Practice Definition Of Pde (3.1.1) - Linear and Non-linear PDEs - Mathematics - iii (Differential Calculus)

Practise this section

9 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
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is a PDE?
Show hintHide hint
Consider how it differs from ODEs.
Question 2.
What is Laplace’s equation an example of?
Show hintHide hint
Think about the powers of the function involved.
3Question 3.
What does PDE stand for?
- Partial Differential Equation
- Partial Derivative Equation
- Partial Differential Express
Show hintHide hint
Remember the full name of the equation.
4Question 4.
True or False: Linear PDEs can have products of the dependent variable and its derivatives.
- True
- False
Show hintHide hint
Consider how the terms in the equation are structured.
Question 5.
Show that the equation $\frac{\partial^2 u}{\partial x^2} + e^{u} \frac{\partial u}{\partial y} = 2$ is a non-linear PDE and explain why.
Show hintHide hint
Look for non-linear functions of the dependent variable.
Question 6.
Derive a second-order linear PDE from physical principles (e.g., heat conduction) and state its physical significance.
Show hintHide hint
Consider the balance of heat energy in a given area.

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