Practice Solution Of The Heat Equation By Separation Of Variables (12.3) - One-Dimensional Heat Equation

Practice: Solution of the Heat Equation by Separation of Variables

Lesson 12.3One-Dimensional Heat Equation

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8 questions

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6 sample questions

Question 1.
What does the assumption $u(x,t) = X(x) T(t)$ represent?
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Think about how we can break the problem into simpler parts.
Question 2.
Name one type of boundary condition we could apply.
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What specifies temperature at the boundaries?
3Question 3.
What does the method of separation of variables aim to do?
- Combine variables into one
- Split functions into separate dependent variables
- Eliminate PDEs altogether
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Think about the word 'separation'.
4Question 4.
True or False: The solution to the heat equation can include both sine and cosine functions.
- True
- False
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Recall how we solved the spatial part.
Question 5.
Given a rod of length $L$ with heat starting at a linear distribution, derive the temperature at later times using separation of variables.
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Begin with writing the equation and identify the boundaries.
Question 6.
How would the solution change if we modified the boundary condition to Neumann conditions?
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Consider how heat flux will reflect in the function behavior.

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