Practice Linear Pdes (3.1.2) - Linear and Non-linear PDEs - Mathematics - iii (Differential Calculus) - Vol 2

Practice: Linear PDEs

Lesson 3.1.2Linear and Non-linear PDEs

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9 questions

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4 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
3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define a linear PDE and give an example.
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Think about equations you've seen that represent physical phenomena.
Question 2.
What is the heat equation?
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Consider the role of time and space in heat transfer.
3Question 3.
What characterizes a linear PDE?
- Terms with higher powers of variables
- Terms only to the first power
- Mixed derivatives only
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Consider how exponents affect linearity.
4Question 4.
True or False: Laplace's Equation is a nonlinear PDE.
- True
- False
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Think about the definition of linear vs. nonlinear.
Question 5.
Prove that if u(x,y) is a solution to $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$ and v(x,y) is a solution, then au + bv is also a solution for constants a and b.
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Break down the terms of both functions.
Question 6.
Calculate the steady-state temperature distribution along a rod described by the heat equation with boundaries held at constant temperatures of T1 and T2.
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Consider the boundary values set for T1 and T2.

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