3.2 - Classification of Second-Order Linear PDEs
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Practice Questions
Test your understanding with targeted questions
Define a discriminant in your own words.
💡 Hint: Think about how the discriminant relates to the solutions.
What is the condition for a PDE to be hyperbolic?
💡 Hint: Remember the symbol >.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the condition for a PDE to be classified as elliptic?
💡 Hint: Think about Laplace's equation.
True or False: Hyperbolic PDEs can describe diffusion processes.
💡 Hint: Recall what hyperbolic equations are used for.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Construct a second-order linear PDE that is hyperbolic, provide the coefficients, and calculate the discriminant. Explain why it is hyperbolic.
💡 Hint: Select coefficients carefully to ensure D remains positive.
Given the equation \( A \frac{\partial^2 u}{\partial x^2}+B\frac{\partial^2 u}{\partial y^2} + C \frac{\partial^2 u}{\partial y^2} = 0 \), determine conditions on A, B, and C so it becomes an elliptic PDE.
💡 Hint: Manipulate A, B, and C values until D < 0 is achieved.
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