Practice Classification Based on Discriminant - 2.1 | 2. Classification of PDEs (Elliptic, Parabolic, Hyperbolic) | Mathematics - iii (Differential Calculus) - Vol 2
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2.1 - Classification Based on Discriminant

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the condition for an elliptic PDE?

πŸ’‘ Hint: Think about what the discriminant represents.

Question 2

Easy

Which type of PDE corresponds to Ξ” = 0?

πŸ’‘ Hint: Remember the heat equation!

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

What is the condition for characterizing an elliptic PDE?

  • Ξ” < 0
  • Ξ” = 0
  • Ξ” > 0

πŸ’‘ Hint: Think about steady-state processes.

Question 2

True or False: Parabolic PDEs require two initial conditions.

  • True
  • False

πŸ’‘ Hint: Recall the heat equation.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given the PDE: 3βˆ‚Β²u/βˆ‚xΒ² + 4βˆ‚Β²u/βˆ‚yΒ² βˆ’ 6βˆ‚u/βˆ‚x + 2u = 0, classify it and provide justification.

πŸ’‘ Hint: Focus on identifying A, B, C first.

Question 2

Classify the PDE: βˆ‚Β²u/βˆ‚xΒ² - βˆ‚Β²u/βˆ‚yΒ² = 0, and explain the classification.

πŸ’‘ Hint: Make sure to compute the discriminant.

Challenge and get performance evaluation