1.4. Final Tip

Try these first

1. 1.

   Define what a Partial Differential Equation (PDE) is.

   Hint

   Think about derivatives with multiple variables.

2. 2.

   What is the first step in eliminating arbitrary constants?

   Hint

   Think about using the definition of derivatives.

3. 3.

   What symbol is often used to denote ∂z/∂x?

   • p
   • q
   • r

   Hint

   Think about how we label derivatives in the examples.

4. 4.

   True or False: Arbitrary functions cannot be eliminated when forming PDEs.

   • True
   • False

   Hint

   Consider the methods we discussed for handling functions.

5. 5.

   Given the function z = e^(ax + by) + c, derive the PDE by eliminating c.

   Hint

   Focus on how the exponential responds to differentiation.

6. 6.

   Take the function z = x^2 + y^2 + f(x-y); eliminate f to derive the PDE.

   Hint

   Pay attention to how the difference in `x` and `y` is expressed in terms of `f`.