Faul - A Concise Introduction to Numerical Analysis

This book has been developed from the notes of lectures on Numerical Analysis held within the MPhil in Scientific Computing at the University of Cambridge, UK. This course has been taught successfully since 2011. Terms at Cambridge University are very short, only eight weeks in length. Therefore lectures are concise, concentrating on the essential content, but also conveying the underlying connecting principles. On the other hand, the Cambridge Mathematical Tripos was established in around 1790. Thus, knowledge has been distilled literally over centuries.

I have tried to carry over this spirit into the book. Students will get a concise, but thorough introduction to numerical analysis. In addition the algorithmic principles are emphasized to encourage a deeper understanding of why an algorithms is suitable (and sometimes unsuitable) for a particular problem.

The book is also intended for graduate students coming from other subjects, but who will use numerical techniques extensively in their graduate studies. The intake of the MPhil in Scientific Computing is very varied. Mathematicians are actually in the minority and share the classroom with physicists, engineers, chemists, computer scientists, and others. Also some of the MPhil students return to university after a professional career wanting to further and deepen their knowledge of techniques they have found they are lacking in their professional life. Because of this the book makes the difficult balance between being mathematically comprehensive, but also not overwhelming with mathematical detail. In some places where further detail was felt to be out of scope of this book, the reader is referred to further reading.

Techniques are illustrated by MATLAB as part of the package K25104_Downloads.zip. Most implementations are in the form of functions returning the outcome of the algorithm. Also examples for the use of the functions are given.

Exercises are put inline with the text where appropriate. Each chapter ends with a selection of revision exercises which are suitable exam questions. A PDF entitled Solutions to Odd-Numbered Exercises for a Concise Introduction to Numerical Analysis can be downloaded at https://www.crcpress.com/A-Concise-Introduction-to-Numerical-Analysis/Faul/9781498712187 as part of the package K25104_Downloads.zip.

Students will find the index comprehensive, making it easy to find the information they are after. Hopefully this will prove the book useful as a reference and make it an essential on the bookshelves of anybody using numerical algorithms.

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First and foremost I have to thank Dr Nikos Nikiforakis without whom this book would not have come into being. I first contacted him in 2011 when I was looking for work which I could balance with being a mum of three. My intention was to supervise small groups of students in Numerical Analysis at Cambridge University. He asked whether I could also lecture the subject for the students undertaking the MPhil in Scientific Computing. My involvement in the MPhil and his research group grew from there. Aside from his unwavering belief in what I can accomplish, he has become one of my best friends supporting me through difficult times.

Next thanks are also due to my PhD supervisor Professor Mike Powell who sadly passed away in April 2014. From him I learnt that one should strive for understanding and simplicity. Some of his advice was, Never cite a paper you havent understood. My citation lists have been short ever since. I more often saw him working through an algorithm with pen and paper than sitting at a computer. He wanted to know why a particular algorithm was successful. I now ask my students, How can you improve on something, if you do not understand it?

Of course I also need to thank all the MPhil students whose questions and quest to find typos have improved this book over several years, especially Peter Wirnsberger, Will Drazin, and Chongli Qin. In addition, Geraint Harcombe contributed significantly to the MATLAB examples of this book.

I would also like to express my gratitude to Cambridge University and the staff and fellows at Selwyn College for creating such a wonderful atmosphere in which to learn and teach.

This book would not have been written without the support of many people in my private life, foremost my parents Helmut and Marieluise Faul, who instilled a love for knowledge in me. Next, my many friends of whom I would like to mention, especially the ones helping out with childcare, and by name, Annemarie Moore (ne Clemence) who was always there when I needed help to clear my head, Sybille Hutter for emotional support, and Karen Higgins who is brilliant at sorting out anything practical.

A.C. Faul

To Philip, Rosemary, and Sheila .

A Concise Introduction to Numerical Analysis

A. C. Faul
University of Cambridge, UK

MATLAB is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy of the text or exercises in this book. This books use or discussion of MATLAB software or related products does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB software.

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