Question 1

a. Explain with equations what is meant by a partial differential equation (PDE)

b. State and briefly explain the types of partial differential equations

c. In each of (b) above, give examples or application areas and the properties of each

type of PDE.

d. Considering the following modified wave equation

(i) Show that this wave equation is of the hyperbolic type of PDES.

(ii) derive the equivalent system of three first order equations from equation (1)

and show that this system is also hyperbolic.

(iii) Further considering the related system of equations, determine the

characteristic directions and show that there is an extra characteristic

equation.