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Iterative solutions to classical second-order ordinary differential equations (2019)
Journal Article
Robin, W. (2019). Iterative solutions to classical second-order ordinary differential equations. Journal of Innovative Technology and Education, 6(1), 1-12

An elementary scheme is detailed for introducing certain basic concepts in the solution of (especially) the basic second-order ordinary differential equations of classical mathematical physics. The method proposed, an integration/iteration process, a... Read More about Iterative solutions to classical second-order ordinary differential equations.

Some new uniform approximate analytical representations of the Blasius function. (2015)
Journal Article
Robin, W. (2015). Some new uniform approximate analytical representations of the Blasius function. Global Journal of Mathematics, 2, 150-155

New uniform approximations of the Blasius velocity profile and Blasius function are developed from existing rational approximations of the Blasius velocity profile and of the Blasius function itself. Essentially, the existing rational approximations... Read More about Some new uniform approximate analytical representations of the Blasius function..

On compact uniform analytical approximations to the Blasius Velocity profile. (2015)
Journal Article
Robin, W. (2015). On compact uniform analytical approximations to the Blasius Velocity profile. International Mathematical Forum, 10, 311-322. https://doi.org/10.12988/imf.2015.514

It is shown that approximate analytical representations of the Blasius function may be developed by using the error function, erf (ax), for positive constant a, as a basic compact approximate form for the derivative of the Blasius function, that is,... Read More about On compact uniform analytical approximations to the Blasius Velocity profile..

Experiences of using Audio Feedback in Engineering Mathematics Modules. (2015)
Presentation / Conference Contribution
Durkacz, K., & Mowat, E. (2015, June). Experiences of using Audio Feedback in Engineering Mathematics Modules. Presented at Barriers and Enablers to Learning Maths: Enhancing Learning and Teaching for All Learners

The main purpose of the Engineering Mathematics modules at Edinburgh Napier University is to explain the underpinning mathematical techniques, in areas such as calculus, series and vectors, which are required by the engineering modules. These modules... Read More about Experiences of using Audio Feedback in Engineering Mathematics Modules..

The Engineering Peer Tutors. (2015)
Presentation / Conference Contribution
Durkacz, K. (2015, June). The Engineering Peer Tutors. Paper presented at Scottish Maths Support Network meeting

Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration (2014)
Journal Article
Robin, W. (2014). Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 953-965. https://doi.org/10.12988/imf.2014.4491

A method is presented (with standard examples) based on an elementary complex integral expression, for developing Frobenius series solutions for second-order linear homogeneous ordinary Fuchs differential equations. The method reduces the task of fin... Read More about Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration.

Ladder-Operator Factorization and the Bessel Differential Equations (2014)
Journal Article
Robin, W. (2014). Ladder-Operator Factorization and the Bessel Differential Equations. International Mathematical Forum, 9, 71-80. https://doi.org/10.12988/imf.2014.311214

We present an alternative approach to the discussion of Bessel equations and Bessel functions, through an elementary factorization method. The various Bessel equations are represented by a single parameterized form and, after a standard transformatio... Read More about Ladder-Operator Factorization and the Bessel Differential Equations.

On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method. (2014)
Journal Article
Robin, W. (2014). On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method. Nonlinear Analysis and Differential Equations, 2, 155-171. https://doi.org/10.12988/nade.2014.4712

The theory of series solutions for two important classes of the general higher-order linear homogeneous ordinary differential equation is developed ab initio, using an elementary complex integral expression derived and applied in previous papers [10,... Read More about On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method..

Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration (2014)
Journal Article
Robin, W. (2014). Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 967-976. https://doi.org/10.12988/imf.2014.4492

A method is presented, with standard examples, based on an elementary complex integral expression, for developing, in particular, series solutions for second-order linear homogeneous ordinary differential equations. Straightforward to apply, the meth... Read More about Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration.

On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation (2013)
Journal Article
Robin, W. (2013). On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation. International Mathematical Forum, 8, 1455-1466. https://doi.org/10.12988/imf.2013.37133

In this paper, we present a new systematic approach to the solution of the hypergeometric-like differential equation and its associated equation. The method produces, tout court, the general solution of these equations in the form of a combination of... Read More about On the Rodrigues Formula Solution of the Hypergeometric-Type Differential Equation.

