Practice Method (1.1.1) - Formation of Partial Differential Equations - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
Define Partial Differential Equation.
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It includes derivatives with respect to multiple variables.
Question 2.
What do we do with arbitrary constants in forming a PDE?
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Think about how we treat z = ax + by + c.
3Question 3.
What does a Partial Differential Equation involve?
- Only single variables
- Partial derivatives of multivariable functions
- Only constants
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Think about derivatives that involve more than one variable.
4Question 4.
True or False: We eliminate arbitrary functions when forming PDEs.
- True
- False
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Consider our discussions on differentiating and substituting.
Question 5.
Given z = 3xy + b, derive a PDE by eliminating b. What is the result?
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Remember how to sub and eliminate constants.
Question 6.
Using z = sin(x) + cos(y) + h(xy), eliminate h to arrive at a new PDE.
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Work through each derivative carefully and use algebra to consolidate.

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