Browsing by Author "Bedding, S. (Stephen)"
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MathsCasts: A Fourier Series Integral
Bedding, S. (Stephen) (Swinburne Commons, 2012)We examine the integration involved in calculating some Fourier coefficients and discuss the approach to be taken when one has a formula sheet in comparison with having to calculate the integral on paper.

MathsCasts: A Geometric Proof of the Sum and Difference Formulae for Sin and Cos
Bedding, S. (Stephen) (Swinburne Commons, 2013)We prove the formula for sin(AB) using rightangled triangles then we show how the corresponding formulae for cos(AB) and sin and cos of A+B can be deduced as a result.

MathsCasts: A Matrix to the Power of a Matrix
Bedding, S. (Stephen) (Swinburne Commons, 2013)We ask if a matrix can be raised to the power of a matrix and do a simple 2 by 2 example.

MathsCasts: A Scheme to Make Integration by Parts Easier: Part 2
Bedding, S. (Stephen) (Swinburne Commons, 2016)The scheme already discussed for writing down the reults from integration by parts is applied to cyclic integration by parts where the integrand contains a product of an exponential and a sin or cosine.

MathsCasts: A Simple Fourier Transform Example: Part 1
Bedding, S. (Stephen) (Swinburne Commons, 2013)The video describes finding the Fourier transform of a simple piecewise function with values 0 and 1.

MathsCasts: Adding and Subtracting Fractions
Bedding, S. (Stephen) (Swinburne Commons, 2013)We look at several examples of adding and subtracting fractions, by first obtaining a common denominator.

MathsCasts: Another 3x3 Eigenvalue Example
Bedding, S. (Stephen) (Swinburne Commons, 2012)We calculate eigenvalues of a 3 by 3 matrix.

MathsCasts: Binomial Series Part 3
Bedding, S. (Stephen) (Swinburne Commons, 2013)We expand the binomial series for the case n = 1/2 to evaluate an approximation for the square root of 2. Convergence is discussed briefly then we deal with the case when the first term in the binomial expression is a ...

MathsCasts: Compass Directions Part 1
Bedding, S. (Stephen) (Swinburne Commons, 2013)We introduce the points of the compass and solve a simple example using distances and basic directions (N,S,E,W) to find resulting distance and angle.

MathsCasts: Compass Directions Part 2
Bedding, S. (Stephen) (Swinburne Commons, 2013)We look at a second example involving combinations of direction, one of which is none of north, south, east or west.

MathsCasts: Complex Impedance Part 1
Bedding, S. (Stephen) (Swinburne Commons, 2013)We investigate the RLC circuit and obtain a relation between voltage and current without use of complex quantities. We see that the relation is rather cumbersome and not transparent.

MathsCasts: Complex Impedance Part 2
Bedding, S. (Stephen) (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: Complex Impedance Part 3
Bedding, S. (Stephen) (Swinburne Commons, 2013)We look at a numerical example for an RLC circuit and calculate the complex impedance and phase difference.

MathsCasts: Converting a Double Integral from Cartesian to Circular Polar Coordinates
Bedding, S. (Stephen) (Swinburne Commons, 2012)After a brief review of circular polar coordinates, a double integral is written using Cartesian coordinates. We draw the region of integration and describe it in terms of polar coordinates in order to rewrite the integral ...

MathsCasts: Determining Linear (in)dependence
Bedding, S. (Stephen) (Swinburne Commons, 2012)We investigate the linear dependence or independence of a set of 3 vectors in 3 dimensions, and show how the determinant of a 3 by 3 matrix can assist in this process.

MathsCasts: Directional Derivative Using the Grad Operator
Bedding, S. (Stephen) (Swinburne Commons, 2016)We write the directional derivative on a surface z=z(x,y) in terms of the grad operator acting on z as a dot product with a unit vector in the direction required.

MathsCasts: Eigenvalues and Eigenvectors
Bedding, S. (Stephen) (Swinburne Commons, 2012)Explains graphically what it means to multiply a matrix and a vector. Then introduces eigenvectors as vectors belonging to the matrix with a special property in matrix vector multiplication. Eigenvalues are also explained ...

MathsCasts: Eigenvalues of a 2x2 Matrix
Bedding, S. (Stephen) (Swinburne Commons, 2013)We show how to find eigenvalues for an NxN matrix then do a 2x2 example. This MathsCast follows from an introductory MathsCast on eigenvalues and eigenvectors and it is also helpful to view the presentations on linear ...

MathsCasts: Eigenvalues of a 3x3 Matrix
Bedding, S. (Stephen) (Swinburne Commons, 2013)Eigenvalues of a 3 by 3 matrix are calculated. Some useful advice is given concerning factorization of the characteristic equation.

MathsCasts: Eigenvectors of a 2x2 Matrix
Bedding, S. (Stephen) (Swinburne Commons, 2013)We use the same 2 by 2 matrix whose eigenvalues were found in another MathsCast (Eigenvalues of a 2 by 2 matrix) and find the associated eigenvectors.