Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package…

The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.

A generalization of a well-known result for the arctangent function poses a number of interesting questions concerning the existence of integer solutions of related problems.

Three techniques for determining a straight line fit to data are compared. The methods are applied to a range of datasets containing one or more outliers, and to a specific example from the field of chemistry. For the method which is the most resistant to the presence of outliers, a Microsoft Excel spreadsheet, as well as two Matlab routines, are…

Two techniques for determining a straight line fit to data are compared. This article reviews two simple techniques for fitting a straight line to a set of data, namely the method of averages and the method of least squares. These methods are compared by showing the results of a simple analysis, together with a number of tests based on randomized…

A class of infinite series is evaluated with the aid of Taylor's theorem and a comparison is made with other methods. In a recent note [1] a class of infinite series was shown to be equivalent to a number of definite integrals, and Taylor's theorem was used to establish convergence and to determine the sums of the series and the integrals to any…

Approaches to the determination of the error in numerical quadrature rules are discussed and compared. This article considers the problem of the determination of errors in numerical quadrature rules, taking Simpson's rule as the principal example. It suggests an approach based on truncation error analysis of numerical schemes for differential…

In this note, the author considers a class of infinite series and shows that these are equivalent to a number of definite integrals, some of which are improper integrals. By using Taylor's theorem in this equivalence the author establishes convergence of each series, and a means of evaluating the sum of the series and the definite integral to any…