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Now showing items 1-10 of 132

#### MathsCasts: Separable Differential Equations: Example 1

(Swinburne Commons, 2012)

This screencast gives an example of how to solve the first order separable differential equation: 2x/((1+x^2)y)

#### MathsCasts: Velocity and Acceleration Given Position Vector

(Swinburne Commons, 2012)

This recording shows how velocity and acceleration of a particle travelling through 3D space are calculated given we have a general vector expression for the position vector at time t - this is then illustrated with a ...

#### MathsCasts: Powers of Complex Numbers

(Swinburne Commons, 2012)

Gives the general formula then applies this to an example. Cartesian form is convert to polar form, then the required power of the number is calculated, and finally the result is converted back into Cartesian form.

#### MathsCasts: Multiplication and Division of Complex Numbers in Polar Form

(Swinburne Commons, 2012)

The general formulae for multiplication and division of complex numbers in polar form are given and their use is then demonstrated in relation to a particular example.

#### MathsCasts: Solving Equations with Complex Roots

(Swinburne Commons, 2012)

An example of solving a degree four polynomial where all powers are even. The substitution w = z^2 is used to rewrite as quadratic, the quadratic formula is applied to find the two solutions and then the complex square ...

#### MathsCasts: Sketching 3D Curves

(Swinburne Commons, 2012)

Shows how to sketch a 3D curves which is given in vector form on 2D paper. The curve is rewritten in scalar parametric form, values for the parameter t are selected, and points on the curve calculated. These are then plotted ...

#### MathsCasts: Converting a Line from Cartesian to Vector Form

(Swinburne Commons, 2012)

Starts with an introduction to the equation of a straight line in 3D in both Cartesian and vector form. An example is then given of converting the Cartesian equations of a straight line into its scalar parametric equations ...

#### MathsCasts: Defined Matrix Operations

(Swinburne Commons, 2012)

A discussion of when matrix addition, subtraction and multiplication are defined, and when it is possible to calculate matrix determinants and inverses, based on the order of the matrices concerned.

#### MathsCasts: Complex Regions

(Swinburne Commons, 2012)

This recording looks at how to identify the nature of the region in the complex plane that satisfies |z-z0|=r. This is then illustrated further with a specific example.

#### MathsCasts: Partial Differentiation Using the Quotient Rule

(Swinburne Commons, 2012)

The quotient rule is reviewed and then demonstrated for an example involving calculation of partial derivatives.