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...
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...
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...
