Practice Linear And Nonlinear Pdes (16.5) - Partial Differential Equations – Basic Concepts

Practice: Linear and Nonlinear PDEs

Lesson 16.5Partial Differential Equations – Basic Concepts

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8 questions

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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define what makes a PDE linear.
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Think about how variables appear in the equation.
Question 2.
Provide one example of a linear PDE.
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Look for an equation where all terms are in the first degree.
3Question 3.
Which of the following equations is a linear PDE?
- \\left( \\frac{\\partial u}{\\partial x} \\right)^2 + \\frac{\\partial u}{\\partial y} = 0
- \\frac{\\partial u}{\\partial t} + k \\frac{\\partial^2 u}{\\partial x^2} = 0
- 2u^2 + \\frac{\\partial u}{\\partial x} = 0
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Look for powers that are only one.
4Question 4.
True or False: Nonlinear PDEs can have superposition applied to their solutions.
- True
- False
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Remember the characteristics of solutions in linear versus nonlinear equations.
Question 5.
Devise a nonlinear PDE that incorporates both x and y derivatives and explain how it fits the definition of nonlinear.
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Make sure one term is a product of derivatives or powers.
Question 6.
Explain the significance of superposition in linear PDEs and why it doesn’t apply to nonlinear PDEs with an example.
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Think of concrete examples showing different behaviors in solutions.

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