Practice Partial Differential Equations – Basic Concepts (16) - Partial Differential Equations

Practise this section

9 questions

Flashcard drill
4 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
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define a partial differential equation (PDE).
Show hintHide hint
Consider how it differs from ordinary differential equations.
Question 2.
What is the order of the equation ∂²u/∂x² + ∂u/∂y = 0?
Show hintHide hint
Look for the highest derivative in the equation.
3Question 3.
What does the order of a PDE refer to?
- The number of variables involved
- The highest derivative present
- The length of the equation
Show hintHide hint
Focus on the derivatives when answering.
4Question 4.
True or False: Linear PDEs contain nonlinear terms.
- True
- False
Show hintHide hint
Recall the definitions of linear and nonlinear.
Question 5.
Given the relation z = ax² + bxy + cy², derive the corresponding PDE.
Show hintHide hint
Focus on differentiating each component step-wise.
Question 6.
Classify the PDE: ∂²u/∂x² - 2∂²u/∂y² + ∂²u/∂y² = 0.
Show hintHide hint
Use the discriminant formula carefully to classify.

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