18 - Separation of Variables, Use of Fourier Series
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Practice Questions
Test your understanding with targeted questions
What is the significance of the separation constant in the method of separation of variables?
💡 Hint: Think about its role in the separation process.
List the three types of second-order PDEs relevant to civil engineering.
💡 Hint: Identify the equilibrium states, steady states, and wave phenomena.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What method simplifies PDEs into ordinary differential equations?
💡 Hint: Think about the name of the technique.
Fourier series can represent any periodic function, true or false?
💡 Hint: Recall its definition and properties.
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Challenge Problems
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Derive the Fourier coefficients for a function f(x) defined on [–L, L] given by f(x) = L + sin(nπx/L).
💡 Hint: Recall the integration formulas for a Fourier series!
Consider a beam resonating at its fundamental frequency. Set up the wave equation and solve for the mode shapes using Fourier methods.
💡 Hint: Examine boundary conditions that are relevant for a beam model.
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