Practice Parabolic Pdes (3.3.1) - Linear and Non-linear PDEs - Mathematics - iii (Differential Calculus)

Practise this section

10 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
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 condition for parabolic PDEs?
Show hintHide hint
Remember how discriminants classify PDE types.
Question 2.
What does the heat equation model?
Show hintHide hint
Think about heat transfer in objects.
3Question 3.
What is the discriminant for parabolic PDEs?
- D > 0
- D = 0
- D < 0
Show hintHide hint
Recall how discriminants classify the types of PDEs.
4Question 4.
The heat equation is an example of:
- True
- False
Show hintHide hint
Consider how we have defined the heat equation.
Question 5.
Given the initial temperature distribution along a rod is T(x,0) = sin(πx) for 0 ≤ x ≤ 1, derive the temperature distribution at time t > 0 using the heat equation.
Show hintHide hint
Consider using Fourier series for periodic initial conditions.
Question 6.
A wire of length L has an initial temperature distribution T(x,0) = T0 at x = 0 and T1 at x = L. How would you set this up as an initial value problem for a parabolic PDE?
Show hintHide hint
Think about how to express constant boundary conditions in terms of heat flow.

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