1.3. Summary

Try these first

1. 1.

   What is a Partial Differential Equation?

   Hint

   Think about functions with more than one variable.

2. 2.

   What do we need to eliminate to form a PDE from a function?

   Hint

   Consider what you differentiate in your example.

3. 3.

   What is the primary purpose of forming a PDE?

   • To model physical phenomena
   • To simplify equations
   • To eliminate constants only

   Hint

   Think about the broad application of PDEs in science.

4. 4.

   True or False: A PDE can only contain constants.

   • True
   • False

   Hint

   Recall the examples we discussed.

5. 5.

   Given the equation z = f(x) + g(y), derive a second-order PDE and describe the steps.

   Hint

   What relationships do you establish between your derivatives?

6. 6.

   Form a PDE from z = ax² + by² + cxy and explain your reasoning.

   Hint

   Explore how differentiation simplifies the function while removing constants!