Practice Half-range Expansions (15.3) - Fourier Series Solutions to PDEs

Practice: Half-Range Expansions

Lesson 15.3Fourier Series Solutions to PDEs

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8 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is a Half-Range Sine Series?
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Think about the symmetry of the graph.
Question 2.
List the conditions for applying Half-Range Expansions.
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Consider the behavior of the function at the endpoints.
3Question 3.
What type of function is suitable for a Half-Range Sine Series?
- Even Functions
- Odd Functions
- Period Functions
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Consider the symmetry of the function at the boundaries.
4Question 4.
True or False: Half-range expansions can only represent functions defined on full periods.
- True
- False
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Remember, we discussed functions only on 0 < x < L.
Question 5.
Given a function f(x) defined on the interval [0, 4] with f(0)=0, f(4)=0, express it using a Half-Range Sine Series.
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Focus on the symmetric properties you use in establishing the sine series formula.
Question 6.
Explain how you would apply Half-Range Cosine Series to model the temperature on a flat plate with even boundary conditions.
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Remember, apply your knowledge of cosine functions and their symmetry at the boundaries.

4 more questions in this section. Enroll free to practise them all.