To be confident with numerical methods, you must be able to:
Locate roots of f(x)=0 by considering changes of sign of f(x) in an interval on which f(x) is sufficently well behaved;
Understand how change of sign methods can fail;
Solve equations approximately using simple iterative methods and be able to draw associated cobweb and staircase diagrams;
Solve equations using Newton-Raphson method and other recurrence relations and understand how these 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 the limits that it must lie between;
Use numerical methods to solve problems in context.
