Practice Solving PDEs with Boundary and Initial Conditions - 16.7 | 16. Boundary and Initial Conditions | Mathematics - iii (Differential Calculus) - Vol 2
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16.7 - Solving PDEs with Boundary and Initial Conditions

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Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is an initial condition in a PDE?

💡 Hint: Think about what information you need at time t = 0.

Question 2

Easy

Name the three types of boundary conditions.

💡 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

💡 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

💡 Hint: Consider what well-posed means in connection with solutions.

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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(πx/L). Solve the PDE for different times t > 0.

💡 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 ∂u/∂t (x,0) = g(x). Derive the general solution of the wave equation subject to Neumann boundary conditions.

💡 Hint: Focus on how the wave behavior is altered based on the boundary at the fixed ends.

Challenge and get performance evaluation