3.1.1. Definition of PDE

Try these first

1. 1.

   What is a PDE?

   Hint

   Consider how it differs from ODEs.

2. 2.

   What is Laplace’s equation an example of?

   Hint

   Think about the powers of the function involved.

3. 3.

   What does PDE stand for?

   • Partial Differential Equation
   • Partial Derivative Equation
   • Partial Differential Express

   Hint

   Remember the full name of the equation.

4. 4.

   True or False: Linear PDEs can have products of the dependent variable and its derivatives.

   • True
   • False

   Hint

   Consider how the terms in the equation are structured.

5. 5.

   Show that the equation $\frac{\partial^2 u}{\partial x^2} + e^{u} \frac{\partial u}{\partial y} = 2$ is a non-linear PDE and explain why.

   Hint

   Look for non-linear functions of the dependent variable.

6. 6.

   Derive a second-order linear PDE from physical principles (e.g., heat conduction) and state its physical significance.

   Hint

   Consider the balance of heat energy in a given area.