Practice Partial Differential Equations - 15 | 15. Fourier Series Solutions to PDEs | Mathematics - iii (Differential Calculus) - Vol 2
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15 - Partial Differential Equations

Learning

Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

Define a Fourier series in your own words.

πŸ’‘ Hint: Think of it as breaking down a complex signal.

Question 2

Easy

List the Dirichlet conditions.

πŸ’‘ Hint: These conditions ensure that the series converges.

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 does a Fourier series represent?

  • A single polynomial function
  • A sum of sine and cosine functions
  • An ordinary differential equation

πŸ’‘ Hint: Think about what functions are used to create a Fourier series.

Question 2

True or False: The Dirichlet conditions are necessary for the convergence of Fourier series.

  • True
  • False

πŸ’‘ Hint: Recall the essential requirements for Fourier representation.

Solve 1 more question and get performance evaluation

Challenge Problems

Push your limits with challenges.

Question 1

Given a non-periodic function defined on \( [0, L] \), apply half-range expansions to derive a Fourier sine series representation.

πŸ’‘ Hint: Think of representing your function in terms of odd extensions.

Question 2

Using the method of separation of variables, derive the solution to the wave equation under given boundary and initial conditions.

πŸ’‘ Hint: Pay close attention to how the initial velocity influences the form of the sine and cosine series.

Challenge and get performance evaluation