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...
Area between 2 curves What is the area between two curves? Ensure you are familiar with … Area under a curve Area between a line and a curve In general find the definite integral of “upper curve” –...
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...
Integration by Parts What is Integration by Parts? For integrating the product of two functions - reverse product rule Crucially the product is made from?u?and?dv/dx?(rather than?u?and?v) Alternati...
Integrating with Trigonometric Identities What are trigonometric identities? Some are given in the formulae booklet Be sure to note the difference between the?±?and???symbols! How do I know which t...
Harder Substitution What is integration by substitution? Make sure you are familiar with Reverse Chain Rule and Substitution (RCR) In more difficult questions the substitution will be given to you ...
Substitution (Reverse Chain Rule) What is integration by substitution? Make sure you are familiar with Chain Rule and Reverse Chain Rule In more awkward problems it is harder to spot the reverse ch...
f'(x)/f(x) Integrating fractions The technique for integrating fractions depends on the type of fraction For?polynomial?denominators?see Integration using Partial Fractions The type of fraction dea...
