Basic Vectors What is a vector? Vectors represent a movement of a certain?magnitude?(size) in a given?direction You should have already come across?vectors?when translating functions of graphs They...
Numerical Methods in Context Numerical Methods Numerical methods?can be used to model a variety of situations, from the motion of planets across the solar system to the depreciation in a cars value...
Trapezium Rule (Numerical Integration) What is the trapezium rule? The?trapezium rule?is a numerical method of integration used to find the?approximate area?under a curve It can be used when?analyt...
Newton-Raphson The Newton-Raphson method The Newton-Raphson method finds?roots?of equations in the form?f(x)?=?0 It can be used to find?approximate solutions?when an equation cannot be solved using...
x = g(x) Iteration What does xn + 1?= f(xn) mean? When an equation cannot be solved using the usual?analytical methods, we can still find?approximate solutions?to a certain degree of accuracy Itera...
Change of Sign Failure When can the sign change method fail? There are certain circumstances where a?change of sign?fails to appropriately reflect the number or existence of roots If the interval i...
Change of Sign What does a change of sign mean? A?sign change?between f(a) to f(b) means there must be a?root?between a and b When an equation cannot be solved using the usual?analytical methods, w...
Modelling with Parametric Equations What can be modelled with parametric equations? A common use for parametric equations is motion in two dimensions x = f(t)?– horizontal position, dependent on ti...
Parametric Integration How does integration work with parametric equations? Integration is used to find the area under a curve where the curve has been defined by parametric equations x = f(t) y = ...
