16 - Partial Differential Equations – Basic Concepts
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Practice Questions
Test your understanding with targeted questions
Define a partial differential equation (PDE).
💡 Hint: Consider how it differs from ordinary differential equations.
What is the order of the equation ∂²u/∂x² + ∂u/∂y = 0?
💡 Hint: Look for the highest derivative in the equation.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the order of a PDE refer to?
💡 Hint: Focus on the derivatives when answering.
True or False: Linear PDEs contain nonlinear terms.
💡 Hint: Recall the definitions of linear and nonlinear.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given the relation z = ax² + bxy + cy², derive the corresponding PDE.
💡 Hint: Focus on differentiating each component step-wise.
Classify the PDE: ∂²u/∂x² - 2∂²u/∂y² + ∂²u/∂y² = 0.
💡 Hint: Use the discriminant formula carefully to classify.
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