rod with extremes with constant zero temperature) and initial condition (distribution initial temperatures given by a cubic polynomial function), solved by the Fourier method, that is, first separating variables, and solving two ordinary differential equations for different possible cases of lambda, calculating the eigenvalues and their corresponding eigenfunctions, and finally using superposition principle to calculate the corresponding sine Fourier series by integrals solved by integration by parts (tabular method).
Everything explained step by step.
#DifferentialEquations #EDP #Fourier #Series #Wave
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** BIBLIOGRAPHY **
- Advanced Mathematics for Engineering, by Peter V. O'Neil
- Introduction to Partial Differential Equations, by Peter J. Olver
- Equations in Partial Derivatives, by Richard Haberman
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Негізгі бет One-dimensional heat EDP, separation of variables, Fourier method
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