Practice Error Estimation - 18.11.2 | 18. Separation of Variables, Use of Fourier Series | Mathematics (Civil Engineering -1)
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18.11.2 - Error Estimation

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Practice Questions

Test your understanding with targeted questions related to the topic.

Question 1

Easy

What is the Gibbs Phenomenon?

💡 Hint: Think about what happens at a jump in a function.

Question 2

Easy

Why is error estimation important when using Fourier series?

💡 Hint: Consider practical applications where accuracy matters.

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 primary issue caused by the Gibbs Phenomenon?

  • Zero oscillations
  • Persistent oscillations near discontinuities
  • Final convergence to the true value

💡 Hint: What happens near a jump in function approximations?

Question 2

True or False: Adding more terms to a Fourier series will completely eliminate the oscillations caused by the Gibbs Phenomenon.

  • True
  • False

💡 Hint: Think about the nature of the oscillations around jumps.

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Challenge Problems

Push your limits with challenges.

Question 1

Given a piecewise function F(x) defined as F(x)=1 for x < 0 and F(x)=2 for x >= 0, compute the first few terms of its Fourier series and analyze the error near the discontinuity.

💡 Hint: What characteristics do you expect to see in the Fourier series for a piecewise constant function?

Question 2

Develop a model for approximating a triangular wave using a Fourier series, and discuss any associated error estimations and the impact of the Gibbs Phenomenon.

💡 Hint: Consider the behavior of triangular waves at their peaks and troughs.

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