Taught every other year by Ms. Dvorsky, Computational Methods deals with how computers and other digital tools used to solve problems can affect the solution the particular tool arrives at, due to the inherent error a digital system introduces to certain problems. In other words, the tool and method one uses to solve a problem affects the answer one arrives at in the end. For example, the various ways one might program a computer to solve a quadratic equation with the quadratic formula can lead to slightly different answers, and the error from one computation to another can ultimately have a dramatic effect on what one is trying to accomplish.

Magnet Juniors and Seniors interested in taking this course must have completed Analysis of Algorithms. Other Blair Juniors and Seniors may take the course if they have completed A.P. Computer Science and are currently taking/have previously taken A.P. Calculus.

Topics of the course may include:

• Computational Techniques
  • Data Storage
  • Causes of Error in Computer Calculations (e.g., rounding and chopping)
  • Floating Point Computer Arithmetic
  • Program Using 3-digit Rounding, 3-digit Chopping and Compression of the Two Methods
• Solutions to Equations in One Variable
  • Root Finding
  • Bisection Method
  • Potential for Error
  • Methods to Eliminate Computer Error
  • Root Finding Program
• Systems of Equations
  • Cramer's Method
  • Elimination with Backward Substitution
  • Gauss Elimination Method
  • Comparison of Errors Between the Two Methods
  • Program Using Two Methods with Chopping/Rounding
• Interpolation Methods
  • Iterated Interpolation
  • Divided Differences
  • Hermite Interpolation
  • Cubic Spline
• Other Topics as Time Allows