This week's book giveaway is in the OCPJP forum. We're giving away four copies of OCA/OCP Java SE 7 Programmer I & II Study Guide and have Kathy Sierra & Bert Bates on-line! See this thread for details.
You can nest layouts.
Panel1 has the result , centered
Panel2 has num1, num2 centered
Panel3 has +,-,/,* centered
DaddyPanel has panel1,panel2 and panel3 aligned vertically
DaddyPanel is added to the content pane.
You need to choose an appropriate layout (there are others besides the FlowLayout you have been using) The link Darryl provided, will help you find out these layouts.