4.2. General Form of First-Order PDE

Try these first

1. 1.

   What is the highest order of derivative in a first-order PDE?

   Hint

   Think about the definition of 'first-order'.

2. 2.

   In the general form of a first-order PDE, what does F represent?

   Hint

   Recall the formula we discussed.

3. 3.

   What is the general form of a first-order PDE?

   • F(x
   • y
   • z
   • p
   • q) = 1
   • F(x
   • y
   • z
   • p
   • q) = 0
   • p + q = 0

   Hint

   What was the equation we discussed?

4. 4.

   True or False: The highest derivative in a first-order PDE can be two.

   • True
   • False

   Hint

   Recall the definition of 'first-order'.

5. 5.

   Consider the function z = xy + c. Formulate it into a first-order PDE and eliminate c.

   Hint

   What does differentiating constant terms result in?

6. 6.

   Identify a real-world scenario where a first-order PDE could be used, and describe its independent and dependent variables.

   Hint

   Consider how temperature varies in space and time.