Aims and scope of the seriesThe series 'Atlantis Studies in Mathematics for Engineering and Science'(AMES) publishes high quality monographs in applied mathematics, computational mathematics, and statistics that have the potential to make a significant impact on the advancement of engineering and science on the one hand, and economics and commerce on the other. We welcome submission of book proposals and manuscripts from mathematical scientists worldwide who share our vision of mathematics as the engine of progress in the disciplines mentioned above.All books in this series are co-published with World Scientific.For more information on this series and our other book series, please visit our website at: For information on all Atlantis Press publications, visit our website at: www.atlantis-press.com. www.atlantis-press.com/publications/books © ATLANTIS PRESS / WORLD SCIENTIFIC AMSTERDAM -PARIS Continued Fractions CopyrightThis book, or any parts thereof, may not be reproduced for commercial purposes in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system known or to be invented, without prior permission from the Publisher. The interest in using continued fractions to approximate special functions has also grown since then. Such fractions are easy to program, they have impressive convergence properties, and their convergence is often easy to accelerate. They even have good and reliable truncation error bounds which makes it possible to control the accuracy of the approximation. The bounds are both of the a posteriori type which tells the accuracy of a done calculation, and of the a priori type which can be used to determine the number of terms needed for a wanted accuracy. This important aspect is treated in this first volume of the second edition, along with the basic theory.

In the late 1990s failure rates in a first-year introductory calculus course at the Norwegian University of Science and Technology reached peak levels. This paper reports on findings from an action research project that was set up in 2002/2003 to improve the situation. The study confirms that students approach their tasks differently which contributes to qualitatively different learning outcomes. Furthermore, patterns of achievement in mathematics and physics in secondary education keep reoccurring in the calculus course, even though the teaching and learning contexts are different. The paper does not provide any definite answer as to why groups of students get involved in distinctly different learning processes, and it will take further research to decide the nature of commitment to the learning tasks. However, inspired by the notion of 'practices' this paper raises a discussion about the role of intentionality in learning processes. When doing mathematics, students are also in a process of being engaged in and developing a practice. It is a major challenge for academic staff to contribute to communities of practice that are conducive to learning.

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