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...
General Solutions What is a differential equation? Any equation, involving a derivative term, is a differential equation Equations involving only first derivative terms are called first order diffe...
Decision Making What is meant by integration and decision making? The hardest part of integration is deciding which technique to use There are lots of them! How do I know which integration method t...
Integration using Partial Fractions What are Partial Fractions? This is the reverse process to adding (or subtracting) fractions The common polynomial denominator is split into factors Make sure yo...
