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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is an initial condition in a PDE?
π‘ Hint: Think about what information you need at time t = 0.
Question 2
Easy
Name the three types of boundary conditions.
π‘ Hint: Recall the DNR acronym.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What do Dirichlet conditions specify?
- The derivative at the boundary
- The function value at the boundary
- No flow at the boundary
π‘ Hint: Recall the type of condition that dictates what is happening right at the edge.
Question 2
True or False: A well-posed problem is one that is stable.
- True
- False
π‘ Hint: Consider what well-posed means in connection with solutions.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A cylindrical rod of length L is held at fixed temperatures at both ends (Dirichlet conditions). The initial temperature distribution is given as u(x,0) = sin(Οx/L). Solve the PDE for different times t > 0.
π‘ Hint: Consider using Fourier series to express the initial condition.
Question 2
A string fixed at both ends vibrates according to the wave equation with initial displacement u(x,0) = f(x) and initial velocity βu/βt (x,0) = g(x). Derive the general solution of the wave equation subject to Neumann boundary conditions.
π‘ Hint: Focus on how the wave behavior is altered based on the boundary at the fixed ends.
Challenge and get performance evaluation