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Now showing items 11-20 of 90

#### MathsCasts: Geometric Series: Part 1

(Swinburne Commons, 2012)

We introduce the basic geometric series in powers of x, investigate the partial sums and demonstrate that the series sums to 1/(1-x) for x between -1 and 1.

#### MathsCasts: Introduction to Sequences

(Swinburne Commons, 2012)

Introduces the concept of finite and infinite sequences with examples and demonstrates examples of using notation to define sequences.

#### MathsCasts: The Exponential of a 2X2 Matrix Using Laplace Transforms: An Unusual Method

(Swinburne Commons, 2014)

We show an unusual approach to finding the exponential of a 2x2 matrix - using the Laplace transform.

#### MathsCasts: Eigenvectors of a 3x3 Matrix

(Swinburne Commons, 2013)

We show how to find the eigenvectors for the 3 by 3 matrix whose eigenvalues were calculated in a separate presentation.

#### MathsCasts: The Vector Triple Product

(Swinburne Commons, 2013)

The video shows a simplification of a vector triple product.

#### MathsCasts: The Vector (Cross) Product of Two Vectors: Part 2

(Swinburne Commons, 2013)

The definition of the vector product is used to identify the cross products of the various basis vectors i, j and k with each-other, in preparation for unravelling a component form for the vector product.

#### MathsCasts: The Vector (Cross) Product of Two Vectors: Part 3

(Swinburne Commons, 2013)

This video explains how cross products between the basis vectors i,j and k identified in part 2 are used to obtain an expression in components for the vector product of any pair of vectors.

#### MathsCasts: The Vector (Cross) Product of Two Vectors: Part 1

(Swinburne Commons, 2013)

In this video the definition of the vector product is explained with reasons for making such a definition.

#### MathsCasts: Introduction to Cartesian Tensors: The Kronecker Delta: Part 1

(Swinburne Commons, 2013)

In this video we introduce the Kronecker delta and identify it as just another way of writing the unit matrix.

#### MathsCasts: The Scalar (Dot) Product of Two Vectors: Part 2

(Swinburne Commons, 2013)

This video covers the definition of the scalar product is used to derive an expression for the product in terms of components. Some properties of the product are then summarized.