Locate roots of \(f(x) = 0\) by considering changes of sign of \(f(x)\) in an interval of \(x\) on which \(f(x)\) is sufficiently well-behaved.

Understand how change of sign methods can fail.

Locating roots by considering changes of sign

Solve equations approximately using simple iterative methods; be able to draw associated cobweb and staircase diagrams.

Solve equations using the Newton-Raphson method and other recurrence relations of the form \(x_{n+1} = g(x_n).\)

Understand how such methods can fail.

Iterative methods The Newton-Raphson method

Understand and use numerical integration of functions, including the use of the trapezium rule and estimating the approximate area under a curve and limits that it must lie between.

The trapezium rule

Use numerical methods to solve problems in context.

Solve problems with numerical methods