Practice Linear And Non-linear Partial Differential Equations (3.1) - Linear and Non-linear PDEs

Practice: Linear and Non-linear Partial Differential Equations

Lesson 3.1Linear and Non-linear PDEs

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9 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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3 questions · about 2 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define what a Partial Differential Equation (PDE) is.
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Think about how it differs from ordinary differential equations.
Question 2.
What is the general form of a linear PDE?
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Remember that the dependent variable and its derivatives should be in first power only.
3Question 3.
What is a partial differential equation (PDE)?
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Recall the definition we discussed.
4Question 4.
Which of the following is a characteristic of a linear PDE?
- A) It involves higher powers of variables.
- B) Variables can be multiplied together.
- C) Dependent variables appear to the first power.
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Think about the structure of linear equations.
Question 5.
Prove that the equation $\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0$ is a linear PDE, and provide a physical interpretation of its meaning.
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Check the way terms are structured; focus on their power.
Question 6.
Create a real-life scenario where a non-linear PDE would be used, and explain the significance of being non-linear in that context.
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Consider the nature of fluid motion and challenges in modeling it accurately.

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