Practice Canonical Forms (2.4) - Classification of PDEs (Elliptic, Parabolic, Hyperbolic)

Practise this section

10 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
4 questions · about 3 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is the discriminant formula for classifying PDEs?
Show hintHide hint
Think of the standard form of a quadratic equation.
Question 2.
Identify the type of PDE if Δ < 0.
Show hintHide hint
This type indicates steady-state behavior.
3Question 3.
What is the value of the discriminant Δ for elliptic PDEs?
- Δ < 0
- Δ = 0
- Δ > 0
Show hintHide hint
Think about the conditions for each type.
4Question 4.
True or False: Hyperbolic PDEs have one real repeated characteristic line.
- True
- False
Show hintHide hint
Recall the behavior of waves and their propagation.
Question 5.
Classify the PDE: ∂²u/∂x² + 4∂²u/∂y² = 0. What conditions do you derive from this?
Show hintHide hint
Calculate the discriminant first!
Question 6.
Transform the given PDE ∂²u/∂x² - 4∂²u/∂t² = 0 into the appropriate canonical form.
Show hintHide hint
Think of the methods required to change coordinates.

6 more questions in this section. Enroll free to practise them all.