Modulus-argument form of a complex number
In this video tutorial you are introduced to the mod-arg [...]
Further transformations
I now look at harder types of questions on transformations [...]
Finding equations of tangents parallel to and perpendicular to the initial line
In these videos I show you how to find the [...]
Area bounded by a cardioid and a loop
In these two videos you are shown a couple of [...]
Area bounded by a polar curve
In this video you are introduced to the method used [...]
Sketching curves the curve r = asin 2θ
I now introduce you to plotting the curve r=a sin2θ. [...]
Sketching curves the cardioid r = a (1+cosθ)
Now I show you a very common curve which you [...]
Sketching curves a circle and arc
Polar equations of circles and arcs. [...]
Sketching polar curves a half-line
I now move on to another common curve, the half-line. [...]
Sketching polar curves a spiral
I now introduce you to plotting some common types of [...]
Converting the equation of a Cartesian curve to polar form
I now work the other way round and show you [...]
Converting the equation of a polar curve to Cartesian form
In this video I now show you how to convert [...]
Converting polar coordinates to Cartesian coordinates
I now run over three examples where you have to [...]
Converting Cartesian coordinates to polar coordinates
I would encourage you to look at or even try [...]
Defining the position of a point
You would have used the cartesian system to define the [...]
Solution to differential equations using Taylor’s series
Taylor's series can be used for solving differential equations as [...]
Taylor’s series
Taylor's series can be used for approximating a function of [...]
Further series
In previous videos I have shown you the series expansions [...]
Series expansion for ln(1+x)
In this video I show you how to derive the [...]
Series expansion for sin(x) and cos(x)
In this video I show you how to derive the [...]
Series expansion for ex
In this video I show you how to derive the [...]
Maclaurin’s series expansion
Maclaurin's series can be used to find expansions of functions [...]
Using substitution to reduce a differential equation to a known form
A substitution can often change a second order differential equation [...]
Particular solutions using boundary conditions to solve differential equations
You can use boundary conditions to find a particular solution [...]
Special types of particular integrals
f(x) = k (constant types) There are times when [...]
General solutions where f(x) = λ cosωx + µ sinωx (trig types)
In this video I give a worked example of the [...]
General solutions where f(x) = kepx (exponential types)
In this video I give a worked example of the [...]
General solutions where f(x) = kx2 (quadratic types)
In this video I give a worked example of the [...]
General solutions where f(x) = kx (linear types)
In this video I give a worked example of the [...]
General solutions where f(x) = k (constant types)
In this video I give a worked example of the [...]
How to solve second order linear differential equations that equal zero
In this video I introduce you to the general solutions [...]
Using substitution to reduce a differential equation to a known form
Often the use of a substitution can alter the format [...]
Solving equations of the form dy/dx + Py = Q using an integrating factor
In this video I show you how to solve the [...]
Exact equations where one side is the exact derivative of a product
In this video I show you how to solve the [...]
Separating the variables and sketching a family of curves
In this video I show introduce you to what [...]
Working with constants in log types
In this video I demonstrate the method of handling [...]
Differential Equations – Finding a general and a particular solution
In this video I introduce you to how we solve [...]
Transformations of the complex plane
In these 3 tutorials I introduce you to transformations of [...]
Using complex numbers to represent regions on an Argand diagram
In this tutorial I look at the locus of a [...]
The locus of a point moving on the arc of a circle
In this tutorial I look at the locus of a [...]
The locus of a point moving along a half-line
In this tutorial I look at the locus of a [...]
The locus of a point moving along a perpendicular bisector
In this tutorial I look at the locus of a [...]
The locus of a point moving in a circle
In this series of videos I look at the locus [...]
nth roots of a complex number
Example - cube roots of 1 In this series of [...]
Expressing sinnθ and cosnθ in terms of sin(kθ) and cos(kθ)
Introduction - new identities you will need In the next [...]
Expressing sin(nθ) and cos(nθ) in terms of sinθ and cosθ
In this video tutorial, I show you how to express [...]
De Moivre’s theorem
In this video I introduce you to De Moivre's theorem [...]
Multiplication and division rules for mod and argument of two complex numbers
Multiplication rule In this video I prove to you the [...]
Exponential Form (Euler’s relation)
In this video I show you how to find the [...]
Method of differences
In this video I show you a method known as [...]
Modulus inequalities fractional type
In these videos I show you how to solve fractional [...]
Fractional inequalities
In this video I show you how to solve fractional [...]
Modulus and argument of a complex number
In this tutorial you are introduced to the modulus and [...]
Differential Equations – Exponential and trig type
In this video I look at exponential and trig [...]