3.1.2 - Linear PDEs
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Practice Questions
Test your understanding with targeted questions
Define a linear PDE and give an example.
💡 Hint: Think about equations you've seen that represent physical phenomena.
What is the heat equation?
💡 Hint: Consider the role of time and space in heat transfer.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What characterizes a linear PDE?
💡 Hint: Consider how exponents affect linearity.
True or False: Laplace's Equation is a nonlinear PDE.
💡 Hint: Think about the definition of linear vs. nonlinear.
1 more question available
Challenge Problems
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Prove that if u(x,y) is a solution to \[ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0 \] and v(x,y) is a solution, then au + bv is also a solution for constants a and b.
💡 Hint: Break down the terms of both functions.
Calculate the steady-state temperature distribution along a rod described by the heat equation with boundaries held at constant temperatures of T1 and T2.
💡 Hint: Consider the boundary values set for T1 and T2.
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