## Browsing by Author "Bedding, S. (Stephen)"

Now showing items 1-20 of 90

• #### MathsCasts: A Fourier Series Integral ﻿

(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 ﻿

(Swinburne Commons, 2013)
We prove the formula for sin(A-B) using right-angled triangles then we show how the corresponding formulae for cos(A-B) and sin and cos of A+B can be deduced as a result.

• #### MathsCasts: A Matrix to the Power of a Matrix ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(Swinburne Commons, 2013)
We look at several examples of adding and subtracting fractions, by first obtaining a common denominator.

• #### MathsCasts: Another 3x3 Eigenvalue Example ﻿

(Swinburne Commons, 2012)
We calculate eigenvalues of a 3 by 3 matrix.

• #### MathsCasts: Binomial Series Part 3 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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.