Intro to Proof by Induction What is proof by induction? Proof by induction is a way of proving a result is true for a set of integers by showing that if it is true for one integer then it is true f...
Damped or Forced Harmonic Motion What is damped harmonic motion? If we add a term representing a resistive force to the simple harmonic motion equation, the new equation describes a particle underg...
Simple Harmonic Motion (SHM) Equations What is simple harmonic motion? A particle undergoing simple harmonic motion moves along a straight line subject to the following constraints: The acceleratio...
Coupled First Order Linear Equations What are coupled first order linear differential equations? Coupled first order linear differential equations are a pair of simultaneous differential equations ...
Second Order Differential Equations What is a second order differential equation? A second order differential equation is an equation containing second order derivatives (and possibly first order d...
Modelling using First Order Differential Equations Why are differential equations used to model real-world situations? A differential equation is an equation that contains one or more derivatives D...
First Order Differential Equations What is a differential equation? A differential equation is simply an equation that contains derivatives For example is a differential equation And so is What is...
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...
Finding Tangents to Polar Curves What is the gradient/tangent of a polar curve? Gradients (and tangents) are the same as using Cartesian coordinates i.e. a gradient of 1 in Cartesian coordinates is...
