- 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.
|
|