You will need a basic calculator but you cannot use a graphing calculator.
Test 3 covers sections 5.1-5.3 & 10.1-10.7.
Be able to find the first terms of a power series solution in all cases.
For simple cases be able to find recurse formula for the series coeffients.
You should understand linear independence and dependence and the Wronskian as applied to power series solutions.
You should be able to find a lower bound for the radius of convergence of power series solution.
Be able to find Fouries Series. Even/odd periodic extensions.
Understand boundary conditions.
Understand seperation of variables.
Understand heat and wave equations: both how to solve them and to know what to expect the solution to look like.