Position Vectors What is a position vector? Position vectors describe the position of a point in relation to the origin They are different to direction vectors which describe the direction and dist...
Vector Addition Vector addition Adding vectors together lets us describes the movement between two points The single vector this creates is called the resultant vector Subtracting a vector is the s...
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...
