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