8 - Partial Differential Equations
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Practice Questions
Test your understanding with targeted questions
Define a Partial Differential Equation (PDE).
💡 Hint: Think about what variables and derivatives are involved.
What distinguishes a linear PDE?
💡 Hint: Recall the characteristics of linear equations.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the general form of a homogeneous linear PDE?
💡 Hint: Recall the properties of homogeneous equations.
True or False: In a homogeneous linear PDE, a free term may be present.
💡 Hint: Think about the definition of homogeneity.
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Challenge Problems
Push your limits with advanced challenges
Solve the PDE ∂²z/∂x² + 3∂²z/∂y² = 0 and interpret the nature of the roots. What kind of solutions would you expect?
💡 Hint: Focus on how each term in the operator form translates to the auxiliary equation.
For the equation ∂²z/∂x² - 6∂²z/∂x∂y + 9∂²z/∂y² = 0, find the general solution and describe the form it takes.
💡 Hint: Recognize how repeated roots influence your complementary function.
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