Mathematics a Graphical Approach (Intermediate)

Your first equation y=x

This is the first of the practice videos that you will see at the end of most of the formal lesson videos. These are informal style videos used to get some practice and add some value to the course.

Let's add some gradient.

A few more lines with y=mx

Let us include ALL lines.

Try drawing some lines of your own

Practice drawing and understanding lines.

Find the equation of a line given a point and a gradient.

A few examples.

Find the equation of a line given 2 points on the line.

See if we can work out the equation of the line.

A look at perpendicular lines.

Practice Perpendicular lines.

A look at some terminology that will provide us with some good example questions.

A quick look at co-linear lines.

An Example of Co-linear lines

Equation of the distance between 2 points on a line.

Another practice question.

This is the general equation of a straight line.

What is composition of functions ?

Some practice in composition of functions.

An intuitive look at how we can change functions.

A mathematical look at how we can change functions.

Some practice manipulating functions

A look at inverse functions.

Some practice with inverse functions.

What happens when we compose inverse functions.

Some practice composing inverse functions

A practical introduction to trigonometry.

Introduction to some new terminology.

A look at the tangent function (TAN)

Some practice using a calculator.

Now let's look at the sine function (SIN)

A couple of examples using the sine function.

Now for the Cosine (COS) function.

Some practice with the cosine function.

Now let us look at all the 3 trigonometric functions in one graph.

Some examples using sin cos and tan

A look at the inverse trigonometric functions.

Some practice with the inverse trigonometric functions.

Value of trigonometric functions in each quadrant.

Each trigonometric function has 2 angles for 1 value

Finding the 2 angles.

Work out trigonometric values for common angles.

Some practice with common angles.

A look at compound angles.

A question on compound angles.

A look at some of the most common trigonometric identities.

An example using trigonometric identities.

A look at radian measure.

Some examples of manipulating radians

What is Differentiation ?

Differentiation

Now let us take a mathematical look at the intuition we have built so far.

A couple of examples of finding derivatives.

Let us use differentiation to find the equation of a tangent to a curve.

Some examples.

Increasing decreasing and stationary points.

Find stationary (turning points) of a function.

A curve sketching example

An example of sketching a curve.

Let us look at optimisation.

Let us look at the mathematical optimisation solution.

An example of optimisation.

Differentiating Sine and Cosine functions.

Another notation for differentiation

Another couple of examples of differentiation using the Leibniz notation.

Try and work through these examples. Pause the video before you watch my worked solutions.

An intuitive introduction to integration.

The mathematics of the fundamental theorem of calculus.

Integration is anti differentiation.

The definite and Indefinite Integral.

Some worked examples.

Some worked examples.

Work out the area between two curves.

Some worked examples.

Integration the Sine and Cosine functions.

An introduction to polynomial functions.

Quick way to find the value of a polynomial.

A couple of worked examples.

We want to be able to divide 2 polynomial functions.

A couple of examples of synthetic division.

We look at the remainder theorem.

Some examples of the remainder theorem.

Now let us look at the factor theorem.

A couple of examples of the factor theorem.

How can we work out the polynomial function from a graph ?

Find the polynomial function from the graph.

How do we create the graph from the function.

Draw the polynomial graph from the function.

An introduction to quadratic functions.

How do we quickly factorise a quadratic equations ?

Some examples of factorising quadratic functions.

How do we sketch the graph given the quadratic function ?

A worked example.

How do we work out the quadratic function given it's graph ?

A worked example finding the function from the graph.

Another way of finding the turning point.

Some examples of completing the square.

Find the roots of a quadratic equation using the quadratic formula.

Some examples using the quadratic formula.

What are the nature of the roots ?

Some examples.

In this lecture we derive the equation of a circle.

Some practice with equation of a circle.

Some more examples.

What is a vector ?

Add , subtract and multiply a vector by a scalar.

Some simple vector arithmetic.

The unit vector and the position vector.

An example of each.

A look at 3 dimensional vectors.

An extension of vectors to 3 dimensional space.

Let us now look at the scalar product also know as the dot product.

Scalar product examples.

Another form of the scalar (dot) product.

Practice Component Form of Dot (scalar) Product

How can we find the angle between two vectors ?

A couple of examples of finding the angle between 2 vectors.

A look at perpendicular vectors.

Examples of Perpendicular Vectors.