Practice Canonical Forms - 2.4 | 2. Classification of PDEs (Elliptic, Parabolic, Hyperbolic) | Mathematics - iii (Differential Calculus) - Vol 2
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Canonical Forms

2.4 - Canonical Forms

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Practice Questions

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Question 1 Easy

What is the discriminant formula for classifying PDEs?

💡 Hint: Think of the standard form of a quadratic equation.

Question 2 Easy

Identify the type of PDE if Δ < 0.

💡 Hint: This type indicates steady-state behavior.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the value of the discriminant Δ for elliptic PDEs?

Δ < 0
Δ = 0
Δ > 0

💡 Hint: Think about the conditions for each type.

Question 2

True or False: Hyperbolic PDEs have one real repeated characteristic line.

True
False

💡 Hint: Recall the behavior of waves and their propagation.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Classify the PDE: ∂²u/∂x² + 4∂²u/∂y² = 0. What conditions do you derive from this?

💡 Hint: Calculate the discriminant first!

Challenge 2 Hard

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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