3.1.1 - Definition of PDE
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Practice Questions
Test your understanding with targeted questions
What is a PDE?
💡 Hint: Consider how it differs from ODEs.
What is Laplace’s equation an example of?
💡 Hint: Think about the powers of the function involved.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does PDE stand for?
💡 Hint: Remember the full name of the equation.
True or False: Linear PDEs can have products of the dependent variable and its derivatives.
💡 Hint: Consider how the terms in the equation are structured.
1 more question available
Challenge Problems
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Show that the equation \( \frac{\partial^2 u}{\partial x^2} + e^{u} \frac{\partial u}{\partial y} = 2 \) is a non-linear PDE and explain why.
💡 Hint: Look for non-linear functions of the dependent variable.
Derive a second-order linear PDE from physical principles (e.g., heat conduction) and state its physical significance.
💡 Hint: Consider the balance of heat energy in a given area.
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