Magnitude & Direction What is the magnitude of a vector? The magnitude of a vector is simply its size It also tells us the distance between two points You can find the magnitude of a vector usi...
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...
