2. General Form of Second-Order PDEs

Try these first

1. 1.

   What is a PDE?

   Hint

   Think about how it relates to derivatives.

2. 2.

   State the general form of a second-order PDE.

   Hint

   Recall the variables involved.

3. 3.

   What is the discriminant used for in PDEs?

   • To solve the PDE
   • To classify the PDE
   • To determine the unknown function

   Hint

   Think about the role of Δ in classification.

4. 4.

   Elliptic PDEs have a discriminant that is:

   • True
   • False

   Hint

   Recall the definition from our class.

5. 5.

   Classify the PDE given by the coefficients A = 1, B = 0, C = -4 and explain your reasoning.

   Hint

   What does the positive discriminant reveal?

6. 6.

   Create a real-world scenario in which you might use a parabolic PDE, describing the problem and its parameters.

   Hint

   Focus on scenarios involving gradual changes over time.