- Introduction
- Ideas of Error Analysis
- Sources of Error
- Floating-Point Numbers
- Propagation of Errors

- Solving Non-linear Equations
- Bisection,
*Regula-Falsi*, secant method
- Newton's method
- Muller's method *
- Fixed-point iteration *
- Convergence analysis

- Curve Fitting, Interpolation and Approximation
- Lagrange Polynomials
- Divided Difference
- Ordinary Difference
- Least Squares *
- Cubic Splines *
- Bezier Curves *
- Chebyshev Polynomials *
- Economized Power Series *

- Numerical Calculus
- Derivatives from Difference Tables
- Higher-Order Derivatives
- Taylor Series
- Richardson Extrapolation
- Newton-Cotes Integration
- The Trapezoid Rule
- Simpson's Rule
- Romberg Integration

- Solving Systems of Equations *
- Matrix Issues
- Gaussian Elimination
- LU Decomposition

- Differential Equations *
- Euler Methods
- Runge-Kutta Methods

(Items marked with * are optional; we will select from these based on the
interests of the class and the time available.)

See the course calendar for details
concerning exams and problem sets.