First-year module, Department of Aeronautics, Imperial College London. Four classes on the numerical methods engineers use when an equation has no closed-form solution. Each class has interactive demos: step through every iteration, change the inputs, and compare the methods. The lecture slides and notes are on Blackboard.
1. How computers count
Binary representation, integer and floating-point storage, rounding and chopping, overflow and underflow, and how errors propagate through a calculation.
- Demos coming soon
2. Solving unsolvable equations
Root finding: bisection, Newton–Raphson, the secant method and fixed-point iteration, with their convergence and failure modes.
Open the demos here: bisection, Newton, secant, cobweb diagrams and a comparison of all four
3. Integrating unintegrable functions
Numerical integration: Riemann sums, the trapezium rule, Simpson's rule, Newton–Cotes formulae and Gauss–Legendre quadrature.
- Demos coming soon
4. Curve fitting and interpolation
Polynomial interpolation in the monomial, Newton and Lagrange forms, why they give the same polynomial, and cubic splines.
- Demos coming soon