A-level Mathematics₇₃₅₇

Locate roots of $\mathrm{f}\left(\mathit{x}\right)$ = 0 by considering changes of sign of $\mathrm{f}\left(\mathit{x}\right)$ in an interval of $\mathit{x}$ on which $\mathrm{f}\left(\mathit{x}\right)$ is sufficiently well-behaved.

Understand how change of sign methods can fail.

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 ${\mathit{x}}_{\mathit{n}\mathsf{+}\mathsf{1}}\mathsf{=}\mathrm{g}\mathsf{\left(}{\mathit{x}}_{\mathit{n}}\mathsf{\right)}$

Understand how such methods can fail.

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.

Use numerical methods to solve problems in context.