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Now showing items 21-30 of 90

#### MathsCasts: The Scalar (Dot) Product of Two Vectors: Part 1

(Swinburne Commons, 2013)

In this video, the definition of the scalar product is explained using the example of work done by a force.

#### MathsCasts: The Scalar (Dot) Product of Two Vectors: Part 3

(Swinburne Commons, 2013)

In this video we investigate and prove frequently used properties of the scalar product.

#### MathsCasts: Solving an Equation of Form Rational Function Equals 0

(Swinburne Commons, 2013)

We discuss the solutions of the equation p(x)/q(x) = 0 where p and q are in principle any functions. We revise the meanings of the terms 'numerator' and 'denominator'.

#### MathsCasts: Complex Impedance Part 2

(Swinburne Commons, 2013)

We continue investigation of the RLC circuit, introducing complex versions of voltage and current. The complex impedance results naturally from these quantities and gives a clear picture of why the current and voltage ...

#### MathsCasts: The Scalar Triple Product

(Swinburne Commons, 2013)

Investigates the scalar triple product in the context of the volume of a parallel pipe.

#### MathsCasts: Political Differentiation, a Quirky Approach to the Product and Quotient Rules

(Swinburne Commons, 2013)

Simple political analogies are used with the intention of aiding the memory on the form of the product and quotient rules.

#### MathsCasts: Adding and Subtracting Fractions

(Swinburne Commons, 2013)

We look at several examples of adding and subtracting fractions, by first obtaining a common denominator.

#### MathsCasts: Laplace Transform Solution of a 2nd Order, Constant Coefficient, Non-Homogeneous ODE with Boundary Conditions

(Swinburne Commons, 2013)

We solve a 2nd order, constant coefficient, non-homogeneous ODE with boundary conditions at t = 0 for y and y'.

#### MathsCasts: The Laplacian of f(r) and Proof that 1 Over r is Harmonic

(Swinburne Commons, 2013)

We derive a general formula for the Laplacian acting on a function f(r) then demonstrate that the Laplacian is zero in the case that f(r) = 1/r, thereby showing that 1/r is harmonic.

#### MathsCasts: Matrix Representation of Complex Numbers

(Swinburne Commons, 2013)

We show how complex number arithmetic can be performed using matrices for the complex numbers.