1.1.1. Method

Try these first

1. 1.

   Define Partial Differential Equation.

   Hint

   It includes derivatives with respect to multiple variables.

2. 2.

   What do we do with arbitrary constants in forming a PDE?

   Hint

   Think about how we treat z = ax + by + c.

3. 3.

   What does a Partial Differential Equation involve?

   • Only single variables
   • Partial derivatives of multivariable functions
   • Only constants

   Hint

   Think about derivatives that involve more than one variable.

4. 4.

   True or False: We eliminate arbitrary functions when forming PDEs.

   • True
   • False

   Hint

   Consider our discussions on differentiating and substituting.

5. 5.

   Given z = 3xy + b, derive a PDE by eliminating b. What is the result?

   Hint

   Remember how to sub and eliminate constants.

6. 6.

   Using z = sin(x) + cos(y) + h(xy), eliminate h to arrive at a new PDE.

   Hint

   Work through each derivative carefully and use algebra to consolidate.