Topics for Midterm 1

• Binary Numbers - Convert from Decimal and Back
• Machine Numbers
• Error - Relative vs. Absolute.
• Round off / Truncation error and subtractive cancellation.
• Convergence / Rate of Convergence.
• Root Finding
• Iteration - local/global convergence conditions.
• Bisection - error analysis.
• Regula Falsi - convergence issues.
• Newton's Method.
• Rates of Convergence.
• Intermediate Value Theorem use in root finding.
• Square root algorithm using Newton's method.
• Graphical interpretation of root finding methods.

Topics for Midterm 2

• Linear Systems
• Back Substitution
• Gaussian Elimination
• Pivoting to avoid division by 0
• Partial Pivoting - error reduction
• LU decomposition
• Extrapolation vs. Interpolation
• Taylor Series
• Error term
• Bounding error
• Lagrange Polynomials
• Newton Polynomials - Difference Tables
• Error in Newton and Lagrange Polynomials

Topics for Final

• Review topics from Midterms
• Numerical Derivative - rounding and truncation error
• Numerical Integrals
• Simpson's and Trapezoidal Methods - Composite
• Error in integration
• Finding number of steps required to limit error
• Numerical ODE
• Euler's and Heun's methods
• Local discretization error
• Final global error
• Numerical instability in ODE solvers