CPSC 303: Numerical Approximation and Discretization
2017/2018 Winter Term 2 (January-April 2018)
Mon/Wed/Fri 14:00-15:00, DMP 110
Tentative Course Outline
- Numerical Algorithms
- Scientific computing
- Problem conditioning and algorithm stability
- Roundoff Errors
- Floating point systems
- The IEEE standard
- Roundoff error accumulation and cancellation error
- Polynomial Interpolation
- Monomial basis
- Lagrange form
- Divided differences and Newton's form
- Error bounds
- Chebyshev points
- Osculating polynomials
- Piecewise Polynomial Interpolation
- Broken line and piecewise Hermite interpolation
- Splines
- Numerical Differentiation
- Deriving differentiation formulas
- Difference formulas using polynomial interpolation
- Roundoff errors
- Richardson extrapolation
- Numerical Integration
- Basic quadrature rules
- Composite numerical integration
- Gaussian quadrature
- Adaptive quadrature
- Numerical Solution of Initial Value Ordinary Differential Equations
- Mathematical modelling of an outbreak of zombie infection
- Euler's method
- Runge-Kutta methods
- Multistep methods
- Absolute stability and stiffness
- Error estimation