Integral representations for a generalized Mathieu series and its companions are used to obtain bounds for their corresponding series. The bounds are procured mainly using results pertaining to theČebyšev functional. The relationship to Zeta type functions are also examined. It is demonstrated that the Zeta companion relations are a particular case of the generalised Mathieu companions.

This is an expository paper in which we present an introduction to a variational approach to spline interpolation. We present a sequence of theorems which starts with Holladay's classical result concerning natural cubic splines and culminates in some general abstract results.

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The paper describes one way to demonstrate the Durbin±Watson statistic to a large class of students.

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