Teacher Delivery Guide Pure Mathematics: Numerical Methods Ref. Learning outcomes Notes Notation Exclusions Specification PURE MATHEMATICS: NUMERICAL METHODS (2) Be able to locate the roots of by considering changes Finding an interval in which a root lies. Solution of Me1 of sign of in an interval of x in which is sufficiently This is often used as a preliminary step equations to find a starting value for the methods in Me3 and Me4. Be aware of circumstances under which change of sign e.g. when the curve of touches the e2 methods may fail. e.g. when the curve of has a vertical asymptote. e.g. there may be several roots in the interval. Be able to carry out a fixed point iteration after e.g. write as and use the iteration iteration, iterate e3 rearranging an equation into the form and be able to with an appropriate starting value. draw associated staircase and cobweb diagrams. Includes use of ANS key on calculator. Be able to use the Newton-Raphson method to find a e4 root of an equation and represent the process on a graph. Understand that not all iterations converge to a Know how Newton-Raphson and fixed e5 particular root of an equation. point iteration can fail and be able to show this graphically. Ref. Learning outcomes Notes Notation Exclusions Specification
Teacher Delivery Guide Pure Mathematics: Numerical Methods Specification Ref. Learning outcomes Notes Notation Exclusions PURE MATHEMATICS: NUMERICAL METHODS (2) Solution of equations Me1 Be able to locate the roots of by considering changes of sign of in an interval of x in which is sufficiently Finding an interval in which a root lies. This is often used as a preliminary step to find a starting value for the methods in Me3 and Me4. e2 Be aware of circumstances under which change of sign methods may fail. e.g. when the curve of touches the e.g. when the curve of has a vertical asymptote. e.g. there may be several roots in the interval. e3 Be able to carry out a fixed point iteration after rearranging an equation into the form and be able to draw associated staircase and cobweb diagrams. e.g. write as and use the iteration with an appropriate starting value. Includes use of ANS key on calculator. iteration, iterate e4 Be able to use the Newton-Raphson method to find a root of an equation and represent the process on a graph. e5 Understand that not all iterations converge to a particular root of an equation. Know how Newton-Raphson and fixed point iteration can fail and be able to show this graphically. Specification Ref. Learning outcomes Notes Notation Exclusions
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