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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a first-order PDE?
💡 Hint: Think about the order of derivatives.
Question 2
Easy
Write the standard form of a first-order linear PDE.
💡 Hint: Recall P, Q, and R represent the coefficients.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
Which of the following is the correct form of a first-order linear PDE?
- Pz + Qy = R
- P(x,y,z)p + Q(x,y,z)q = R(x,y,z)
- d/dx(P) + d/dy(Q) = R
💡 Hint: Pay attention to the variables involved in the equation.
Question 2
True or False: Auxiliary equations for Lagrange’s method come from the solution of the PDE itself.
- True
- False
💡 Hint: Think about how we arrive at the auxiliary equations.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove the effectiveness of Lagrange’s method by solving a non-homogeneous first-order linear PDE such as z + 2x = y.
💡 Hint: Start with the ratios from the coefficients.
Question 2
Explore the limits of Lagrange's method by attempting to apply it to a non-linear PDE and discuss the Schrodinger analogy.
💡 Hint: Focus on the non-linearity aspect when setting up your approach.
Challenge and get performance evaluation