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...
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 Iter...
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...
Solving & Interpreting Differential Equations How do I solve a differential equation? Solving differential equations uses integration! The precise integration method will depend on the type of ...
Modelling with Differential Equations What can be modelled with differential equations? There are many situations that involve “change” Temperature Radioactivity Medication Sales How do I set up ...
Separation of Variables What does separation of variables mean? Many differential equations used in modelling either … … have two variables involved (ie x and y), or, ... involve a function of the ...
Particular Solutions What is a particular solution? Ensure you are familiar with General Solutions first With extra information, the constant of integration, c, can be found This means the particul...
