3.3.1 - Parabolic PDEs
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is the discriminant condition for parabolic PDEs?
💡 Hint: Remember how discriminants classify PDE types.
What does the heat equation model?
💡 Hint: Think about heat transfer in objects.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the discriminant for parabolic PDEs?
💡 Hint: Recall how discriminants classify the types of PDEs.
The heat equation is an example of:
💡 Hint: Consider how we have defined the heat equation.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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.
💡 Hint: Consider using Fourier series for periodic initial conditions.
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?
💡 Hint: Think about how to express constant boundary conditions in terms of heat flow.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.