Some Remarks on the Homotopy-Analysis Method and Series Solutions to the Blasius Equation (2013)
Journal Article
Robin, W. (2013). Some Remarks on the Homotopy-Analysis Method and Series Solutions to the Blasius Equation. International Mathematical Forum, 8, 1205-1213. https://doi.org/10.12988/imf.2013.3478

We present an new angle on the introduction of the homotopy-analysis method of Liao [6]. The homotopy-analysis method is then applied to produce a series solution of the Blasius problem in two different ways and comparison made with the work of Wang... Read More about Some Remarks on the Homotopy-Analysis Method and Series Solutions to the Blasius Equation.

Sharing Assessment across Institutions and VLEs. (2013)
Presentation / Conference Contribution
Milne, S., McVey, M., Barr, N., Davis, M., Mason, J., Greenhalgh, R., Barnes, S., Durkacz, K., & Fletcher, L. (2013, September). Sharing Assessment across Institutions and VLEs. Paper presented at CETL-MSOR Conference 2013

IMS Question and Test Interoperability version 2.1 (QTI 2.1) provides
a flexible and powerful way of specifying computer delivered assessment
questions and tests in an XML format that can be used by different
delivery systems, including Moodle. Th... Read More about Sharing Assessment across Institutions and VLEs..

On the Rodrigues’ Formula Approach to Operator Factorization (2012)
Journal Article
Robin, W. (2012). On the Rodrigues’ Formula Approach to Operator Factorization. International Mathematical Forum, 7(45-48), 2333-2351

In this paper, we derive general formulae that reproduce well-known instances of recurrence relations for the classical orthogonal polynomials as special cases. These recurrence relations are derived, using only elementary mathematics, directly from... Read More about On the Rodrigues’ Formula Approach to Operator Factorization.

Investigating the Use of Audio Feedback in Engineering Mathematics Modules. (2012)
Presentation / Conference Contribution
Durkacz, K., & Mowat, E. (2012, July). Investigating the Use of Audio Feedback in Engineering Mathematics Modules. Presented at 4th International Symposium of Engineerign Education

Assessment and feedback are an important part of student learning, and there is evidence that good feedback
leads to improvements in both learning and student engagement.
This work is concerned with the use of audio feedback on two Engineering Math... Read More about Investigating the Use of Audio Feedback in Engineering Mathematics Modules..

Evaluation of a new photodiode sensor for measuring global and diffuse irradiance, and sunshine duration. (2007)
Journal Article
Wood, J., Muneer, T., & Kubie, J. (2007). Evaluation of a new photodiode sensor for measuring global and diffuse irradiance, and sunshine duration. Journal of Solar Energy Engineering, 125, 1-6. https://doi.org/10.1115/1.1531149

A new integrated device (called the BF3) has been developed, which enables the simultaneous measurement of horizontal global and diffuse irradiance as well as sunshine presence at any time. The sensor needs no specific polar alignment or routine adju... Read More about Evaluation of a new photodiode sensor for measuring global and diffuse irradiance, and sunshine duration..

Modelling how changes in the driving cycle affect fuel consumption and carbon dioxide emission rates: the first stage. (2006)
Presentation / Conference Contribution
Kirby, H. (2006, November). Modelling how changes in the driving cycle affect fuel consumption and carbon dioxide emission rates: the first stage

This paper describes a simplified procedure for estimating the fuel consumed and carbon dioxide emitted as a result of traffic demand management measures or other policy instruments. The usual methods may be based on second-by-second traffic simulati... Read More about Modelling how changes in the driving cycle affect fuel consumption and carbon dioxide emission rates: the first stage..

Eight-node Reissner–Mindlin plate element based on boundary interpolation using Timoshenko beam function (2006)
Journal Article
Zhang, H., & Kuang, J. S. (2007). Eight-node Reissner–Mindlin plate element based on boundary interpolation using Timoshenko beam function. International Journal for Numerical Methods in Engineering, 69(7), 1345-1373. https://doi.org/10.1002/nme.1809

A new eight-node Reissner-Mindlin plate element is developed with a special interpolation within the element. This special interpolation is an extension of the element boundary interpolation that employs Timoshenko beam function for the boundary segm... Read More about Eight-node Reissner–Mindlin plate element based on boundary interpolation using Timoshenko beam function.

Road Simulators: The iterative algorithm for drive file creation. (2006)
Presentation / Conference Contribution
Hay, N. C., & Roberts, D. E. (2006, April). Road Simulators: The iterative algorithm for drive file creation. Presented at SAE 2006 World Congress & Exhibition

Road simulators reproduce measured service environments in laboratory based test rigs and have contributed significantly to improving the structural integrity and quality of modern vehicles. These rigs are driven by data that are derived from a speci... Read More about Road Simulators: The iterative algorithm for drive file creation..