Preliminaries

• How a computer can be used
  • to solve problems that may not be solvable by hand
  • to solve problems (that you may have solved before) in a different way
• Many of these simplified examples can be solved analytically (by hand)
  
  $$x^3-x^2-3x+3=0,with~solution~\sqrt3$$
  
  

• But most of the examples can not be simplified and can not be solved analytically
• mathematical relationships $\Longrightarrow$ simulate some real word situations