2.3 - Characteristic Curves
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Practice Questions
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What type of PDE is defined by a discriminant Δ < 0?
💡 Hint: Think of someone being steady.
Which equation represents a parabolic PDE?
💡 Hint: Remember diffusion.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What type of PDE is represented by Δ < 0?
💡 Hint: Think steady-state.
True or False: All hyperbolic PDEs require two initial conditions.
💡 Hint: Remember wave motions.
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Challenge Problems
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Classify the PDE ∂²u/∂x² + 2∂²u/∂y² - ∂u/∂y = 0 and discuss the implications of its classification.
💡 Hint: Revisit the discriminant calculation.
Derive the characteristic curves for the wave equation ∂²u/∂t² - c²∂²u/∂x² = 0.
💡 Hint: Think about shifting variables in the equation.
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