Practice Legendre Functions - 10.2 | Partial Differential Equations | Mathematics III (PDE, Probability & Statistics)
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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the Legendre differential equation?

πŸ’‘ Hint: Look for the equation that defines Legendre functions.

Question 2

Easy

What does 'n' represent in the Legendre equation?

πŸ’‘ Hint: It's related to the degree of the polynomial.

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 general form of the Legendre differential equation?

  • \\(\\frac{d}{dx}((1 - x^2)\\frac{dy}{dx}) + n(n + 1)y = 0\\)
  • \\(\\frac{d^2y}{dx^2} + p(x)\\frac{dy}{dx} + q(x)y = 0\\)

πŸ’‘ Hint: Check for the terms involving 'n'.

Question 2

True or False: Legendre polynomials are orthogonal over the interval [-1, 1].

  • True
  • False

πŸ’‘ Hint: Think about the definition of orthogonality.

Solve and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Prove the orthogonality of the first three Legendre polynomials over the interval [-1, 1].

πŸ’‘ Hint: Set up the integrals accordingly.

Question 2

Using Legendre polynomials, derive a series solution for a given potential in a gravitational field based on spherical symmetry.

πŸ’‘ Hint: Think about how they approximate potentials.

Challenge and get performance evaluation