# CPSC 303: Numerical Approximation and Discretization

## 2016/2017 Winter Term 2 (January-April 2017)

### MWF 12-1pm, Dempster (DMP) 301

Tentative course outline

- Numerical algorithms and roundoff errors
- Scientific computing
- Matlab introduction
- Numerical algorithms and errors
- Roundoff errors and computer arithmetic

- Polynomial interpolation
- General interpolation, polynomial interpolation, and monomial basis
- Lagrange form
- Divided differences and Newton's form
- Error bounds
- Osculating polynomials and Chebyshev points

- Piecewise polynomial interpolation
- Piecewise polynomial interpolation
- Cubic spline
- Hat functions and B-splines

- Orthogonal polynomials and Fourier transform
- Orthogonal polynomials
- Continuous and discrete Fourier transform
- Fast Fourier transform (FFT)

- Numerical differentiation and integration
- Deriving differentiation formulas
- Difference formulas using polynomial interpolation
- Roundoff errors
- Basic quadrature rules
- Composite numerical integration
- Gaussian quadrature
- Adaptive quadrature
- Richardson extrapolation and Romberg integration

- Numerical solution of initial value ordinary differential equations
- Differential equations
- Euler's method
- Runge-Kutta methods
- Multistep methods
- Absolute stability and stiffness
- Error estimation