Exercise 1: Describe where the PDE is hyperbolic, parabolic, or elliptic.
Exercise 2: Classfication of the PDE.
Exercise 3: The formulation of a PDE in regard to your area of specialization.
Exercise 4: The construction of a program to solve an equation, the storage of the data, the use of some visualization software.
Exercise 5: The determination of the initial and boundary conditions of the wave equation, and plotting the results.
Exercise 6: Plot the solution of the diffusion equation.
Exercise 7: A consideration of practical application leads to Laplace's equation, which reduces to an ODE.