2.4 - Canonical Forms
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Practice Questions
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What is the discriminant formula for classifying PDEs?
💡 Hint: Think of the standard form of a quadratic equation.
Identify the type of PDE if Δ < 0.
💡 Hint: This type indicates steady-state behavior.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the value of the discriminant Δ for elliptic PDEs?
💡 Hint: Think about the conditions for each type.
True or False: Hyperbolic PDEs have one real repeated characteristic line.
💡 Hint: Recall the behavior of waves and their propagation.
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Challenge Problems
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Classify the PDE: ∂²u/∂x² + 4∂²u/∂y² = 0. What conditions do you derive from this?
💡 Hint: Calculate the discriminant first!
Transform the given PDE ∂²u/∂x² - 4∂²u/∂t² = 0 into the appropriate canonical form.
💡 Hint: Think of the methods required to change coordinates.
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